07.22.2021
## Happy Pi Approximation DayJuly 22 Well, basically, it's just an excuse for mathematicians – particularly faculty members in university math departments – to get together, talk trash about the Tauist splinter group (more on that later), tell obscure math jokes and eat slices of pie. Apple, in honor of Sir Isaac Newton, seems to be the flavor of choice. Also called "Casual Pi Day", the date was chosen because, in European notation, the date 22/7 is the same as 22 divided by 7, which gives an approximation of pi (the lower-case Greek letter pi). Pi is the mathematical symbol for the relationship between a circle's diameter and its circumference (expressed as C = pi times
The earliest recorded attempt to understand how circles "work" – what the relationship is among the circumference, diameter and area – took place in Babylon (in what is modern Iraq) about 1900 BC. Their calculations were
But pi, even though it wasn't called that yet, really got its start in ancient Greece. Archimedes of Syracuse (287-212 BC) decided to take a circle and draw a polygon that inscribed it (that is, where the corners of the figure just touched the inside of the circle) and another that circumscribed it (the lines of the polygon just touched the outside of the circle). By calculating the perimeter of the two polygons (dividing up each figure into right triangles and using the Pythagorean Theorem to determine the length of the outer side), he estimated circumference as being between those two limits. Assigning the symbols Pn for the perimeter of the inscribed circle and P
Since there is no limit to the number of sides that a polygon can have, the estimate can get closer and closer to the actual value of the circumference of a circle without actually reaching the true, complete value. It has been determined that pi is an irrational number, meaning that it is infinite and, in decimal notation, does not have a repeated pattern of numbers. By using formulae to calculate an infinite series, Febrice Bellard, a French computer programmer, calculated pi to 2,699,999,990,000 (that is nearly 2,700
On the other hand, the approximation 22/7 is not irrational, although it is infinite. Expressed in decimal notation, it is 3.142857142857142857… which, as you can see, repeats the same six digits to the right of the decimal over and over. Compared to the actual value of pi, 3.1415926535… , 22/7 is only accurate to two digits past the decimal. That's good enough for rough calculations, and certainly good enough when slicing up an apple pie.
Oh, and the Tauists mentioned before? It seems that not everyone celebrates Pi Approximation Day, or even accepts the purity of pi. In 2010, physicist Michael Hartl published a paper "The Tau Manifesto", which presents the heretical view that "Pi is Wrong!" Instead of using pi, the ratio of the circumference of a circle to its diameter, he proposed using a ratio of the circumference to the circle's
So, Happy 3.142857 Day! |