World Explorer Books - Children's Books About Exploration

Follow the Dream: The Story of Christopher Columbuswritten and illustrated by Peter Sis; ages 5 and upOver 500 years ago a little boy was born in the city of Genoa, Italy. His father was a weaver, but Christopher Columbus dreamed of faraway places, adventure, and discovery. He observed the ships that sailed into the harbor and listened to the sailors and merchants as they told tales of their

Read more »

Exploration Kids Books - American Exploer Books

Who Was First? Discovering the AmericasRussell Freedman; ages 11 and upHistorian Russell Freeman explores the various claims to the "discovery" of the American continents. Every U.S. school child knows the story of Columbus, but what about the Chinese explorer, Zheng He? This lavishly illustrated volume traces explorers' journeys with archival maps, charts, and timelines. Freeman discusses the

Read more »

Reading Readiness Books: ages 3-4

Get your 3 to 4 year old ready to read and learn with these age-appropriate story recommendations.How can we help our children as they are learning to read?  One of the building blocks of reading competency is phonetic awareness. What are the sounds that make up a written word? Phonemic awareness refers to the ability to hear and tell the difference between words, sounds, and syllables in

Read more »

Best Music Books For Children

Teach your child all about instruments, melody, and more with these recommended music books for preschoolersKids Go!by They Might Be Giants; illustrated by Pascal CampionHipster rock group They Might Be Giants return after their Grammy-winning CD for kids, Here Come the 123s, with a book and song combination to get kids off the couch and get moving. The song was originally created in 2008 for a

Read more »

Top 10 Kids Math Web Sites

FunbrainA math arcade and interactive math games are only two of the many features of this site, which offers games in a wide variety of topics. Classic games on this site include math car racing. Check out the teacher's resource page and the curriculum guide. Time4LearningComplete online curriculum for preschool through the eighth grade. 

Read more »

Middle School Educational Software

QuickStudy English VocabularyTake the quick path to writing success! Quickstudy English Vocabulary provides a solid educational foundation that will raise grades and test scores and improve vocabulary and writing skills in the classroom and beyond. The curriculum-based lessons are designed by educators to help students expand their vocabulary in an engaging, interactive learning

Read more »

Software For Kids

Millie's Math HouseDevelop a love for math with Millie! In seven fun-filled activities, kids explore fundamental math concepts as they learn about numbers, shapes, sizes, quantities, patterns, sequencing, addition, and subtraction. They count critters, build mouse houses, create crazy-looking bugs, make jellybean cookies for Harley the horse, and find just the right shoes for Little,

Read more »

Boom!

Boom! by Mark Haddon

2010

for ages 8-12 years

Jim and Charlie are regular boys until they overhear two teachers in the teacher's lounge. Mr. Kidd and Mrs. Pearce appear to be normal teachers, but they talk to each other in a very strange language when no one else is around. Out of curiosity Charlie says, "spudvetch" to Mr. Kidd and that's when they know things will never be the same.

Charlie soon disappears and it's up to Jim to find him. With the help of his sister Becky, Jim heads to the Isle of Sky in Scotland with nothing but mysterious coordinates to guide him. What he finds there is beyond belief! Before he knows it he must save mankind.-sc-

Check our catalog for this title.

Read more »

Posted in: New Book Review-fiction

Gobble, Gobble

Thanksgiving is more than stuffing and mashed potatoes! Take some time to read about why we celebrate this holiday.


Thanksgiving Day by Rebecca Rissman
Big color photos and simple text explain why we celebrate this holiday.

Check our catalog for this title.







Pilgrims by Mary Pope Osborne
What it was really like to sail to the New World on the Mayflower.

Check our catalog for this title.






Pardon That Turkey by Susan Sloate
Explains how Thanksgiving became a national holiday and why the president always pardons a turkey.

Check our catalog for this title.







Happy Thanksgiving by Abbie Mercer
All the fun of the holiday plus how to make a pinecone turkey.

Check our catalog for this title.








Celebrate Thanksgiving Day by Elaine A. Kule
For older readers, this includes the history and traditions and ways to give back to your community on this holiday.

Check our catalog for this title.


-gw-

Read more »

Posted in: Non-Fiction

Best Books for 10 Year Old Boys

There are many overlaps between books ‘for’ boys and books ‘for’ girls (and the gender divide was really driven by the twitter enquiry that prompted the list of best books for girls), but there are differences too. However much of an old-style Doc-Marten-wearing feminist Kate was (is…), and however much she swore that she would not encourage her own children into gender stereotypes, she’s come to

Read more »

5th Grade Math Worksheets - 5th Grade Math Test (3)

Question 1: 6.2% written as a decimal is: 0.620.0620.00626.2Question 2: 13/25 may be written as a percent as:13%26%44%52%Question 3: 74 - 73 = 4924013432058Question 4: There are 12 milk containers in a box. Each container weighs 5/6 pounds. How many pounds does the box weigh?12 pounds5 pounds10 pounds8 poundsQuestion 5: m = 15n + 2What is m if n = 3?m = 2m = 15m = 45m = 47Question 6: 2(6x - 1) =

Read more »

Math 5th Grade Test - 5th Grade Math Test (2)

Question 1: What is the perimeter of the rectangular in the figure below?6.2m6.6m8m8.2mQuestion 2: What is the area of triangle ABC if AD = BC = 6 inches?12 square inches16 square inches18 square inches22 square inchesQuestion 3: Which of the following is not a composite number?13141516Question 4: A group of middle school student has made $46.5 by selling lemonade. They charged $1.5 for a cup of

Read more »

Math 5th Grade Test - 5th Grade Math Test (1)

Question 1: 4521 × 613 = 1,771,3731,871,3732,871,3732,771,373Question 2: 4/5 - 1/2 =3/102/51/103/5Question 3: How many integers between 1 and 50 contain the digit 3?12141518Question 4: A middle school has 116 students enrolled in four classes. If there is an equal number of students in each class, what is a way to determine the number of students in 5th grade?subtract 4 from 116add 116 to

Read more »

15th Swedish Mathematical Society Problems 1975

1.  A is the point (1, 0), L is the line y = kx (where k > 0). For which points P (t, 0) can we find a point Q on L such that AQ and QP are perpendicular?2.  Is there a positive integer n such that the fractional part of (3 + √5)n > 0.99? 3.  Show that an + bn + cn ≥ abn-1 + bcn-1 + can-1 for real a, b, c ≥ 0 and n a positive integer. 4.  P1,

Read more »

Posted in: Swedish Mathematical Society

14th Swedish Mathematical Society Problems 1974

1.  Let an = 2n-1 for n > 0. Let bn = ∑r+s≤n aras. Find bn - bn-1, bn - 2bn-1 and bn.2.  Show that 1 - 1/k ≤ n(k1/n - 1) ≤ k - 1 for all positive integers n and positive reals k. 3.  Let a1 = 1, a2 = 2a1, a3 = 3a2, a4 = 4a3, ... , a9 = 9a8. Find the last two digits of a9. 4.  Find all polynomials p(x) such that p(x2) = p(x)

Read more »

Posted in: Swedish Mathematical Society

13th Swedish Mathematical Society Problems 1973

1.  log82 = 0.2525 in base 8 (to 4 places of decimals). Find log84 in base 8 (to 4 places of decimals). 2.  The Fibonacci sequence f1, f2, f3, ... is defined by f1 = f2 = 1, fn+2 = fn+1 + fn. Find all n such that fn = n2. 3.  ABC is a triangle with ∠A = 90o, ∠B = 60o. The points A1, B1, C1 on BC, CA, AB respectively are such that

Read more »

Posted in: Swedish Mathematical Society

12th Swedish Mathematical Society Problems 1972

1.  Find the largest real number a such that x - 4y = 1, ax + 3y = 1 has an integer solution. 2.  A rectangular grid of streets has m north-south streets and n east-west streets. For which m, n > 1 is it possible to start at an intersection and drive through each of the other intersections just once before returning to the start? 3.  A steak

Read more »

Posted in: Swedish Mathematical Society

11th Swedish Mathematical Society Problems 1971

1.  Show that (1 + a + a2)2 < 3(1 + a2 + a4) for real a ≠ 1. 2.  An arbitrary number of lines divide the plane into regions. Show that the regions can be colored red and blue so that neighboring regions have different colors. 3.  A table is covered by 15 pieces of paper. Show that we can remove 7 pieces so that the remaining 8 cover at least 8/15 of

Read more »

Posted in: Swedish Mathematical Society

10th Swedish Mathematical Society Problems 1970

1.  Show that infinitely many positive integers cannot be written as a sum of three fourth powers of integers. 2.  6 open disks in the plane are such that the center of no disk lies inside another. Show that no point lies inside all 6 disks.3.  A polynomial with integer coefficients takes the value 5 at five distinct integers. Show that it does not take the value 9

Read more »

Posted in: Swedish Mathematical Society

Chapter Book Chips - "The Year Money Grew On Trees" by Aaron Hawkins

Jackson Jones faces the prospect of a summer vacation spent working in a scrap yard. But fate intervenes in the form of his neighbor, Mrs. Nelson. She wants to find someone to take care of her late husband's apple orchard. She and Jackson sign a contract that says if he can sell $8,000.00 worth of apples she will sign over the orchard to him. Jackson thinks this sounds like a much better way to spend his summer. He enlists the help of his siblings and his cousins and together they set to work to raise and harvest the apples from 300 trees. But they have no idea what hard work they have let themselves in for. First the trees need pruning, then there is the danger of a freeze. After that, they must protect the trees from worms. And they need manure spread to fertilize them and an irrigation system set up to water them. They accomplish all of this with incredible dedication, but just when the apples are ready to harvest they face some bad luck. Will they get the apples picked in time? And will Mrs. Nelson live up to her agreement to give Jackson the orchard if he is successful? "The Year Money Grew on Trees" is a story of the satisfaction of seeing a project through to the finish and the joy of growing and harvesting a crop of your own.

-gw-


Check our catalog for this title.

Read more »

Posted in: Chapter Book Chips

9th Swedish Mathematical Society Problems 1969

1.  Find all integers m, n such that m3 = n3 + n. 2.  Show that tan π/3n is irrational for all positive integers n. 3.  a1 ≥ a2 ≥ ... ≥ an is a sequence of reals. b1, b2, b3, ... bn is any rearrangement of the sequence B1 ≥ B2 ≥ ... ≥ Bn. Show that ∑ aibi ≤ &sum aiBi. 4.  Define g(x) as the largest value of |y2 - xy| for

Read more »

Posted in: Swedish Mathematical Society

8th Swedish Mathematical Society Problems 1968

1.  Find the maximum and minimum values of x2 + 2y2 + 3z2 for real x, y, z satisfying x2 + y2 + z2 = 1. 2.  How many different ways (up to rotation) are there of labeling the faces of a cube with the numbers 1, 2, ... , 6? 3.  Show that the sum of the squares of the sides of a quadrilateral is at least the sum of the squares of the diagonals. When

Read more »

Posted in: Swedish Mathematical Society

7th Swedish Mathematical Society Problems 1967

1.  p parallel lines are drawn in the plane and q lines perpendicular to them are also drawn. How many rectangles are bounded by the lines? 2.  You are given a ruler with two parallel straight edges a distance d apart. It may be used (1) to draw the line through two points, (2) given two points a distance ≥ d apart, to draw two parallel lines, one

Read more »

Posted in: Swedish Mathematical Society

6th Swedish Mathematical Society Problems 1966

1.  Let {x} denote the fractional part of x = x - [x]. The sequences x1, x2, x3, ... and y1, y2, y3, ... are such that lim {xn} = lim {yn} = 0. Is it true that lim {xn + yn} = 0? lim {xn - yn} = 0? 2.  a1 + a2 + ... + an = 0, for some k we have aj ≤ 0 for j ≤ k and aj ≥ 0 for j > k. If ai are not all 0, show that a1 + 2a2 + 3a3 + ..

Read more »

Posted in: Swedish Mathematical Society

5th Swedish Mathematical Society Problems 1965

1.  The feet of the altitudes in the triangle ABC are A', B', C'. Find the angles of A'B'C' in terms of the angles A, B, C. Show that the largest angle in A'B'C' is at least as big as the largest angle in ABC. When is it equal? 2.  Find all positive integers m, n such that m3 - n3 = 999. 3.  Show that for every real x ≥ ½ there is an integer n such

Read more »

Posted in: Swedish Mathematical Society

4th Swedish Mathematical Society Problems 1964

1.  Find the side lengths of the triangle ABC with area S and ∠BAC = x such that the side BC is as short as possible. 2.  Find all positive integers m, n such that n + (n+1) + (n+2) + ... + (n+m) = 1000. 3.  Find a polynomial with integer coefficients which has √2 + √3 and √2 + 31/3 as roots. 4.  Points H1, H2, ... , Hn are arranged in the

Read more »

Posted in: Swedish Mathematical Society

1.  How many positive integers have square less than 107? 2.  The squares of a chessboard have side 4. What is the circumference of the largest circle that can be drawn entirely on the black squares of the board? 3.  What is the remainder on dividing 1234567 + 891011 by 12?

1.  Find all polynomials f(x) such that f(2x) = f '(x) f ''(x). 2.  ABCD is a square side 1. P and Q lie on the side AB and R lies on the side CD. What are the possible values for the circumradius of PQR? 3.  Find all pairs (m, n) of integers such that n2 - 3mn + m - n = 0.

1.  Let S be the system of equations (1) y(x4 - y2 + x2) = x, (2) x(x4 - y2 + x2) = 1. Take S' to be the system of equations (1) and x·(1) - y·(2) (or y = x2). Show that S and S' do not have the same set of solutions and explain why. 2.  Show that x1/xn + x2/xn-1 + x3/xn-2 + ... + xn/x1 ≥ n for any positive reals x1, x2, ... , xn.

Read more »

Posted in: Swedish Mathematical Society

Quadratic reciprocity via generalized Fibonacci numbers?

This is a pet idea of mine which I thought I'd share. Fix a prime q congruent to 1mod4 and define a sequence Fn by F0=0,F1=1, andFn+2=Fn+1+q−14Fn.Then Fn=αn−βnα−β where α,β are the two roots of f(x)=x2−x−q−14. When q=5 we recover the ordinary Fibonacci numbers. The discriminant of f(x) is q, so it splits modp if and only if q is a quadratic residue modp. If (qp)=−1, then the Frobenius

Read more »

What's the value of this Vieta-style product involving the golden ratio?

One way of looking at the Vieta product 2π=2√22+2√√22+2+2√√√2…is as the infinite product of a series of successive 'approximations' to 2, defined by a0=2√, ai+1=2+ai√ (or more accurately, their ratio to their limit 2). This allows one to see that the product converges; if |ai−2|=ϵ, then |ai+1−2|≈ϵ/2 and so the terms of the product go as roughly (1+2−i). Now, the sequence of infinite radicals a0

Read more »

Imaginalis

Imaginalis
by J.M. Matteis
2010

The kids at school think Mehera Crosby is a dork because, among other things, she really loves a book series called Imaginalis. She's been writing book reports about it for years! She is deeply disappointed when she finds out the final book in the series has been cancelled! Mehera believes so much in the book that she is able to receive a distress call from the beings in Imaginalis, who are slowly disappearing. In fact, she believes so much that she is able to construct the Unbelievable Bridge, over which she is able to bring her favorite characters from Nolandia to Earth. Unfortunately, she also brings over the bad guy, Pralaya. Can she save the people of Nolandia in time?-sc-

Check our catalog for this title.

Read more »

Posted in: New Book Review-fiction

Division, Multiplication, Fraction Division Books for Kids

Books about long division for kidsMathimagination Series: Book A, beginning multiplication and division; Book B, operations with whole numbers; Book C, number theory, sets and number bases; Book D, fractions; Book E, decimals and percentDecimals and Percentages With Pre- And Post-Tests: Place Value, Addition, Subtraction, Multiplication, DivisionBooks about multiplication and division for kids

Read more »

Posted in: Math Books for Kids

Make Learning Math A Fun Time For Your Child Your child can have fun learning math. Learning math could be difficult to kids sometimes. Considering a different approach on getting your child to learn math and become smarter might be a good idea. why not have your child play and learn math at the same time? Math do not have to be a dull anymore.

Search Amazon.com for Math Games for Kids 

Read more »

How to Do Long Division - Understanding long division as repeated subtraction

Understanding long division as repeated subtractionMany children find the traditional long division method far to complex to understand. Below are two different ways for you to help your children understand long division. The first method uses repeated subtraction and the second is a grid method. Question: 765÷12 12x10=120   765-120=645 12x10-120   645-120=525 12x10=120   525-120=405

Read more »

Posted in: Long Division

Division Lesson Plans

Introduction to division lesson plan:                   Division lesson plans is nothing but a one of the arithmetic operations of division, Division means that the reverse of multiplication operation. Division  is mainly used to reduce the whole part of item. Symbol of division is represented as (/) .When we have to perform the division operation. In basic division contains two parts, one

Read more »

Lesson Plans for Division

Introduction to Lesson Plans for Division:                 A division method can be done by the division symbol ÷.  The number present in the left of the division symbol is dividend and the number present in the right of the division symbol is divisor. The answer you get from the division process is called quotient. The number after dividing process over the remaining number left below the

Read more »

Multiplication and Division Property

Introduction on multiplication and division property:           Multiplication: One of the fundamental mathematical operations is called multiplication. The multiplication is the method of scaling one number with another number. It creates the product of numbers. It is denoted by a symbol "×".           Division: One of the fundamental arithmetic operations is called division. It is the

Read more »

How to do fraction division?

How to do fraction division? How to solve fraction division?Teaching division usually leads to the concept of fractions being introduced to students. Unlike addition, subtraction, and multiplication, the set of all integers is not closed under division. Dividing two integers may result in a remainder. To complete the division of the remainder, the number system is extended to include

Read more »

Introduction to 4 digit division:        Meaning of the term division is dividing the group into equal parts. Use of the term division is dividing. During the division we can get the quotient and the reminder. We can do division in single digit, double digit, treble digit, 4 digits and 5 digits etc. Let us see 4 digit divisions in this article.

Read more »

Top 10 Maths Books

Lecture Notes on Mathematical Olympiad Courses: For Junior Section (Mathematical Olympiad Series) http://amzn.to/OlympiadCoursesAmazon.com: Lecture Notes on Mathematical Olympiad Courses: For Junior Section (Mathematical Olympiaamzn.toAmazon.com: Lecture Notes on Mathematical Olympiad Courses: For Junior Section (Mathematical Olympiad Series) (9789814293532): Xu Jiagu: Books 15 000 problems

Read more »

Ahhh, nostalgia

We love our books here at the library and I am going to venture to guess that those of us working in the Children's department have special memories of books and libraries from our own childhoods. I asked my colleagues to tell me about one of their favorite books when they were a child and why it was special to them.

The Stinky Cheese Man and Other Fairly Stupid Tales
By Jon Scieszka

"It's silly and a little bit gross and has the word 'stupid' right there in the title"
-Jennifer's Pick

Find this title in our catalog


Burt Dow Deep-Water Man
By Robert McCloskey

"The thing that most fascinated me was the pink color inside the whale's tummy. I wanted to get swallowed by a whale just so I could check it out for myself."

--Ginny's Pick

Find this title in our catalog



Edith & Mr. Bear A Lonely Doll Story
By Dare Wright

"The doll and the bear were kind of frightening, but also fascinating. I had never seen a book like this before. It was so real!"

--Sandy's Pick


Find this title in our catalog




Where the Wild Things Are
By Maurice Sendak

" I guess I liked the boy's costume and how his bedroom became a forest. I think I also liked that, although they were monsters, they were nice (they sort of reminded me of the giant muppets)."

--Sarah's Pick

Find this title in our catalog



Bread and Jam For Frances
By Russell Hoban

This was definitely my favorite in the Frances series. I
have always loved the songs Frances invents, especially when she is singing to her poached egg. I also remember being envious of Frances' packed lunch that included a vase of violets."

--Carson's Pick

Find this title in our catalog

--cm

Read more »

Geography Books

Free world geography quiz & games at http://www.worldgeographyquiz.net

Read more »

Scientific Method Limitations

ntroduction to Scientific Method Limitations:              This article is showing the limitations for scientific method. Scientific method is otherwise said to be as scientific notation which helps to show the big numbers into simplest form of a number. Scientific method is of positive and negative method. Example for scientific Method:Positive Method: 170000000 this can be expressed as

Read more »

How to do long division with two digit quotients?

We've learned that we can figure out the single-digit quotient, or answer, for two-digit divisor problems using estimation. This time around, we'll use estimation to determine two-digit quotients for two-digit divisor problems.Let's look at this division problem, which has a two-digit quotient:To start, it's important to determine the first part of 741 that we can divide by 32. That

Read more »

Posted in: Long Division

Two-digit divisor in long division - How to do long division with 2 digit divisor?

When the divisor has two digits, the procedure works the same way but instead of using facts from multiplication tables when dividing, we might have to use pencil and paper to perform helping multiplications on the side, so to speak. 14    7  4  3  4  14 goes into 7 zero times, so we look at 74. To find how many times does 14 go into 74, you probably have to do

Read more »

Posted in: Long Division

How to do long division with 2 digit divisor

Introduction of division with 2 digit divisor:          In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.Specifically, if c time’s b equals a, written:           c x b = aWhere b is not zero, then a divided by b equals c, written:             = c.In the above expression, a is called the dividend. Source: Wikipedia

Read more »

Posted in: Long Division

Long Division of Polynomials Step by Step

Introduction to long division of polynomials:               In arithmetic, long division is the standard procedure suitable for dividing simple or complex multi digit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient.  (Source

Read more »

Posted in: Long Division

No Storytimes October 26, 27 & 28. Join us for Spooky Babies!

Please note: There will be no library storytimes October 26th, 27th and 28th, 2010. Please join us for Spooky Babies instead.

Spooky Babies
Tuesday, October 26, 2010
10:30 a.m. - 11:30 a.m.
Meeting Rooms A & B

Get your wiggly shivers out and dance, dance, dance to some spooky fun music! Don't forget to come in your Halloween costume. For ages birth to six years and accompanying adult.

No registration required.

-sv-

Read more »

The Free Ride In Public Schools

To protect children's self-esteem or deflect complaints by parents, many public schools today automatically advance failing students to the next grade level. In other schools, some students are left back a maximum of one year, then promoted again regardless of their academic skills.The No Child Left Behind Act tries to solve this problem. The federal government is pressuring public schools to set

Read more »

Math Games and Activities for kids

Mathematics is said to be the study of the structure, change, quantity and space. Mathematicians, or those who work in this field, tend to study patterns and conjectures using the principles of deduction derived from definitions and axioms. Looking at this definition of mathematics, you will certainly remember those days when you were dreaded by the thought of learning math. Well, your kids

Read more »

Math Homework Help

Are you struggling with mathematics in school or college, TutorsOnnet math tutoring can provide help in a convenient and effective way. Math can be a major struggle for children ' starting in Grade 1 and continuing throughout their high school years and beyond. Children who find the subject less intuitive than others can often face hours of frustrating homework, alongside equally frustrated

Read more »

Information YOU need to know that you shouldn't share on the internet.

Your first assignment is to use a program you are familiar with to answer some questions you have heard before. You are to open the application and type in the answers to the following questions:

1. What is your NAME (first and Last)?
2. When were you born (date of birth-DOB)?
3. What is your address (where do you live)?
4. What is your mother of father's phone number?

You are to use at least two different type faces or font styles. You are to use two different point sizes and you are to use two colors. Once you complete these tasks you may decorate the page, BUT the answers to your questions must remain readable.
These questions are considered personal information. In the event of an emergency or if you were to get lost you should know this information. This information though should never be given to anyone you don't know, unless it is someone in a position of authority ( a police officer, fireman, school administrator). Do you know people who might ask you for this information over the internet? In many cases you don't, if you are asked for this information you should tell your parents or an adult who is monitoring your computer activity. This is one of the most important rules of Internet Safety, which we will be discussing this year.

Read more »

1.  Knowing that 23 October 1948 was a Saturday, which is more frequent for New Year's Day, Sunday or Monday? 2.  A convex polyhedron has no diagonals (every pair of vertices are connected by an edge). Prove that it is a tetrahedron.

1.  Prove that 462n+1 + 296·132n+1 is divisible by 1947. 2.  Show that any graph with 6 points has a triangle or three points which are not joined to each other. 3.  What is the smallest number of disks radius ½ that can cover a disk radius 1?

1.  Show that a graph has an even number of points of odd degree. 2.  P is any point inside an acute-angled triangle. D is the maximum and d is the minimum distance PX for X on the perimeter. Show that D ≥ 2d, and find when D = 2d.

1.  Show that no triangle has two sides each shorter than its corresponding altitude (from the opposite vertex). 2.  a, b, c, d are integers. For all integers m, n we can find integers h, k such that ah + bk = m and ch + dk = n. Show that |ad - bc| = 1.

1.  Prove that (1+x)(1+x2)(1+x4) ... (1+x2n-1) = 1 + x + x2 + x3 + ... + x2n-1. 2.  The a parallelogram has its vertices at lattice points and there is at least one other lattice point inside the parallelogram or on its sides. Show that its area is greater than 1.

1.  Each button in a box is big or small, and white or black. There is at least one big button, at least one small button, at least one white button, and at least one black button. Show that there are two buttons with different size and color. 2.  m and n are different positive integers. Show that 22m + 1 and 22n + 1 are coprime.

1.  Show that (a + a')(c + c') ≥ (b + b')2 for all real numbers a, a', b, b', c, c' such that aa' > 0, ac ≥ b2, a'c' ≥ b'2. 2.  Find the highest power of 2 dividing 2n! 3.  ABC is

Read more »

Posted in: Eötvös Competition Problems

42nd Eötvös Competition Problems 1938

1.  Show that a positive integer n is the sum of two squares iff 2n is the sum of two squares. 2.  Show that 1/n + 1/(n+1) + 1/(n+2) + ... + 1/n2 > 1 for integers n > 1. 3.  Show that for

Read more »

Posted in: Eötvös Competition Problems

41st Eötvös Competition Problems 1937

1.  a1, a2, ... , an is any finite sequence of positive integers. Show that a1! a2! ... an! < (S + 1)! where S = a1 + a2 + ... + an. 2.  P, Q, R are three points in space. The circle CP passes through Q and R, the circle CQ passes through R and P, and the circle CR passes through P and Q. The tangents to CQ and CR at P coincide. Similarly, the

Read more »

Posted in: Eötvös Competition Problems

1.  Show that 1/(1·2) + 1/(3·4) + 1/(5·6) + ... + 1/( (2n-1)·2n) = 1/(n+1) + 1/(n+2) + ... + 1/(2n). 2.  ABC is a triangle. Show that, if the point P inside the triangle is such that the triangles PAB, PBC, PCA have equal area, then P must be the centroid.

1.  x1, x2, ... , xn is any sequence of positive reals and yi is any permutation of xi. Show that ∑ xi/yi ≥ n. 2.  S is a finite set of points in the plane. Show that there is at most one point P in the plane such that if A is any point of S, then there is a point A' in S with P the midpoint of AA'.

1.  E is the product 2·4·6 ... 2n, and D is the product 1·3·5 ... (2n-1). Show that, for some m, D·2m is a multiple of E. 2.  Given a circle, find the inscribed polygon with the largest sum of the squares of its sides.

1.  If x2 + y2 = u2 + v2 = 1 and xu + yv = 0 for real x, y, u, v, find xy + uv. 2.  S is a set of 16 squares on an 8 x 8 chessboard such that there are just 2 squares of S in each row and column. Show that 8 black pawns and 8 white pawns can be placed on these squares so that there is just one white pawn and one black pawn in each row and column.

1.  Show that if m is a multiple of an, then (a + 1)m -1 is a multiple of an+1. 2.  ABC is a triangle with AB and AC unequal. AM, AX, AD are the median, angle bisector and altitude. Show that X always lies between D and M, and that if the triangle is acute-angled, then angle MAX < angle DAX. 

1.  Prove that there is just one solution in integers m > n to 2/p = 1/m + 1/n for p an odd prime. 2.  Show that an odd square cannot be expressed as the sum of five odd squares. 3.  Find the

Read more »

Posted in: Eötvös Competition Problems

1.  How many integers (1) have 5 decimal digits, (2) have last digit 6, and (3) are divisible by 3? 2.  A straight line is drawn on an 8 x 8 chessboard. What is the largest possible number of the unit squares with interior points on the line?

1.  Coins denomination 1, 2, 10, 20 and 50 are available. How many ways are there of paying 100? 2.  Show that ∑i=0 to k nCi (-x)i is positive for all 0 ≤ x < 1/n and all k ≤ n, where nCi is the binomial coefficient.

By Mo Willems
Call number: ER Willems
Best for kids ages 4-8

He has done it again! Mo Willems has produced another book that makes me laugh my pants off. You may remember Mo from his excellent Pigeon books.* His early reader series Elephant & Piggie is a great introduction for first time readers, with Gerald the Elephant and his dear friend Piggie speak in simple speech bubbles and solve complex problems such as having a bird on one’s head and being invited to a party for the first time. (What if it is a fancy-pool-costume party? You MUST be ready!)

In this newest installment, Elephant and Piggie realize they are in a book. They discover they can make the Reader say ANY word they want… but what happens when the book comes to an end?

Check out We are in a Book to find out!

Click here to view this title in the catalog

-JW-

*Psst! Don’t forget to sign up for the Pigeon Party! Registration begins Oct. 22.

Read more »

Posted in: New Book Review,Picture Books

There's Nothin' Like a Pumpkin

Get your gourd on with some facts about fall's favorite kind, the pumpkin.




The Story of the Jack O'Lantern by Katherine Brown Tegan The legend of why we carve pumpkins into Halloween jack-o-lantern.


Check our catalog for this title.



Seed, Sprout, Pumpkin pie by Jill Esbaum
The story of how a pumpkin turns into a delicious pie.

Check our catalog for this title.







Pumpkins! by Jacqueline Farmer
The history of pumpkins plus some recipes.

Check our catalog for this title.








Pumpkins by Ken Robbins
Gorgeous photographs will make you wish for a pumpkin patch of your very own.

Check our catalog for this title.




From Seed to Pumpkin by Wendy Pfeffer
The growing process for youngest readers.

Check our catalog for this title.

-gw-

Read more »

Posted in: Non-Fiction

y3 mario

Y3 mario

Gangster Bros. 1.1

Infomation: The latest version of Gangster Bros, with bug fixes and improved gameplay.

How to play: Use WASD keys to move.Mouse to aim and shoot.

Tags: 1 Player, Action, Arcade, Flash, Mario, Parody, Series, Shoot Em Up, Shotgun, Side Scrolling

http://www.y3.vc/

Super Mario 63

Infomation: This awesome Super Mario Bros platform jump and run adventure game is not only advisable for Mario or Luigi fans! Use the arrow keys, Z, X and C to explore the world. Use your arrow keys to play this free online flash game.

How to play: Arrow keys- To move.Z/X/C- To take action.

Tags: 1 Player, Action, Adventure, Arcade, Collecting Games, Flash, Fun, Mario, Platforms

http://www.y3.vc/

Super Mario Sunshine

Infomation: In this game Mario fights an evil witch. To complete the levels you'll need your backpack.

How to play: Use arrow keys to move.Space bar to use the hydro pump.

Tags: 1 Player, Flash, Mario, Platforms

http://www.y3.vc/

Mario Combat

Infomation: You are super Mario! It means you've got to go and kick Bowser's ass. Get massive combos to boost your score!

How to play: Arrow keys left/right- Move left/right.A- Attack.Arrow up- Jump.

Tags: 1 Player, Action, Arcade, Beat Em Up, Flash, Mario, Platforms

http://www.y3.vc/

Super Chick Sisters

Infomation: Similar to Mario except with little chicklettes. Save the chicklettes from a KFC death!

How to play: Arrow Keys - Move.

Tags: 1 Player, Adventure, Animal, Chicken, Flash, Jumping, Mario, Rescue

http://www.y3.vc/

Read more »

y3 satan

Y3 satan

Ninjai Scroll

Infomation: Help Ninjai retrieve the sacred scroll.

How to play: Arrow keys - To move. Space bar - To Attack. 1- Use sword. 2- Use Shurikens.

Tags: Unrated games,Flash,Throwing,Beat Em Up,1 Player,Action,Shooting,Satan,Platforms,Ninja,Killing,Fighting

http://www.y3.vc/

ít Loki

Infomation: Thoát khỏi địa ngục bằng cách nhảy lên trên và tránh dung nham hoành dưới đây và cũng có thể thu thập chiếc sọ cuối cùng trước khi tiếp cận với cờ. |

How to play: Phím mũi tên để di chuyển.Phím dài để nhảy.

Tags: Tro-choi-mot-nguoi-choi=Một Người Chơi, Collecting Games, Escape, Flash, Obstacle, Satan

http://www.y3.vc/

мало Локи

Infomation: избежать ада, прыгая вверх и избежать бушует лава ниже, а также собирать черепа перед тем как достичь за флагом. |

How to play: клавиши стрелок для перемещения.Пробел, чтобы прыгать.

Tags: 1 Player, Collecting Games, Escape, Flash, Obstacle, Satan

http://www.y3.vc/

Loki poco

Infomation: Escapar del infierno al saltar hacia arriba y evitar la lava furiosa continuación, así como recoger cráneos antes de llegar a la bandera.

How to play: Teclas de flecha para mover. barra espaciadora para saltar.

Tags: 1 Player, Collecting Games, Escape, Flash, Obstacle, Satan

http://www.y3.vc/

Ninjai scroll

Infomation: Ninjai ajudar a recuperar o pergaminho sagrado.

How to play: Teclas de seta para mover-se. barra de espa

Tags: ,jogos-flash=Jogos Flash,jogos-throwing=Jogos Throwing,jogos-de-beat-em-up=Jogos de Beat Em Up,1-jogador=1 jogador,jogos-de-accao=Acção,jogos-de-tiros=Jogos de Tiros,jogos-de-satanas=jogos de Satanás,jogos-de-plataformas=Jogos de Plataformas,jogos-de-ninj

http://www.y3.vc/

Read more »

8 Tips to Help Your Child Adjust to a New School

By Rebecca VanderMeulen Every year, school boards across the country grapple with the issue of redistricting: Drawing new lines to decide which kids go to which schools, thanks to the opening of a new building, the closure of an old school or lopsided class sizes among schools in the same district. Once these new lines are drawn, many kids end up stuck in the

Read more »

What is the Scientific Method?

The scientific method involves following six general steps in sequence.  The basic steps are:Problem, Purpose, or Research Question: The problem or research question is the single most important part of the scientific method. Every part of your project is done to answer this question. The research question is sometimes formed as a statement and is called the "Problem" or "Problem Statement."

Read more »

32nd Eötvös Competition Problems 1928

1.  Show that for any real x, at least one of x, 2x, 3x, ... , (n-1)x differs from an integer by no more than 1/n. 2.  The numbers 1, 2, ... , n are arranged around a circle so that the difference between any two adjacent numbers does not exceed 2. Show that this can be done in only one way (treating rotations and reflections of an arrangement as the same

Read more »

Posted in: Eötvös Competition Problems

1.  a, b, c, d are each relatively prime to n = ad - bc, and r and s are integers. Show ar + bs is a multiple of n iff cr + ds is a multiple of n. 2.  Find the sum of all four digit numbers (written in base 10) which contain only the digits 1 - 5 and contain no digit twice.

1.  Show that for any integers m, n the equations w + x + 2y + 2z = m, 2w - 2x + y - z = n have a solution in integers. 2.  Show that the product of four consecutive integers cannot be a square. 3.  A circle or

Read more »

Posted in: Eötvös Competition Problems

29th Eötvös Competition Problems 1925

1.  Given four integers, show that the product of the six differences is divisible by 12. 2.  How many zeros does the the decimal representation of 1000! end with? 3.  Show that the inradius of a right-angled

Read more »

Posted in: Eötvös Competition Problems

27th Eötvös Competition Problems 1923

1.  The circles OAB, OBC, OCA have equal radius r. Show that the circle ABC also has radius r. 2.  Let x be a real number and put y = (x + 1)/2. Put an = 1 + x + x2 + ... + xn, and bn = 1 + y + y2 + ... + yn. Show that ∑0n am (n+1)C(m+1) = 2n bn, where aCb is the binomial coefficient a!/( b! (a-b)! ). 3.  Show that an infinite arithmetic progression

Read more »

Posted in: Eötvös Competition Problems

1.  Show that given four non-coplanar points A, B, P, Q there is a plane with A, B on one side and P, Q on the other, and with all the points the same distance from the plane. 2.  Show that we cannot factorise x4 + 2x2 + 2x + 2 as the product of two quadratics with integer coefficients.

1.  The positive integers a, b, c are such that there are triangles with sides an, bn, cn for all positive integers n. Show that at least two of a, b, c must be equal. 2.  What is the locus of the point (in the plane), the sum of whose distances to a given point and line is fixed? 3.  Given three points in the plane, how does one construct three distinct

Read more »

Posted in: Eötvös Competition Problems

1.  AC is the long diagonal of a parallelogram ABCD. The perpendiculars from C meet the lines AB and AD at P and Q respectively. Show that AC2 = AB·AP + AD·AQ. 2.  Find three distinct positive integers a, b, c such that 1/a + 1/b + 1/c is an integer.

1.  a, b are integers. The solutions of y - 2x = a, y2 - xy + x2 = b are rational. Show that they must be integers. 2.  A square has 10s digit 7. What is its units digit? 3.  A, B are two points inside a given

Read more »

Posted in: Eötvös Competition Problems

1.  a, b are positive reals. Show that 1/x + 1/(x-a) + 1/(x+b) = 0 has two real roots one in [a/3, 2a/3] and the other in [-2b/3, -b/3]. 2.  ABC is a triangle. The bisector of ∠C meets AB at D. Show that CD2 < CA·CB.

1.  Given any reals A, B, C, show that An2 + Bn + C < n! for all sufficiently large integers n. 2.  A triangle lies entirely inside a polygon. Show that its perimeter does not exceed the perimeter of the polygon. 3.  Show that a triangle inscribed in a parallelogram has area at most half that of the parallelogram. SolutionsProblem 1Given any reals A, B, C, show

Read more »

Posted in: Eötvös Competition Problems

1.  Circles C and C' meet at A and B. The arc AB of C' divides the area inside C into two equal parts. Show that its length is greater than the diameter of C. 2.  a, b, c are reals such that |ax2 + bx + c| ≤ 1 for all x ≤ |1|. Show that |2ax + b| ≤ 4 for all |x| ≤ 1.

1.  Prove that n! n! > nn for n > 2. 2.  Let A and B be diagonally opposite vertices of a cube. Prove that the midpoints of the 6 edges not containing A or B form a regular (planar) hexagon. 3.  If d is the

Read more »

Posted in: Eötvös Competition Problems

19th Eötvös Competition Problems 1912

1.  How many n-digit decimal integers have all digits 1, 2 or 3. How many also contain each of 1, 2, 3 at least once? 2.  Prove that 5n + 2 3n-1 + 1 = 0 (mod 8). 3.  ABCD is a quadrilateral with vertices in

Read more »

Posted in: Eötvös Competition Problems

1.  Real numbers a, b, c, A, B, C satisfy b2 < ac and aC - 2bB + cA = 0. Show that B2 ≥ AC. 2.  L1, L2, L3, L4 are diameters of a circle C radius 1 and the angle between any two is either π/2 or π/4. If P is a point on the circle, show that the sum of the fourth powers of the distances from P to the four diameters is 3/2.

1.  α, β, γ are real and satisfy α2 + β2 + γ2 = 1. Show that -1/2 ≤ αβ + βγ + γα ≤ 1. 2.  If ac, bc + ad, bd = 0 (mod n) show that bc, ad = 0 (mod n). 3.  ABC is a triangle with angle C = 120o. Find the

Read more »

Posted in: Eötvös Competition Problems

16th Eötvös Competition Problems 1909

1.  Prove that (n + 1)3 ≠ n3 + (n - 1)3 for any positive integer n. 2.  α is acute. Show that α < (sin α + tan α)/2. 3.  ABC is a triangle. The feet of the altitudes from A, B, C are P, Q, R respectively, and P,

Read more »

Posted in: Eötvös Competition Problems

15th Eötvös Competition Problems 1908

1.  m and n are odd. Show that 2k divides m3 - n3 iff it divides m - n. 2.  Let a right angled triangle have side lengths a > b > c. Show that for n > 2, an > bn + cn. 3.  Let the vertices of a regular 10

Read more »

Posted in: Eötvös Competition Problems

1.  Show that the quadratic x2 + 2mx + 2n has no rational roots for odd integers m, n. 2.  Let r be the radius of a circle through three points of a parallelogram. Show that any point inside the parallelogram is a distance ≤ r from at least one of its vertices.

1.  Let α be a real number, not an odd multiple of π. Prove that tan α/2 is rational iff cos α and sin α are rational. 2.  Show that the centers of the squares on the outside of the four sides of a rhombus form a square.

1.  For what positive integers m, n can we find positive integers a, b, c such that a + mb = n and a + b = mc. Show that there is at most one such solution for each m, n. 2.  Divide the unit square into 9 equal squares (forming a 3 x 3 array) and color the central square red. Now subdivide each of the 8 uncolored squares into 9 equal squares and color each

Read more »

Posted in: Eötvös Competition Problems

11th Eötvös Competition Problems 1904

1.  A pentagon inscribed in a circle has equal angles. Show that it has equal sides. 2.  Let a be an integer, and let p(x1, x2, ... , xn) = ∑1n k xk. Show that the number of integral solutions (x1, x2, ... , xn) to p(x1, x2, ... , xn) = a, with all xi > 0 equals the number of integral solutions (x1, x2, ... , xn) to p(x1, x2, ... , xn) = a -

Read more »

Posted in: Eötvös Competition Problems

10th Eötvös Competition Problems 1903

1.  Prove that 2p-1(2p - 1) is perfect when 2p - 1 is prime. [A perfect number equals the sum of its (positive) divisors, excluding the number itself.] 2.  α and β are real and a = sin α, b = sin β, c = sin(α+β). Find a polynomial p(x, y, z) with integer coefficients, such that p(a, b, c) = 0. Find all values of (a, b) for which there are less than four

Read more »

Posted in: Eötvös Competition Problems

9th Eötvös Competition Problems 1902

1.  Let p(x) = ax2 + bx + c be a quadratic with real coefficients. Show that we can find reals d, e, f so that p(x) = d/2 x(x - 1) + ex + f, and that p(n) is always integral for integral n iff d, e, f are integers. 2.  P is a variable point outside the fixed sphere S with center O. Show that the surface area of the sphere center P radius PO which lies

Read more »

Posted in: Eötvös Competition Problems

1.  Show that 5 divides 1n + 2n + 3n + 4n iff 4 does not divide n. 2.  Let α = cot π/8, β = cosec π/8. Show that α satisfies a quadratic and β a quartic, both with integral coefficients and leading coefficient 1.

1.  d is not divisible by 5. For some integer n, a n3 + b n2 + c n + d is divisible by 5. Show that for some integer m, a + b m + c m2 + d m3 is divisible by 5. 2.  Construct the triangle ABC given c, r and r', where c = |AB|, r is the radius of the inscribed circle, and r' is the radius of the other circle tangent to the segment AB and the lines BC and CA

Read more »

Posted in: Eötvös Competition Problems

1.  ABCDE is a regular pentagon (with vertices in that order) inscribed in a circle of radius 1. Show that AB·AC = √5. 2.  The roots of the quadratic x2 - (a + d) x + ad - bc = 0 are α and β. Show that α3 and β3 are the roots of x2 - (a3 + d3 + 3abc + 3bcd) x + (ad - bc)3 = 0.

1.  For which positive integers n does 3 divide 2n + 1? 2.  Triangles ABC, PQR satisfy (1) ∠A = ∠P, (2) |∠B - ∠C| < |∠Q - ∠R|. Show that sin A + sin B + sin C > sin P + sin Q + sin R. What angles A, B, C maximise sin A + sin B + sin C?

1.  ABC is a right-angled triangle. Show that sin A sin B sin(A - B) + sin B sin C sin(B - C) + sin C sin A sin(C - A) + sin(A - B) sin(B - C) sin(C - A) = 0. 2.  ABC is an arbitrary triangle. Show that sin(A/2) sin(B/2) sin(C/2) < 1/4. 3.  The line L contains the distinct points A, B, C, D in that order. Construct a rectangle whose sides (or their

Read more »

Posted in: Eötvös Competition Problems

3rd Eötvös Competition Problems 1896

1.  For a positive integer n, let p(n) be the number of prime factors of n. Show that ln n ≥ p(n) ln 2. 2.  Show that if (a, b) satisfies a2 - 3ab + 2b2 + a - b = a2 - 2ab + b2 - 5a + 7b = 0, then it also satisfies ab - 12a + 15b = 0. 3.  Given three points P, Q, R in the plane, find points A, B, C such that P is the foot of the perpendicular from A to BC,

Read more »

Posted in: Eötvös Competition Problems

1.  n cards are dealt to two players. Each player has at least one card. How many possible hands can the first player have? 2.  ABC is a right-angled triangle. Construct a point P inside ABC so that the angles PAB, PBC, PCA are equal.

1.  Show that { (m, n): 17 divides 2m + 3n} = { (m, n): 17 divides 9m + 5n}. 2.  Given a circle C, and two points A, B inside it, construct a right-angled triangle PQR with vertices on C and hypoteneuse QR such that A lies on the side PQ and B lies on the side PR. For which A, B is this not possible?

Please plan to join us for our annual Family Resource Fair on Saturday, October 16, 2010 from 10:00 a.m. to 2:00 p.m. in the meeting rooms on the first floor of the library. There will be 30 family-friendly community organizations present, along with books and activities for kids and raffle prizes donated by local Beaverton businesses. This is a great opportunity to discover all the resources and services for families that are available in the Beaverton area. We look forward to seeing you there! -gw-

Read more »

Posted in: Special Programs

18th Iberoamerican Mathematical Olympiad Problems 2003

A1.  Let A, B be two sets of N consecutive integers. If N = 2003, can we form N pairs (a, b) with a ∈ A, b ∈ B such that the sums of the pairs are N consecutive integers? What about N = 2004? A2.  C is a point on the semicircle with diameter AB. D is a point on the arc BC. M, P, N are the midpoints of AC, CD and BD. The circumcenters of ACP and BDP are O, O'

Read more »

Posted in: Iberoamerican Mathematical Olympiad

17th Iberoamerican Mathematical Olympiad Problems 2002

A1.  The numbers 1, 2, ... , 2002 are written in order on a blackboard. Then the 1st, 4th, 7th, ... , 3k+1th, ... numbers in the list are erased. Then the 1st, 4th, 7th, ... 3k+1th numbers in the remaining list are erased (leaving 3, 5, 8, 9, 12, ... ). This process is carried out repeatedly until there are no numbers left. What is the last number to be erased?

Read more »

Posted in: Iberoamerican Mathematical Olympiad

16th Iberoamerican Mathematical Olympiad Problems 2001

A1.  Show that there are arbitrarily large numbers n such that: (1) all its digits are 2 or more; and (2) the product of any four of its digits divides n. A2.  ABC is a triangle. The incircle has center I and

Read more »

Posted in: Iberoamerican Mathematical Olympiad

15th Iberoamerican Mathematical Olympiad Problems 2000A1.  Label the vertices of a regular n-gon from 1 to n > 3. Draw all the diagonals. Show that if n is odd then we can label each side and diagonal with a number from 1 to n different from the labels of its endpoints so that at each vertex the sides and diagonals all have different labels.

A1.  Find all positive integers n < 1000 such that the cube of the sum of the digits of n equals n2. A2.  Given two circles C and C' we say that C bisects C' if their common chord is a diameter of C'. Show that for any two circles which are not concentric, there are infinitely many circles which bisect them both. Find the locus of the centers of the

Read more »

Posted in: Iberoamerican Mathematical Olympiad

13th Iberoamerican Mathematical Olympiad Problems 1998

A1.  There are 98 points on a circle. Two players play alternately as follows. Each player joins two points which are not already joined. The game ends when every point has been joined to at least one other. The winner is the last player to play. Does the first or second player have a winning strategy? A2.  The incircle of the triangle ABC touches BC, CA, AB

Read more »

Posted in: Iberoamerican Mathematical Olympiad

12th Iberoamerican Mathematical Olympiad Problems 1997

A1.  k ≥ 1 is a real number such that if m is a multiple of n, then [mk] is a multiple of [nk]. Show that k is an integer. A2.  I is the incenter of the triangle ABC. A circle with center I meets the side BC at D and P, with D nearer to B. Similarly, it meets the side CA at E and Q, with E nearer to C, and it meets AB at F and R, with F nearer to A. The

Read more »

Posted in: Iberoamerican Mathematical Olympiad

A1.  Find the smallest positive integer n so that a cube with side n can be divided into 1996 cubes each with side a positive integer. A2.  M is the midpoint of the median AD of the triangle ABC. The ray BM meets AC at N. Show that AB is tangent to the circumcircle of NBC iff BM/MN = (BC/BN)2.

Arithmetic FourA game like Fraction Four but instead of fraction questions the player must answer arithmetic questions (addition, subtraction, multiplication, division) to earn a piece to place on the board. Arithmetic Quiz Arithmetic Quiz gives the user randomized questions to answer on arithmetic with whole numbers and integers. Bounded Fraction Pointer

Read more »

How to Study Mathematics

INTRODUCTIONWhy aren't you getting better grades in mathematics? Do you feel that you have put in all the time on it that can be expected of you and that you are still not getting results? Or are you just lazy? If you are lazy, this material is not intended for you. But if you have been trying and your grades still don't show your ability, or if you have been getting good grades but

Read more »

A1.  Find all possible values for the sum of the digits of a square. A2.  n > 1. Find all solutions in real numbers x1, x2, ... , xn+1 all at least 1 such that: (1) x11/2 + x21/3 + x31/4 + ... + xn1/(n+1) = n xn+11/2; and (2) (x1 + x2 + ... + xn)/n = xn+1.

A1.  Show that there is a number 1 < b < 1993 such that if 1994 is written in base b then all its digits are the same. Show that there is no number 1 < b < 1992 such that if 1993 is written in base b then all its digits are the same. A2.  ABCD is a cyclic quadrilateral. A circle whose center is on the side AB touches the other three sides. Show that AB = AD

Read more »

Posted in: Iberoamerican Mathematical Olympiad

8th Iberoamerican Mathematical Olympiad Problems 1993

A1.  A palindrome is a positive integers which is unchanged if you reverse the order of its digits. For example, 23432. If all palindromes are written in increasing order, what possible prime values can the difference between successive palindromes take? A2.  Show that any convex polygon of area 1 is contained in some parallelogram of area 2. A3.

Read more »

Posted in: Iberoamerican Mathematical Olympiad

7th Iberoamerican Mathematical Olympiad Problems 1992

A1.  an is the last digit of 1 + 2 + ... + n. Find a1 + a2 + ... + a1992. A2.  Let f(x) = a1/(x + a1) + a2/(x + a2) + ... + an/(x + an), where ai are unequal positive reals. Find the sum of the lengths of the intervals in which f(x) ≥ 1. A3.  ABC is an equilateral triangle with side 2. Show that any point P on the incircle satisfies PA2 +

Read more »

Posted in: Iberoamerican Mathematical Olympiad

6th Iberoamerican Mathematical Olympiad Problems 1991

A1.  The number 1 or the number -1 is assigned to each vertex of a cube. Then each face is given the product of its four vertices. What are the possible totals for the resulting 14 numbers? A2.  Two perpendicular lines divide a square into four parts, three of which have area 1. Show that the fourth part also has area 1. A3.  f is a function defined on all

Read more »

Posted in: Iberoamerican Mathematical Olympiad

5th Iberoamerican Mathematical Olympiad Problems 1990

A1.  The function f is defined on the non-negative integers. f(2n - 1) = 0 for n = 0, 1, 2, ... . If m is not of the form 2n - 1, then f(m) = f(m+1) + 1. Show that f(n) + n = 2k - 1 for some k, and find f(21990). A2.  I is the incenter of the triangle ABC and the incircle touches BC, CA, AB at D, E, F respectively. AD meets the incircle again at P. M

Read more »

Posted in: Iberoamerican Mathematical Olympiad

4th Iberoamerican Mathematical Olympiad Problems 1989

A1.  Find all real solutions to: x + y - z = -1; x2 - y2 + z2 = 1, -x3 + y3 + z3 = -1. A2.  Given positive real numbers x, y, z each less than π/2, show that π/2 + 2 sin x cos y + 2 sin y cos z > sin 2x + sin 2y + sin 2z. A3.  If a, b, c, are the sides of a triangle, show that (a - b)/(a + b) + (b - c)/(b + c) + (c - a)/(a + c) < 1/16.

Read more »

Posted in: Iberoamerican Mathematical Olympiad

A1.  The sides of a triangle form an arithmetic progression. The altitudes also form an arithmetic progression. Show that the triangle must be equilateral. A2.  The positive integers a, b, c, d, p, q satisfy ad - bc = 1 and a/b > p/q > c/d. Show that q ≥ b + d and that if q = b + d, then p = a + c.

A1.  Find f(x) such that f(x)2f( (1-x)/(1+x) ) = 64x for x not 0, ±1. A2.  In the triangle ABC, the midpoints of AC and AB are M and N respectively. BM and CN meet at P. Show that if it is possible to inscribe a circle in the quadrilateral AMPN (touching every side), then ABC is isosceles.

A1.  Find all integer solutions to: a + b + c = 24, a2 + b2 + c2 = 210, abc = 440. A2.  P is a point inside the equilateral triangle ABC such that PA = 5, PB = 7, PC = 8. Find AB. A3.  Find the roots r1, r2, r3, r4 of the equation 4x4 - ax3 + bx2 - cx + 5 = 0, given that they are positive reals satisfying r1/2 + r2/4 + r3/5 + r4/8 =

Read more »

Posted in: Iberoamerican Mathematical Olympiad

a3 + b3 = c3 a3 + b3 = c3 + d3 This has no solutions when a, b and c are whole numbers 13 +123 = 93 + 103 93 +153 = 23 + 163 Can you find others?

How can you tell if a number divides exactly by 2? Answer: If it ends in an even number.   How can you tell if a number divides exactly by 5? Answer: If it ends in a 0 or a 5.  

Read more »

Posted in: Amazing Number Facts No

Amazing Number Facts No (part 2)

Here is a remarkable formula: f(n) = n2-n+41 f(1) = 12-1+41 = 41 a prime number f(2) = 22-2+41 = 43 a prime number f(3) = 32-3+41 = 47 a prime number f(4) = 42-4+41 = 53 a prime number   How many prime numbers does this formula produce? A formula that always produces prime numbers in this way has never been found. So just how

Read more »

Posted in: Amazing Number Facts No

Amazing Number Facts No (part 1)

Since 32 + 42 = 52 does it follow that 33 + 43 + 53 = 63 ? Check it out ! Does this pattern continue to be true?The factors of 28 (not including itself) are 1, 2, 4, 7 and 14. Astonishingly these

Read more »

Posted in: Amazing Number Facts No

Scumble

by Ingrid Law (Childrens New Books)(J Law)(2010)

for ages 8-12 years

In this follow up to Savvy, when you turn 13 in Legder Kale's family you find yourself with a savvy. In the first book Ledge's cousin Mibs turns 13 with a bang. Now it's Ledge's turn, but his savvy is a let down. He can disassemble watches, but what good is that?

His family sets out for Wyoming for a savvy-filled family wedding. Just about the time he gets there he realizes his savvy can disassemble a lot more than just watches! To make things worse, an outsider named Sarah Jane witnesses his skills. Not only that, but she's the town snoop, too!

Ledge must learn how to scumble his savvy, which just means he needs to learn to finesse it. He must also keep Sarah Jane's dad from foreclosing on his uncle's ranch, and keep Sarah Jane from revealing all his family's secrets!

This book has just the right amount of action and intrigue to keep any reader wanting to read more!-sc-

Check our catalog for this title.

Read more »

1.  Let A = 44...4 (2n digits) and B = 88...8 (n digits). Show that A + 2B + 4 is a square. 2.  A1, A2, ... , An are points in the plane, so that if we take the points in any order B1, B2, ... , Bn, then the broken line B1B2...Bn does not intersect itself. What is the largest possible value of n?

1.  The triangle ABC has CA = CB. P is a point on the circumcircle between A and B (and on the opposite side of the line AB to C). D is the foot of the perpendicular from C to PB. Show that PA + PB = 2·PD. 2.  The circles center O1 and O2 meet at A and B with the centers on opposite sides of AB. The lines BO1 and BO2 meet their respective circles

Read more »

Posted in: Junior Balkan Mathematical Olympiad Problems

1.  Find all positive integers a, b, c such that a3 + b3 + c3 = 2001. 2.  ABC is a triangle with ∠C = 90o and CA ≠ CB. CH is an altitude and CL is an angle bisector. Show that for X ≠ C on the line CL, we have ∠XAC ≠ ∠XBC. Show that for Y ≠ C on the line CH we have ∠YAC ≠ ∠YBC.

1.  x and y are positive reals such that x3 + y3 + (x + y)3 + 30xy = 2000. Show that x + y = 10. 2.  Find all positive integers n such that n3 + 33 is a perfect square. 3.  ABC is a triangle. E, F are

Read more »

Posted in: Junior Balkan Mathematical Olympiad Problems

1.  a, b, c are distinct reals and there are reals x, y such that a3 + ax + y = 0, b3 + bx + y = 0 and c3 + cx + y = 0. Show that a + b + c = 0. 2.  Let an = 23n + 36n+2 + 56n+2. Find gcd(a0, a1, a2, ... , a1999).

1.  The number 11...122...25 has 1997 1s and 1998 2s. Show that it is a perfect square. 2.  The convex pentagon ABCDE has AB = AE = CD = 1 and angle ABC = angle DEA = 90o and BC + DE = 1. Find its area. 3.

Read more »

Posted in: Junior Balkan Mathematical Olympiad Problems

1.  Show that given any 9 points inside a square side 1 we can always find three which form a triangle with area < 1/8. 2.  Given reals x, y with (x2 + y2)/(x2 - y2) + (x2 - y2)/(x2 + y2) = k, find (x8 + y8)/(x8 - y8) + (x8 - y8)/(x8 + y8) in terms of k.

A1.  Find the smallest positive integer N which is a multiple of 83 and is such that N2 has exactly 63 positive divisors. A2.  Given two circles (neither inside the other) with different radii, a line L, and k > 0, show how to construct a line L' parallel to L so that L intersects the two circles in chords with total length k.

A1.  Let S be the set of all points in the plane with integer coordinates. Let T be the set of all segments AB, where A, B ∈ S and AB has integer length. Prove that we cannot find two elements of T making an angle 45o. Is the same true in three dimensions?

A1.  Show that √x + √y + √(xy) = √x + √(y + xy + 2y√x). Hence show that √3 + √(10 + 2√3) = √(5 + √22) + √(8 - √22 + 2√(15 - 3√22)). A2.  Every point of the plane is painted with one of three colors. Can we always find two points a distance 1 apart which are the same color?

The Tilting House by Tom Llewellyn
The Peshik family has finally found a house they can afford. There are a few problems. All the floors in the house tilt. And there are funny diagrams drawn on almost every wall. But they decide to buy the house anyway and so begins their adventure in "The Tilting House." Slanting floors and pictures on the wall are just the start of their troubles. Mr. Peshik accidently makes an enemy out of a family of talking rats living in the attic. Josh and Aaron, the Peshik boys, find some magic grow powder which turns a hiking trip into a survival test. Next, the dimmer switch in the dining room goes on the blink and makes the house disappear from sight . The biggest mystery of all is the story of the man who built the house and the treasure that might be hidden deep inside the basement. A good read for 4th and 5th graders, "The Tilting House" is just spooky enough for this haunting time of year. And for more about this story, visit www.thetiltinghouse.com. -gw-

Check our catalog for this title.

Read more »

Posted in: Chapter Book Chips

Simple Probability

total ways a specific outcome will happenProbability =total number of possible outcomesExample: There are 87 marbles in a bag and 68 of them are green. If one marble is chosen, what is the probability that it will be green?SolutionDivide the number of ways to choose a green marble (68) by the total number of marbles (87)68 ÷ 87 = 0.781609Round to the desired precision (e.g. 0.781609 rounded to

Read more »

Posted in: Probability

2nd Irish Mathematical Olympiad Problems 1989

A1.  S is a square side 1. The points A, B, C, D lie on the sides of S in that order, and each side of S contains at least one of A, B, C, D. Show that 2 ≤ AB2 + BC2 + CD2 + DA2 ≤ 4. A2.  A sumsquare is a 3 x 3 array of positive integers such that each row, each column and each of the two main diagonals has sum m. Show that m must be a multiple of 3 and

Read more »

Posted in: Irish Mathematical Olympiad,IrMO

1.  One face of a pyramid with square base and all edges 2 is glued to a face of a regular tetrahedron with edge length 2 to form a polyhedron. What is the total edge length of the polyhedron? 2.  P is a point on the circumcircle of the square ABCD between C and D. Show that PA2 - PB2 = PB·PD - PA·PC.

1.  A chess board is placed on top of an identical board and rotated through 45 degrees about its center. What is the area which is black in both boards? 2.  AB is a diameter of the circle C. M and N are any two points on the circle. The chord MA' is perpendicular to the line NA and the chord MB' is perpendicular to the line NB. Show that AA' and BB' are

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

14th All Soviet Union Mathematical Olympiad Problems 1980

1.  All two digit numbers from 19 to 80 inclusive are written down one after the other as a single number N = 192021...7980. Is N divisible by 1980? 2.  A square is divided into n parallel strips (parallel to

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

13th All Soviet Union Mathematical Olympiad Problems 1979

1.  T is an isosceles triangle. Another isosceles triangle T' has one vertex on each side of T. What is the smallest possible value of area T'/area T? 2.  A grasshopper hops about in the first quadrant (x, y >= 0).

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

12th All Soviet Union Mathematical Olympiad Problems 1978

1.  an is the nearest integer to √n. Find 1/a1 + 1/a2 + ... + 1/a1980. 2.  ABCD is a quadrilateral. M is a point inside it such that ABMD is a parallelogram. ∠CBM = ∠CDM. Show that ∠ACD = ∠BCM. 3.  Show that there is no

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

1.  P is a polygon. Its sides do not intersect except at its vertices, and no three vertices lie on a line. The pair of sides AB, PQ is called special if (1) AB and PQ do not share a vertex and (2) either the line AB intersects the segment PQ or the line PQ intersects the segment AB. Show that the number of special pairs is even.

1.  50 watches, all keeping perfect time, lie on a table. Show that there is a moment when the sum of the distances from the center of the table to the center of each dial equals the sum of the distances from the center of the table to the tip of each minute hand.

1.  (1) O is the circumcenter of the triangle ABC. The triangle is rotated about O to give a new triangle A'B'C'. The lines AB and A'B' intersect at C'', BC and B'C' intersect at A'', and CA and C'A' intersect at B''. Show that A''B''C'' is similar to ABC. (2) O is the center of the circle through ABCD. ABCD is rotated about O to give the quadrilateral A'B'C'D'.

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

8th All Soviet Union Mathematical Olympiad Problems 1974

1.  A collection of n cards is numbered from 1 to n. Each card has either 1 or -1 on the back. You are allowed to ask for the product of the numbers on the back of any three cards. What is the smallest number of questions which will allow you to determine the numbers on the backs of all the cards if n is (1) 30, (2) 31, (3) 32? If 50 cards are arranged in a

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

7th All Soviet Union Mathematical Olympiad Problems 1973

7th All Soviet Union Mathematical Olympiad Problems 19731.  You are given 14 coins. It is known that genuine coins all have the same weight and that fake coins all have the same weight, but weigh less than genuine coins. You suspect that 7 particular coins are genuine and the other 7 fake. Given a balance, how can you prove this in three weighings (assuming that you

Read more »

Posted in: All Soviet Union Mathematical Olympiad Problems,ASU

6th All Russian Mathematical Olympiad Problems 19661.  There are an odd number of soldiers on an exercise. The distance between every pair of soldiers is different. Each soldier watches his nearest neighbour. Prove that at least one soldier is not being watched.

5th All Russian Mathematical Olympiad Problems 19651. (a)  Each of x1, ... , xn is -1, 0 or 1. What is the minimal possible value of the sum of all xixj with 1 ≤ i < j ≤ n? (b)  Is the answer the same if the xi are real numbers satisfying 0 ≤ |xi| ≤ 1 for 1 ≤ i ≤ n?

4th All Russian Mathematical Olympiad Problems 19641.  In the triangle ABC, the length of the altitude from A is not less than BC, and the length of the altitude from B is not less than AC. Find the angles. 2.  If m, k, n are natural numbers and n>1, prove that we cannot have m(m+1) = kn. 3.  Reduce each of the first billion natural numbers (billion = 109)

Read more »

Posted in: ARMO,Russian Mathematical Olympiad

3rd All Russian Mathematical Olympiad Problems 1963

3rd All Russian Mathematical Olympiad Problems 19631.  Given 5 circles. Every 4 have a common point. Prove that there is a point common to all 5. 2.  8 players compete in a tournament. Everyone plays everyone else just once. The winner of a game gets 1, the loser 0, or each gets 1/2 if the game is drawn. The final result is that everyone gets a different score

Read more »

Posted in: ARMO,Russian Mathematical Olympiad

2nd All Russian Mathematical Olympiad Problems 19621.  ABCD is any convex quadrilateral. Construct a new quadrilateral as follows. Take A' so that A is the midpoint of DA'; similarly, B' so that B is the midpoint of AB'; C' so that C is the midpoint of BC'; and D' so that D is the midpoint of CD'. Show that the area of A'B'C'D' is five times the area of ABCD.

1.  Given 12 vertices and 16 edges arranged as follows:Draw any curve which does not pass through any vertex. Prove that the curve cannot intersect each edge just once. Intersection means that the curve crosses the edge from one side to the other. For example, a circle which had one of the edges as tangent would not intersect that edge.

In the last column, I discussed ellipses and how drawing them involves the fluid, fairly fast movement of the hand, letting your reflexes carry out the kind of rounded shape you intend to make. Now we’ll move on to shading the pot that we previously described in simple outline, using curving lines that are like segments of the ellipse.James McMullanThese are what I think of as “cat stroking

Read more »

Little Builders date change in November

The Little Builders club will not be held November due to the Thanksgiving holiday weekend. Instead it will be held Saturday, December 4.

This is a club for children ages 3 through 5 to play with Duplo blocks. Space is limited and registration is required. There will also be a conflict for the Christmas holiday, so stay tuned.

Little Builders
Saturday, December 4
10:30-11:30 AM
Storytime Room

Registration is required. Please phone (503)350-3600 to register or sign-up in person at the Children’s Desk on the first floor of the library. Registration begins one month before the session.

Read more »