Easy As Pie!
I've been reading an interesting mathematics book about pi. The book contains an amazing history of the development of estimates for pi.
According to the book, ancient mathematicians developed a number of simple approximations to pi; Babylonian, 3 1/8; Eqyptian, 256/81; Chinese, sqrt(10); Archimedes, 22/7; Tsu-Ching Chih (Chinese), 355/113.
The last of these is by far the most accurate. In fact, it is accurate to five decimal places. Obviously any third rate mathematician such as myself can remember pi to five decimal places. It is a basic thing; 3.14159. But, the ratio 355/113 is easier to remember; 113,355; with the inverse fractional ratio in the middle.
Even more interesting is the method Tsu-Ching Chih used to determine his estimate. He used the classic ancient method of almost infinitely many sided polygons, then determined the estimate for pi from the calculated area of the many sided polygon. Which is real easy, unless you're doing what Tsu-ching Chih did and use a 12,288 sided polygon.
According to the book, ancient mathematicians developed a number of simple approximations to pi; Babylonian, 3 1/8; Eqyptian, 256/81; Chinese, sqrt(10); Archimedes, 22/7; Tsu-Ching Chih (Chinese), 355/113.
The last of these is by far the most accurate. In fact, it is accurate to five decimal places. Obviously any third rate mathematician such as myself can remember pi to five decimal places. It is a basic thing; 3.14159. But, the ratio 355/113 is easier to remember; 113,355; with the inverse fractional ratio in the middle.
Even more interesting is the method Tsu-Ching Chih used to determine his estimate. He used the classic ancient method of almost infinitely many sided polygons, then determined the estimate for pi from the calculated area of the many sided polygon. Which is real easy, unless you're doing what Tsu-ching Chih did and use a 12,288 sided polygon.