FutureAstronaut wrote:Pi isn't 22/7, that's just an estimate...
After a little search I see what you mean, 22/7 is an estimate, my mistake. pi is the ratio of the circumference of a circle to its diameter, thus if you measure the diameter and the circumference of the circle accurately you will get two values which you can use in the same method that I stated above.
The method used is to apply calculus to the perimeter if an infinitely-sided regular polygon. The limit of the ratio of perimeter (which in a circle becomes the circumference) to a bisecting line segment (which in a circle becomes the "diameter") as the number of identical facets approaches infinity is Pi.
For example, an equilateral triangle is a very poor estimate. If you look at a triangle inscribed in a circle, it becomes intuitively obvious that the perimeter of the triangle is far smaller than the perimeter of the circle. Now try a square. It is a closer approximation. Now try a regular octagon. It is closer. Now try a 100-sided polygon. It will look almost like the polygon and circle are the same. By the time you get to a 1000-sided polygon, the difference between the inscribed polygon and circle will undoubtedly be indistinguishable to the naked eye unless drawn on a massive scale.
Now imagine a polygon with infinite sides. Literally, a polygon with a an infinite number of sides, each with a side length of one (infineitly small) point. This becomes a set of all points in a plane equidistant from a focus. It may appear that definitionally, it is a circle. The problem is that the number of sides (infinite) and the length of the sides (infinitely small) is undefined, so you can't say they are the same thing. But the limit, applying calculus, of the polygon IS definitionally the same as a circle, and, therefore, the relationship that comprises pi can be described and calculated to an obscene number of digits.
Additionally, it is interesting to note that the man who performed the feat has a Japanese name. The japanese educational system relies heavily on rote memorization, as opposed to the Socratic method employed in the West. Their system places more value on learning what you are told, as opposed to asking questions. This was also the case in many ancient Western cultures, especially those that relied very heavily on oral histories, like the ancient Irish. There are many tales of amazing feats of memorization among cultures that, even though they now record events in writing, have a relatively recent tradition of oral histories. Literary historian and author Frank O'Connor tells of a Kerry fisherman who could recite then painfully verbose Lament for Art O'Leary some number of decades after the only time he had ever heard it. It is quite amazing the memorizational abilities fostered in cultures that value them.