# High School Math

MISSION STATEMENT: To encourage and promote a greater use of the internet and computer technology in the math classroom. For educators, students, parents and homeschoolers.

## Thursday, June 22, 2006

### Secret Word

When in the Course of human Events, it becomes necessary for one People to dissolve the Political Bands which have connected them with another, and to assume, among the Powers of the Earth, the separate and equal Station to which the Laws of Nature and of Nature's God entitle them, a descent Respect to the Opinions of Mankind requires that they should declare the causes which impel them to the Separation.

Printed above is the first paragraph of the U.S. Declaration
of Independence. Select any one of the first 20 words. Count the letters and call that number n. Move ahead n words, beginning with the word after your selected word. When you reach that nth word, count its letters and move ahead as many words as the new letter count. Continue in this manner, counting letters and moving ahead words, until you stop on a word that's beyond the fourth line.
On what word did you stop? Magic created by Martin Gardner.

Your word is posted in the Subscriber Area at www.TheMathWebSite.com.
To enter the Subscriber Area, click on the Enter Link at the bottom of
the Index of Topics page. To subscribe, simply enter your email address. Your password will be emailled to you.

### Magic 8

Multiply your phone number, a seven-digit number
(no area code) by the number 8.
Then write down the following three numbers:
(i) your phone number,
(ii) the number 8,
(iii) the product of your phone number times 8.
Add up the numeric values all the individual digits in those three numbers. If the sum is more than one digit, take that sum and add up its digits. Continue adding up digits until only one digit is left.
What is that single digit? Magic created by Martin Gardner.

Your number is posted in the Subscriber Area at www.TheMathWebSite.com.
To enter the Subscriber Area, click on the Enter Link at the bottom of
the Index of Topics page. To subscribe, simply enter your email address. Your password will be emailled to you.

### Number Names

Think of any number from 1 through 100. (Say 10)
Write down its name. (ten)
Count the number of letters in its name to obtain a second number. (3 letters)
Count the number of letters in the second number to obtain a third number. (three,5 letters)
Continue in this way until the chain of numbers ends on a number that keeps repeating.
What is the final repeating number? Magic created by Martin Gardner.

Your number is posted in the Subscriber Area at www.TheMathWebSite.com.
To enter the Subscriber Area, click on the Enter Link at the bottom of
the Index of Topics page. To subscribe, simply enter your email address. Your password will be emailled to you.

### Remarkable Number

Enter 999999 into your calculator.
Divide the above number by seven.
The result will be a mysterious number!
Throw a die, or randomly pick a number from 1 to 6.
Multiply the result times the mysterious number.
Arrange the digits of the product from lowest to highest from left to right to form a six-digit number.
What is the number? Magic created by Martin Gardner.

Your number is posted in the Subscriber Area at www.TheMathWebSite.com.
To enter the Subscriber Area, click on the Enter Link at the bottom of
the Index of Topics page. To subscribe, simply enter your email address. Your password will be emailled to you.

### Magic Number

Write down any 3-digit number. (Let's say, 276)
Write it down again beside itself. (This means 276276)
Divide that result by 7. (Answer is 39468)
Divide that result by 11. (Answer is 3588)
Divide that result by 13. (Answer is 276, the original number)
Why does this happen?
Writing a 3-digit number beside itself is equivalent to multiplying it by 1001 because 1001 = 7 x 11 x 13. So, all that is being done by dividing the large number by 7, 11 and 13, is to return it to the original 3-digit number.

More Magic at www.TheMathWebSite.com.

### Tautonymic Numbers

A Tautonymic number is one which can be broken into two equal non-palindromic halves
and with each part having at least two different digits.
Examples of tautonymic numbers are 5656, 2525, 3737, 4141, 165165, 34723472 etc..

How many bygone tautonymic years can you write down?

More Numbers at www.TheMathWebSite.com.

### Tetradic Numbers

A Tetradic Number is one which is both strobogrammatic and palindromic in nature. It is the same when viewed from left to right, right to left, top to bottom or upside down. This four-way symmetry explains the name, tetra- being the greek prefix for four.
The only digits that can be found in a tetradic number are 0, 1 and 8, since although matched pairs of 6 and 9 can be used in strobogrammatic numbers, they won't yield a palindrome. Thus the first few tetradic numbers are 0,1,8,11,88,101.
Given a tetradic number, a larger one can always be generated by adding another tetradic number to each end, retaining the symmetry. There are tetradic primes, the first half dozen being 11, 101, 181, 18181, 1008001, and 1180811.

More Numbers at www.TheMathWebSite.com.

### Strobogrammatic Numbers

A Strobogrammatic Number is a number that appears the same whether viewed normally or upside down. In base 10, given that 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down, the first few strobogrammatic numbers are:
1, 8, 11, 69, 88, 96, 101,
111, 181, 609, 619, 689, 808,
818, 888, 906, 916, 986, 1001

What years are strobogrammatic?

More Numbers at www.TheMathWebSite.com.

### Kaprekar Number

The Kaprekar Number is 6174.
(1) Take any four-digit number.
(2) Form the largest and the smallest numbers from these four digits.
(3) Find the difference between those digits. Maybe this is 6174.
If it is not, form the largest and the smallest number from the difference and subtract these numbers again. You may have to repeat this procedure.
The end result is always 6174, with no more than 7 steps.

Take the number 3546.
1st step: 6543 - 3456 = 3087
2nd step: 8730 - 0378 = 8352
3rd step: 8532 - 2358 = 6174

Take the number 5184.
1st step: 8541 - 1458 = 7083
2nd step: 8730 - 0378 = 8532
3rd step: 8532 - 2358 = 6174

More Numbers at www.TheMathWebSite.com.

### Josephus Problem

The Classic Josephus Problem :
X people stand in a circle. An extra person goes round the circle eliminating every Yth person. When the start of the circle is reached, we continue going round again, ignoring the people who have already been eliminated, and still eliminating every Yth person.
The Problem : Given the values of X and Y, where should you stand in the circle so that you will be the last to be eliminated?

More Problems at www.TheMathWebSite.com.

## Monday, June 12, 2006

### Math Phrases

Common Phrases Used in Math Class -
FINALLY: Only a few more steps to go...
Q.E.D. : Quite easily done.
PROOF OMITTED: Trust me, it's true.
ONE MAY SHOW: I will leave it to you to prove this.
SIMILARLY: Most of this proof is the same as before.
CLEARLY: I don't want to write down all the in-between steps.
TWO LINE PROOF: I'll leave out everything but the conclusion.
TRIVIAL: If I have to show you this, you're in the wrong class.
OBVIOUSLY: I hope you weren't asleep, because I refuse to repeat it.
RECALL: I shouldn't really have to tell you this, but here it is again.
WITHOUT LOSS OF GENERALITY: I did one case, so now you figure out the rest.
IT IS WELL KNOWN: Don't embarrass yourself by asking any questions about this.
CHECK FOR YOURSELF: This is boring, so you can do it on your own time.
BRUTE FORCE: If you understand this overblown proof, then you are really good.
ELEGANT PROOF: Above your head, and less than six lines long.
THESE ARE EQUIVALENT: Since this shows that, and that shows this, then the other thing must also be correct.
BY A PREVIOUS THEOREM: I forgot how it goes, but I'm sure this is right.
BRIEFLY: I'm running out of time, so I'll just write and talk faster.
LET'S TALK IT THROUGH: I don't really want to write it on the board
because I might make a mistake.
PROCEED FORMALLY: Manipulate symbols randomly with confusing explanations.
QUANTIFY: I can't find anything wrong with your proof
except that it doesn't work.

More Math Stuff at www.TheMathWebSite.com.

## Sunday, June 04, 2006

### Galileo

Galileo Galilei was born on February 15, 1564 in Pisa, Italy. He was the first to use a refracting telescope to make important astronomical discoveries.
In 1609 Galileo learned of the invention of the telescope in Holland. From the barest description he constructed a vastly superior model. Galileo made a series of profound discoveries using his new telescope, including the moons of the planet Jupiter and the phases of the planet Venus.
As a professor of astronomy at University of Pisa, Galileo taught the accepted theory of his time that the sun and all the planets revolved around the Earth. Later at University of Padua he was exposed to a new theory, proposed by Copernicus, that the Earth and all the other planets revolved around the sun. Galileo's observations with his new telescope convinced him of the truth of Copernicus's sun-centered or heliocentric theory.
Galileo's support for the heliocentric theory got him into trouble with the Roman Catholic Church. In 1633 the Inquisition convicted him of heresy and forced him to recant his support of Copernicus. They sentenced him to life imprisonment, but because of his advanced age allowed him serve his term under house arrest at his villa outside of Florence, Italy.

More Biographies at www.TheMathWebSite.com.

### Copernicus

Nicolas Copernicus is the founder of modern astronomy. He was born in Poland, and went to Cracow University to study mathematics and optics. Later was appointed as a canon in the cathedral of Frauenburg where he spent a sheltered and academic life for the rest of his days. His interest in astronomy gradually grew to be one in which he had a primary interest. He made his celestial observations from a turret situated on the protective wall around the cathedral, one hundred years before the invention of the telescope.
In 1530, Copernicus asserted that the earth rotated on its axis once daily and traveled around the sun once yearly: a fantastic concept for the times.
Copernicus was in no hurry to publish his theory, though parts of his work were circulated among a few of the astronomers that were giving the matter some thought. Copernicus was reluctant to publish, -- not so much that he was concerned with what the church might say about his novel theory, but rather because he was a perfectionist and he never thought, even after working on it for thirty years, that his complete work was ready.
Copernicus' original manuscript, lost to the world for 300 years, was located in Prague in the middle of the 19th century. Copernicus died in 1543 and was never to know what a stir his work had caused. It went against the philosophical and religious beliefs that had been held during the medieval times. Copernicus' theories might well lead men to think that they are simply part of nature and not superior to it and that ran counter to the theories of the politically powerful churchmen of the time.
Galileo embraced the Copernican theory unreservedly and as a result suffered much personal injury at the hands of the powerful church inquisitors. The most important aspect of Copernicus' work is that it forever changed the place of man in the cosmos.

More Biographies at www.TheMathWebSite.com.

### Number 8

9 x 9 + 7 = 88
9 x 98 + 6 = 888
9 x 987 + 5 = 8888
9 x 9876 + 4 = 88888
9 x 98765 + 3 = 888888
9 x 987654 + 2 = 8888888
9 x 9876543 + 1 = 88888888
9 x 98765432 + 0 = 888888888.

More Patterns at www.TheMathWebSite.com.

### Weird Numbers

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

More Puzzles at www.TheMathWebSite.com.

### Curious Numbers

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321

12345679 x 9 = 111 111 111
12345679 x 8 = 98765432

More Numbers Stuff at www.TheMathWebSite.com.

## Thursday, June 01, 2006

### Numerology

Calculate Your Numerology Number
1=A,J,S 2=B,K,T 3=C,L,U
4=D,M,V 5=E,N,W 6=F,O,X
7=G,P,Y 8=H,Q,Z 9=I,R

Personality Characteristics
1 = ambitious, independent, and self-sufficient.
2 = supportive, diplomatic, and analytical.
3 = enthusiastic, optimistic, and fun-loving.
4 = practical, traditional, and serious.
5 = adventurous, mercurial, and sensual.
6 = responsible, careful, and domestic.
7 = spiritual, eccentric, and a bit of a loner.
8 = money-oriented, decisive, and stern.
9 = multi-talented, compassionate, and global.

To Find Your Number Add Values of Letters of Your Name
If your name is Tom, your number is 2+6+4=12 and 1+2= 3
And you are enthusiastic, optimistic, and fun-loving.
If your name is Helen, your number is 8+5+3+5+5=25 and 2+5= 7
And you are spiritual, eccentric, and a bit of a loner.

More Amusements at www.TheMathWebSite.com.

### Baking

1)Mother bought three different types of apples.
2)She made 3 items - pies, muffins and tarts.
3)She used only one type of apple in each item.
4)She added raisins, pecans, or walnuts to one item.
5)The pies did not contain any nuts.
6)Cortland apples were used in the muffins.
7)The McIntosh apples were mainly red.
8)The raisins tasted great with the McIntosh apples.
9)The walnuts were not in the muffins.
10)The tarts were made with multigrain flour.
11)The pies were not made from the Empire apples.
Which apple and which ingredient went into each item?

The answer is posted in the Subscriber Area at www.TheMathWebSite.com. To enter the Subscriber Area, click on Enter Subscriber Area at the bottom of the Index of Topics page. To subscribe, simply enter your email address. Your password will be emailled to you.