This is the 1st math book that I truly enjoyed. I was captivated by all the stories. My father also loved the book; his favorite part was the analysis of Joe Di Maggio's hitting streak. My father & I now share a delight with math -April Cody HS

Math Fun for Everyone

By Werner Weingartner

iUniverse, Inc.

Copyright © 2012 Werner Weingartner
All right reserved.
ISBN: 978-1-4759-3614-8

Contents

Chapter One

MY MATH HISTORY

Kindergarten 1941—We learned how to count from 1-100. I asked the teacher what is after 100? Does it ever end? At night I looked at the stars and wondered what's behind the star etc. etc. I was trying to understand infinity. A real shock came 12/7/1941, Pearl Harbor.

In 3rd grade I was very fortunate to have the greatest teacher in my learning career the one and only Miss Dancing. One day she asks the class, "does anyone know what 12×12 is?" I answered 144 and she said that was wonderful. It was one of the happiest moments of my life. She took me aside one day and told me a story of this brilliant kid, Karl Fred Gauss (he lived when George Washington was alive) who amazed the teacher with the following problem. His 3rd grade class had misbehaved and the students had to come in after school and add the numbers from 1 to 99. In order to show me what he did, Miss Dancing prepared me by looking at a simple problem: adding up the numbers from 1 to 9

1+9=10=5+5

2+8=10=5+5

3+7=10=5+5

4+6=10=5+5

5=5=5

We have now replaced all the numbers from 1-9 with a 5, therefore we have 9 5's= 9X5= 45

In other words, he changed an addition problem to a multiplication problem. Now we are prepared to add the numbers from 1-99.

1+2+3+4......96+97+98+99

1+99=100=50+50

2+98=100=50+50

3+97=100=50+50

4+96=50+50

He replaced each number by 50, therefore we have 99 50's=99X50= 4950. He changed a long addition problem into a multiplication problem. Obviously the teacher was amazed at the 3rd graders brilliance, wow!

Problems for the Reader: All solutions are at the end of each Chapter

Add all the numbers from 1-49

Add all the odd numbers from 1-99

Add all the even numbers from 1-99

Add the first 20 [5, 10, 15, 20, 25, 30 ...]

What is the 100th term?

Another problem Miss Dancing showed me was squaring numbers ending with 5.

Example:

25×25= 625 5×5 = 25; 3×2 = 6; = 625

35×35= 1225 5×5 = 25; 4×3 = 12; = 1225

65×65= 4225 5×5 = 25; 7×6 = 42; = 4225

85×85= 7225 5×5 = 25; 9×8 = 72; = 7225

Do you see what she did? I really enjoyed this problem.

A story comes to mind of a non math lesson she taught me. There was a girl, Roberta, who sat next to me that I had a crush on. I couldn't let any of the boys know about this because they would call me a sissy. One day I gave Roberta an ice cream cone that held two scoops. She was very impressed and mentioned to me that she is rooting for me to win the class president election. I was running against a very popular student and I knew I couldn't win. But I wanted to win this election and show Roberta what a big shot I was. I asked myself how can I win and I came up with an idea that I would give each student who voted for me a free comic book. Miss Dancing found out about my scheme and told me that this was wrong (she used the word bribery-I never heard that word before). Well if Miss Dancing said it was wrong then it was wrong. I took back the offer and lost the election. It was a bitter blow. Fifteen years later I met Roberta again and she was not anywhere as charming as she was in 3rd grade.

In 4th grade I had the mean spirited of Miss Fry. As much as I loved Miss Dancing, Miss Fry was no joy. One day she put the following problems on the board: 6 ÷ ½ = 6 × 2 = 12, 6 ÷ 2/3= 6 × 3/2 = 9. I asked her what gives you the right to do that. She repeated invert and multiply. I asked her again why that does work. She was annoyed and said, "Just do it". For the next two hours I worked on this problem, I was thrilled when I uncovered the mystery. Teachers like Miss Fry should not be teaching, she was more suited to be a prison guard.

When I have 13½, I had the good luck to work with Irving Yano, who owned a very popular grocery store (this was before the big supermarkets). My job was to wait on customers, deliver orders and everyday have a math puzzle for him. Irving was a big husky man, a Russian immigrant who barely had an education in Russia but he loved math. Irving was a great story teller; he had an excellent sense of humor. His grocery store was so popular because of his compelling personality. This was a real fun job and I couldn't wait to get to my job after school. I can see him now with a sugar cube in his mouth drinking tea. Every day he was eager to get his math problem and find out what I did in math and science.

Irving had several vices which were real eye openers for a 14 year old. Every day Al, the bookie, had a card game in the back of the store. It was common knowledge that Al sold untaxed liquor and had connections with some of the criminal elements. Al was 45 year old, a very likeable man but unbelievably he was a real momma's boy, who lived with his widowed mother. He jumped when mom gave an order. Irving, Al and Dr. Hess were all good friends, they told their family they were playing cards Wednesday nights, but they were not playing cards, they were involved in a different type of entertainment which didn't come up to standards of good family men.

One of Irving's favorite problems was the 12 coin problem. The problem goes like this. You have a balance scale and 12 coins. One of the coins had a different weight then the 11 good ones. In 3 balance scale you are to be about to find the bad coin. Irving told me only two of his friends could solve the problem I and was intensely pleased to receive Irving's congratulations when I solved it.

Can you solve the 12 coin problem? It is not easy but doable. *Hint*- you can move the weights from one side to the other side of the scale. Call the coins A₁, A₂, A₃, B₁, B₂, B₃, B₄, C₁, C₂, C₃, C₄ at weighing #1 weigh A₁, A₂, A₃, A₄ Vs. B₁, B₂, B₃, B₄.

Another problem that Irving gave me and I solved was the four- 4's problem. Using four 4's write all the numbers from 1-22. Using +, -, ×, ÷, .4, &radius;4. Note; you must use all four 4's.

For example: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Irving was somewhat familiar with algebra and some of the laws of physics using the language of science, algebra. Irving stressed again and again, look for patterns. I was able to generate many problems using simple algebra. For example:

X 1 2 3 5 10

Y 2 4 6 10 20

Y=2X

X 1 2 3 5 10

Y 6 7 8 10 15

Y=X + 5

X 1 2 3 5 10

Y 3 5 7 12 22

Y= 2X + 1

X 1 2 3 5 10

Y 1 4 9 25 100

Y=X²

Then I gave more difficult patterns:

X 1 2 3 4 5 6 10

Y 0 2 6 12 20 30 90

Y=X²-X

X 1 2 3 4 5 6 10

Y 1 8 27 64 125 216 1000

Y=X³

X 1 2 3 4 5 6 7 10

Y -1 1 -1 1 -1 1 -1 1

Y=(-1)^X

X 1 2 3 4 5 6

Y 2 -2 2 -2 2 -2

Y=2(-1)^x+1

I was able to come up with many combinations using X and Y. It often led to important scientific concepts. For example:

T 0 1 2 3 4 5 6 10

S 0 2 8 18 32 50 72 200

S=2T²

It just so happens on the moon objects drop 2 feet in 1 second, 8 feet in 2 seconds, 18 feet in 3 seconds. In other words, we have a formula for falling objects on the moon.

Irving was quite taken with Einstein's E= mc². This simple equation shows the relationship of mass and energy. He would point to a crumb and say this little crumb has enormous energy. I pointed out a lot of things take on the form y=kx². For example, take Galileo's famous equation for falling objects on the planet earth; s=16t². In one second an object falls 16 feet. When t=2, s= 64 feet. When t=3, s= 144 feet.

Irving was familiar with the inverse relationship. Note as X gets bigger, y gets smaller. y= 24/x

But he was not familiar with the inverse square concept. This is a more difficult concept. As x is doubled, y is divided by 4, as X is tripled, y is divided by 9.

y= 24/x²

He was very excited when I showed him some of the most important ideas in science. The Law of Gravity: G m₁m₂/r²

In other words we can calculate the force of attraction between the earth and the sun, the earth and the moon, the sun and the moon. Both of us agreed how extraordinary it was that man can uncover the secrets of nature that follows such simple formulas. We had many philosophical discussions on how God let us in on his plan. As you can see this was more than just a fun job. God let man into the inner sanctuary of his/her domain. E = mc² x C 186,000 miles a second and [186,000]² implied that even his cube of sugar had so much energy. We both agreed it was almost as if man had a direct connection with God. There is order in the universe and man has a chance to uncover these secrets. At the time I had the most philosophical discussions I ever had. Irving stressed again and again to look for patterns. This idea really stuck with me. Newtons equation for gravity had a profound effect on me at age 14. Sixty years later I wrote the following memorable Valentine's card to my wife on February 14, 2010:

Dear Mary Anne,

There are two great mysteries of life: gravity and love. We know how each feels bu we can't explain how they work. For gravity, there is a formula which shows the relationship between the apple and the stars. For love, there is no such formula, but I an in your gravitational field which I feel every day in every way. Love, Werner

When I was 14½ years old, there was an incident in the store which I will never forget. A very nice man, Fred, used to deliver supplies to the store every Wednesday. One Wednesday, there was a substitute for Fred who made deliveries. None of us knew that this was his 2nd week out from prison and he was not making a good adjustment to his unfamiliar surroundings. He came in with his hook moving boxes around and showing complete disregard for Irving's costumers. Irving took exception and told this man not to mistreat his customers. A big argument developed and matters were clearly getting closer and closer to violence. The man threatened him with his hook and Irving who never backed off from a fight broke a large bottle of beer exposing the jagged edges. I had to do something and I was scared out of my wits. I stepped in between the two men and said, "Gentlemen I am sure this problem can be solved." My peacemaking effort had been ignored and the men were cursing and threatening each other. It was clear to everyone this was a very dangerous situation. Finally I said today is Sunday and you men should not be fighting on a Sunday. This broke the ice because it was a Wednesday and not a Sunday, and it was clear I was beside myself to keep the peace. I told the man I would bring in the delivery and everyone should calm down. Irving had enough sense to back off and let me take in the delivery without a hook. I know Irving was grateful to me for de-escalating this life threatening situation.

In 1952 Irving informed me that in his opinion the neighborhood was changing and a little grocery store would be replaced by supermarkets. He bought a supermarket in an up and coming neighborhood and he prospered financially but unfortunately the story does not have a happy ending. He had a son Lester who caused a lot of trouble in school. Teachers sent notes home about his unacceptable behavior in school. I urged Irving to give this matter careful consideration and discipline his son. It was Irving's opinion that's the way boys behave. In 1955, Lester got in big trouble getting involved in an armed robbery in Athens, Georgia. Irving was heartbroken and in four months he died of a heart attack. Irving treated me like a son and I lost one of my big heroes.

I had a lot of interesting different jobs which were more fun than school. Unfortunately I didn't have much time for homework and it negatively impacted my grades. One of my little jobs was working for Mr. Eggenhaus who had a linoleum and rug business. One of my jobs was to take measurements in people's homes to determine how many square yards were needed. One very memorable experience was when Mr. Eggenhaus sold a very large roll of linoleum (which had already been partially cut). He didn't know its area so he considered rolling the piece down Broadway to get the measurement. I told him I could calculate the area without unrolling this huge piece. He said that was impossible but I assured him I could do it. Here is what I did: I found the outside and inside radius, took the average, multiplied the average by the radius × height 6' × 2π R [the number of rings]÷ 9 and came up with the answer. He asked me to double check and I told him I was positive. He thought I was a genius when in reality it was not a hard problem.

At 15 another one of my jobs was to tutor math where I was paid $3.50 an hour. I tutored Susan, Dr. Hess's daughter. I was given the task to help Susan pass the geometry regents. She was not a bad student but she really disliked math and did as little work as possible. I tried very hard to direct her to her studies, but she had other ideas. In the middle of the lesson she wanted to practice her romantic skills with me. Net result, we spent half our lessons on things other than math. I felt a little guilty of accepting $3.50 an hour for these romantic adventures.

A real tough case was the Prystowsky family. I was very friendly with Seymour and he always complained how his mother was always on his back about school. The Prystowskys were a Russian immigrant family and Mrs. Prystowsky wanted in the worst way to set her High School Diploma. One thing stood in her way she had to pass the geometry regency. She took the regency 2 years ago and she got an 18. The next year she took it again and she got a 24. I had the reputation in the neighborhood as being a miracle worker in helping students pass math. She told me she was desperate and she will put herself in my hands. She was a very hard working highly motivated; her favorite expression was "Education comes first in this house". Unfortunately she had lost complete confidence in her math skills and she had unbelievably little talent in math. She asked me, "Do you think you can do something with me." I lied to her and said yes I can get her to pass the exam. This was a real challenge. I designed a plan for her who was to concentrate on calculation and bypass the formal proofs. To get her confidence back I gave very easy problems which she solved. It was my plan to give her feeling that she had a real chance of passing.

Euclid would not have approved of my method but Mrs. Prystowsky was thrilled to get a 72 on the regency and she got her High School Diploma. Her son Seymour complained a lot about his oppressive mother, but Seymour is now a very successful doctor.

Answers Chapter I Tests

1 to 49

1 + 2...48 + 49

replace each number by 25

25×49 = 1225

Sum of the odd numbers to 100

1 + 3 + 5 + 7 ... 97 + 99

replace each number by 50 (there are 50 numbers) 50×50 = 2500

Sum of the even numbers to 100

2 + 4 + 6 ... 98

replace each number by 50 (there are 49 even numbers)

50×49 = 2450

Sum of all numbers divisible by 5 to 100

5, 10 ... 95, 100

replace each number by 50.5

(50.5)(20) = 1010

500

12 coin problem A₁, A₂, A₃, B₁, B₂, B₃, B₄, C₁, C₂, C₃, C₄

Weighing I: A₁, A₂, A₃ Vs. B₁, B₂, B₃, B₄ if they balance then one of the C's is odd coin. If a side goes down, then either one of A's is heavy or one of B's is light. If a side goes down place A₂ B₂ aside.

Weighing II: [TEXT NOT REPRODUCIBLE IN ASCII.]

You should now be able to finish.

4-4 Problem

At the end of each chapter, I would like to present a little surprise that has little to do with math. Here are three of my favorite works of art.

The Luncheon of the Boat Party By Renoir

2. The Great Wave Off Kanagawa

By Hokusai (1831)

3. Potato Eaters By Van Gogh

Chapter Two

FOR THOSE WHO HATE MATH

Do math and computers make you unhappy?

YOU ARE NOT ALONE

In 2008, I wrote this book called Math Fun for Everyone. It was filled with exciting problems, puzzles, and aspects of math which I thought would appeal to a broad base of the population. My wife looked over my first try at this book and told me if I was serious about having this book accepted, it would have to be more appealing to a broader base than just math nerds. I have learned again and again to listen to my wife. I have lightened up on some of the math and mixed in stories that are tangentially involved with math.

The net change has markedly improved this book.

In my opinion, Chapter Two will prove to be one of the all-time most exciting and adventurous chapters in your reading history. I will start with ten little stories.

November 10, 1938

I was a two-and-a-half year old living in Germany when Crystal Night occurred. All over Germany, Jewish shops and synagogues were set on fire. Germany was a very dangerous place for Jewish people to be. On November 11, 1938, Kate Smith introduced and sang Irving Berlin's "God Bless America," for the first time.

In February 1939, this blessed country saved our lives by opening its doors to us. This one short song so captures my feelings for America.

While the storm clouds gather far across the sea, Let us swear allegiance to a land that's free, Let us all be grateful for a land so fair, As we raise our voices in a solemn prayer

God Bless America, Land that I love, Stand beside her and guide her Thru the night with a light from above;

From the mountains, to the prairies, To the oceans white with foam, God bless America, My home, sweet home. God bless America, My home, sweet home.

I was so moved by this song that in high school, I would argue with English teachers that the lyrics of this song is poetry of the highest order. I still feel that the Gettysburg Address, Declaration of Independence contain poetry that far surpasses the poetry that so many English teachers cherish.

Mr. Eggenhaus story

On July 3, 1951, three interesting things happened to me within a two day period. Mr. Eggenhaus, who owned a linoleum and rug store, presented me with a problem. He had a big roll of linoleum and it was important for him to find the area. He asked me if it was possible to calculate the area without having to roll open the piece down Broadway.

I told him I was fairly certain he could calculate the area without having to open it up. Here is what I did. The inside radius of the linoleum roll was two inches, and the outside radius was ten inches, and there were 36 rings in the roll. The average radius was six inches (0.5 feet). The area of the linoleum roll was 2× ×0.5, which I then multiplied by the height of the roll (6 feet), and then again by 36 to account for each ring. I divided by 9 to determine the area in square yards, and found out that this linoleum roll had an area of approximately 75 square yards. Mr. Eggenhaus thought I was a genius but in reality, it wasn't a very hard problem.

(Continues...)

Excerpted from Math Fun for Everyoneby Werner Weingartner Copyright © 2012 by Werner Weingartner. Excerpted by permission of iUniverse, Inc.. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.