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#### Pi Approximation Day

#### Jul 22

#### Other Scottish Country Dances for this Day

#### Today's Musings, History & Folklore

"So here we have pi squared, which an engineer would call 10." – Frank King

Ouch! Pi approximation day, July 22 or 22/7 is for those who write the date in the day/month format and is another one of the fun days recognized by mathematics students and teachers in addition to March 14, 3/14 (for those partial to the month/day format), both relating to approximations of the most well known of irrational constants, pi, the ratio of a circle's circumference to its diameter. Pi has been calculated with great precision by many different methods since ancient times. However, one of the more infamous stories surrounding the value of pi has to do with the notorious Indiana Pi Bill of 1897 which attempted to legislate the value of pi (incorrectly). Entitled "A Bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the Legislature of 1897". The main result claimed by the proposed bill utilizes a faulty method to "square the circle," an ancient unsolvable classical problem. Amateur mathematician Edward J. Goodwin, used this method to imply various incorrect values of π, such as 3.2! Due to the intervention of Professor C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote, this bill did not become law. Thanks, professor! Celebrate significant figures and contribute to your own with a piece of pie! 🥧

#### The Mathematicians

Today is Pi Approximation Day or Casual Pi Day!

One of the most widely recognized mathematical constants, π, is an irrational number, the digits of which repeat in a random fashion and are never ending.

Pi denotes the relationship between a circle’s circumference and its diameter and is denoted by the fraction 22/7 which calculates approximately to 3.14. This fraction is often used for rough calculations particularly by students in the early years.

Pi has been calculated with great precision by many different methods: using polygons (Ancient Greeks), using infinite series, etc ... .

However, one of the more infamous stories surrounding the value of pi has to do with the notorious Indiana Pi Bill which attempted to legislate the value of pi (incorrectly).

The bill was titled "A Bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the Legislature of 1897".

Despite its name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π, the ratio of the circumference of a circle to its diameter. The bill, written by amateur mathematician Edward J. Goodwin, does imply various incorrect values of π, such as 3.2.

The bill never became law, due to the intervention of Professor C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote.

The impossibility of squaring the circle using only compass and straightedge constructions, suspected since ancient times, was rigorously proven in 1882 by Ferdinand von Lindemann. Better approximations of π than those implied by the bill have been known since ancient times.

To learn more about pi, click the cartoon!