PI

And things it concerns

What is pi?

• Here are two different dictionary definition of pi : the ratio of the circumference to the diameter of a circle; approximately equal to 3.14159265358979323846...

• Pi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.14159…

How was pi started?

• Historians guess that around 2000 B.C. humans noticed that the ratio of circumference to diameter was the same for all circles. This discovery was based on the idea of proportion. Humans also noticed that if you double the distance across a circle, then you double the distance around it. In today's algebraic notation this implied the formula

where Pi is constant

Image of what the last side was talking about

 

                                                         

       

Why do we need pi?

• The importance of the discovery is: Circles are everywhere - in the sun, the moon, the pupils of our eyes, the most basic shapes and the earliest man-made structures. Coming up with a greater mathematical understanding of Pi would lead to scientific and technological advances. Which would help to further the development of civilization, and also create some very interesting problems in pure math.

• But one problem remained - what is the numerical value of Pi?

 

• Here are a few images showing the numerical value of pi

But one problem was left - what is the numerical value of Pi?

Person/People Year ValueBabylonians ~2000 B.C. 3 1/8Egyptians ~2000 B.C. (16/9)^2= 3.1605Chinese ~1200 B.C. 3Old Testament ~550 B.C. 3Archimedes ~300 B.C. proves 3 10/71<Pi<3 1/7Ptolemy ~200 A.D. 377/120=3.14166...Chung Huing ~300 A.D. sqrt(10)=3.16...Wang Fau 263 A.D. 157/50=3.14Tsu Chung-Chi ~500 A.D. proves 3.1415926<Pi<3.1415929Aryabhatta ~500 3.1416Brahmagupta ~600 sqrt(10)

Graph I created on Microsoft Excel to display the gradual change and development of pi

Graph cont.

Fibonacci 1220 3.141818

Ludolph van Ceulen 1596 Calculates Pi to 35 decimal places

Machin 1706 100 decimal places

Lambert 1766 Proves Pi is irrational

Richter 1855 500 decimal places

Lindeman 1882 Proves Pi is transcendental

Ferguson 1947 808 decimal places

Pegasus Computer 1957 7,840 decimal places

IBM 7090 1961 100,000 decimal places

CDC 6600 1967 500,000 decimal places

Important people in the discovery of pi

• François Viète was a French amateur mathematician and astronomer who introduced the first systematic algebraic notation in his book In artem analyticam isagoge . He was also involved in deciphering codes.

• François Viète (1540-1603) determined that:

Cont.

• John Wallis was an English mathematician who built on Cavalieri's method of indivisibles to devise a method of interpolation. Using Kepler's concept of continuity he discovered methods to evaluate integrals.

• John Wallis (1616-1703) showed that:

Cont.

• Leonhard Euler was a Swiss mathematician who made enormous contibutions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory.

• Leonhard Euler (1707-1783) derived his famous formula:

Facts about pi

• Pi is a mathematical term

• Pi is an infinite number that will never stop

• Pi has an official symbol which is

• Pi has its own day

• Pi has been studied and improved upon over many years

My opinions on pi

• Pi is an incredibly important discovery in mathematics today and in the past.

• I think it is great that pi has it own official holiday although few people know about it is still important and should continue to have its own day.

• Pi is a huge number that personally blows my mind and its also great.

Pi pictures

Celebratory pi day video

• http://www.youtube.com/watch?v=NBqVvAU-gdg&NR=1

Cartoon to celebrate pi day

Happy pi day

• Mrs. Smith is my favorite teacher ever and I wish you luck with your baby.

By: Jesse Matthews

Work sited page

• http://mathforum.org/isaac/problems/pi2.html• http://www.angio.net/pi/piquery• http://www.newton.dep.anl.gov/askasci/

math99/math99010.htm• http://www.iit.edu/~smile/ma9709.html• http://www.book-of-thoth.com/archives-article-

7390.html• http://mathforum.org/isc/problems/pi1.html• http://answers.yahoo.com/question/index?

qid=20080226020909AAPDiqZ