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Muddled history of Pi comes to forefront on 3/14/15

Posted March 14, 2015

Pi is a big part of what NASA does. How many times will each of Opportunity's 25 cm wheels rotate when it reaches this marathon milestone?

Saturday, 3/14/15, marks a once-in-a-century Pi Day, corresponding to the first four digits of 3.1415.

If you really want to celebrate in mathematical style, take it out a few more places and clink your glasses at 9:26:53 a.m. (3.141592653). Those nine digits are more than enough for most applications requiring pi.

Some state legislators had a different idea about how exact pi needed to be. In 1897, Indiana House Bill No. 246 attempted to redefine pi as 3.2 based on a “new mathematical truth” formulated by Dr. Edwin Goodwin. Goodwin sought to charge royalties for his innovative new definition of pi. The Pi Bill offered this new mathematical marvel to Indiana schools free of charge.

Buried in a lot of nonsensical math that most legislators probably did not bother to read was Goodwin’s assertion that "the ratio of the diameter and circumference is as five-fourths to four" which is a somewhat confusing way to say 3.2. While this is a convenient number, it doesn’t even round properly from the true number 3.141592653 (and so on).

As the bill came up for a vote, professor Clarence Abiathar Waldo, chair of the math department at Purdue University (and author of the book Manual of Descriptive Geometry) stepped in. Waldo “coached” (his word) senators on the mathematical details. When the bill came up for a vote, instead of setting mathematics back a few thousand years, it was met with 30 minutes of ridicule. The Indianapolis Journal reported “all of the senators who spoke on the bill admitted that they were ignorant of the merits of the proposition.”

The accuracy of the calculated value of pi has improved over history. Ahmes, an Egyptian scribe, wrote the oldest known mention of pi. While the value isn’t mentioned in the Ahemes’ Rhind Mathematical Papyrus, researchers approximated it to 256/81 based his descriptions. While only correct to one digit, overall the approximation is about 0.6 percent off, not bad.

Babylonian mathematicians used 25/8 to approximate pi in the 19th century B.C. This was about 0.5 percent off. Indian astronomer Yajnavalkya used 339/108 in the 5th century B.C. adding another correct decimal place and improving accuracy to 0.09 percent. Second century AD astronomy Ptolemy added the third digit of accuracy. Chinese mathematician Liu Hui brought accuracy to 0.01 percent in 263 A.D.

Pi is an infinite, non repeating decimal, but that hasn't stopped us from going deeper and deeper into calculations. Today the world record for calculating pi is held by Alexander Yee out to 13 trillion digits. Akira Haraguchi, a 69 year old Japanese man recited 111,700 of those digits from memory at a recent public event. Even for the most complex cosmological calculations (such as the size of the universe), Jörg Arndt and Christoph Haenel state that 39 digits is sufficient in their 2001 book "Pi - Unleashed."

NASA uses pi everyday. It is essential to the search for exoplanets. As planets beyond our solar system pass in front of their host star, the decrease in the brightness of that star combined with the area of the circle (pi * r^2). Propulsion engineers use pi in analyzing spherical propellant tanks on spacecraft to calculate the amount of liquid propellant to keep the spacecraft going. Astronomers use pi to calculate the density of an asteroid based on its size and mass giving insight into the asteroid’s composition (ice, rock, iron or some combination).

NASA has issued a Pi Day challenge. The Mars rover Opportunity is approaching marathon distance of 42.195 kilometers. How many times will its 25-centimeter diameter wheels have rotated when it reaches this milestone?

The Dawn spacecraft is orbing the dwarf planet Ceres with an average radius of 475km. The camera onboard snaps images that cover 26km on a side, from an altitude of 370km. Assuming Ceres is spherical, a perfectly circular orbit, and no overlap in the images how many images must Dawn take to fully map the surface? If you’ve survived those questions, there is one more even more fun one at the link above. Answers will be posted Monday.

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