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