Happy Pi Day!

Post Reply New Topic

"Pi Day" - an annual celebration commemorating the mathematical constant π (pi). Pi Day is observed on March 14 (or 3/14 in month/day date format), since 3, 1 and 4 are the three most significant digits of π in the decimal form. In 2009, the United States House of Representatives supported the designation of Pi Day.

"Pi Approximation Day" is observed on July 22 (or 22/7 in day/month date format), since the fraction 22⁄7 is a common approximation of π.

Single-precision approximation is all that is needed for most terrestrial calculations: 3.141,593 (this will get you within a few meters of your departure point on a trip around the world.)

Double-precision approximation is used in the Global Positioning System (GPS): 3.141,592,653,589,793 (this will get you within a few micrometers.)

The approximation of π = 3.141,592,653,589,793,238,462,643,383,279,502,884 uses a level of precision that is appropriate only for objects below the theoretical Planck Radius of 1.616199(97)×10−35 meters.

History

~1750 B.C.: (Approximate Year) A Babylonian clay tablet has a geometrical statement that, by implication, treats Pi as 25/8 = 3.1250. This is correct to within ~99.472%.

~560 B.C.: (Approximate Year) An unidentified Biblical author implies that the value of Pi is exactly 3 (in 1st Kings, Chapter 7, Verse 23). The error of this value is more than 4.5 percent.

434 B.C.: The first recorded attempt to determine the value of Pi by "Squaring the Circle" with a compass and straightedge by the Greek mathematician Anaxagoras.

~0250 B.C.: (Approximate Year) In "Measurement of the Circle", Archimedes gives an approximation of the value of Pi with a method which will allow improved approximations.

~150 A.D.: (Approximate Year) Rabbi Nehemiah explains in his early work of geometry, the "Mishnat ha-Middot", that the value of Pi is three and one-seventh (~3.142857), which is correct to two decimal places (~99.9598%).

263 A.D.: By using a regular polygon with 192 sides, Liu Hui calculates the value of Pi as 3.14159 which is correct to five decimal places (99.999%).

~460 A.D.: (Approximate Year) Zu Chongzhi gives the approximation 355/113 to Pi which is correct to 6 decimal places (99.9999%).

1400 A.D.: Madhava of Sangamagramma proves a number of results about infinite sums giving Taylor expansions of trigonometric functions. He uses these to find an approximation for Pi correct to 11 decimal places (99.999999999%).

1593 A.D.: Van Roomen calculates Pi correctly to 16 decimal places.

1706 A.D.: Jones introduces the Greek letter Pi ("π") to represent the ratio of the circumference of a circle to its diameter in his “Synopsis Palmariorum Matheseos” (“A New Introduction to Mathematics”).

1748 A.D.: Euler publishes Analysis Infinitorum ("Analysis of the Infinite") which is an introduction to mathematical analysis. He defines a function and says that mathematical analysis is the study of functions. This work bases the calculus on the theory of elementary functions rather than on geometric curves, as had been done previously. The famous formula e x π = -1 appears for the first time in this text.

1761 A.D.: Lambert proves that Pi is irrational (e.g., it can not be expressed as the ratio of two integer numbers). He publishes a more general result in 1768.

1853 A.D.: Shanks gives Pi to 527 decimal places.

1882 A.D: Lindemann proves that Pi is transcendental. This proves that it is impossible to construct a square with the same area as a given circle using a ruler and compass. The classic mathematical problem of "Squaring the Circle" dates back to ancient Greece and had proved a driving force for mathematical ideas through many centuries.

1946 A.D.: D. F. Ferguson, using a desk calculator, calculates Pi to 620 decimal places.

From this time forward, calculating machines take over, and the resolution of the value of Pi has been accurately calculated to well beyond 10,000,000,000,000 decimal places.

Happy Pi Day!

Hey man, thanks for that cool post!!

That formula is not right, it should be exp(i·π) = -1. But the post is still very cool!!

Good catch!

In analytical mathematics, Euler's Identity (also known as Euler's Equation - named for the Swiss mathematician Leonhard Euler), is the equality:

e^(i x π) = -1

Where:

e is Euler's Number, the base of natural logarithms

i is the imaginary unit, which satisfies i^2 = −1

π is pi, the ratio of the circumference of a circle to its diameter

I've already used pi in 5 equations today! Thank you pi!

we live on a sphere. On a sphere pi is less than 3.14. It can be as small as 2.

ruveyn

[img][800:617]http://carlaspeaks.files.wordpress.com/2012/03/pi-pie5.jpg[/img]

On the surface of a sphere, Pi seems to be less than its accepted value, but only because the inner surface area of the circle isn't flat.

Nice trick, though!

also people could go out and see the movie Life of Pi today too. know its not a mathematical movie but its in the name.

Behold my avatar!

Very cool

Thank you.

We live on the surface. If you plan a route over the ocean do not use Euclidean geometry to get the best route.

ruveyn

Use the "Great Circle" route ... I learned this when my dad was in pilot's school.

You'd be amazed (maybe not) over the number of people who believe that the quickest way from Los Angeles to Japan is to head due west.

Happy Pi Day to all!

Many people don't have any remote understanding of fondamental law of physic like entropy... Many of them rule the planet. That explain a lot of things...