Happy Pi Day!!!

Hoyun Cho

1. What is pi (π)? Who first used pi? How do you find its value? What is it for? How many digits is it?
By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it. For the sake of usefulness people often need to approximate pi. For many purposes you can use 3.14159, which is really pretty good, but if you want a better approximation you can use a computer to get it. Here's pi to many more digits: 3.14159265358979323846.

The area of a circle is pi times the square of the length of the radius, or "pi r squared":
A = pi*r^2

2. A very brief history of pi
Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3; the Babylonians had an approximation of 3 1/8 (3.125), and the Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484), which is slightly less accurate and much harder to work with. For more, see A History of Pi by Petr Beckman (Dorset Press).

The modern symbol for pi [ ] was first used in our modern sense in 1706 by William Jones, who wrote:
There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to (16/5 - 4/239) - 1/3(16/5^3 - 4/239^3) + ... = 3.14159... = π
(see A History of Mathematical Notation by Florian Cajori).

Pi (rather than some other Greek letter like Alpha or Omega) was chosen as the letter to represent the number 3.141592... because the letter [π] in Greek, pronounced like our letter 'p', stands for 'perimeter'.

3. About Pi
Pi is an infinite decimal. Unlike numbers such as 3, 9.876, and 4.5, which have finitely many nonzero numbers to the right of the decimal place, pi has infinitely many numbers to the right of the decimal point.

If you write pi down in decimal form, the numbers to the right of the 0 never repeat in a pattern. Some infinite decimals do have patterns - for instance, the infinite decimal .3333333... has all 3's to the right of the decimal point, and in the number .123456789123456789123456789... the sequence 123456789 is repeated. However, although many mathematicians have tried to find it, no repeating pattern for pi has been discovered - in fact, in 1768 Johann Lambert proved that there cannot be any such repeating pattern.

As a number that cannot be written as a repeating decimal or a finite decimal (you can never get to the end of it) pi is irrational: it cannot be written as a fraction (the ratio of two integers).


pi=

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944

59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647

09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559

64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165

27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273

72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360

01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953

09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724

89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737

19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132

00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901



Pi in the Bible

This is a power point by Hoyun Cho.

Does God know π?


Rabbi Belaga presents the following explanation: The Hebrew word for line or circumference is written in the Bible as a 3 letter Hebrew word
transliterated as kaveh, and whose equivalent English letters are KVH (kof, vav, hei). Yet, that word is read as a 2 letter Hebrew word whose equivalent English letters are KV.

Hebrew letters have numerical values (Gematria), and the letters in question have values kof = 100, vav = 6, and hei = 5. So KVH = 100 + 6 + 5 = 111, and KV = 100 + 6 = 106. The ratio of KVH to KV is 111/106, which when multiplied by the value of 3 that was implied by 1 Kings 7:23, gives 3.141509 (rounded), which is again pretty close to π.

Originally found in http://www.math.ubc.ca/people/faculty/israel/bpi/bpi.html, but link no longer exists

Roy Dixon's Pie Crust

1 cup flour
1/2 tsp salt
1/3 cup shortening
2 tablespoons cold water


Apple Pie Filling

5 apples (peeled)
3/4 cup fine sugar
2 tablespoons all-purpose flour
1 teaspoon cinnamon
Read more at: http://www.foodnetwork.com/recipes/bobby-flay/apple-pie-recipe/index.html?oc=linkback

Blueberry Pie Filling

3/4 cup sugar
2 tablespoons cornstarch
1/2 teaspoon ground cinnamon
1/2 cup water
3 cups blueberries
1 tablespoon fresh lemon juice
Read more at: http://www.foodnetwork.com/recipes/all-american-festivals/country-blueberry-pie-recipe/index.html?oc=linkback


pi marriage counseling.jpg