The computation of Certain Numbers Using a Rule and Compass
Abstract
We present a method for computing some numbers bit by bit using only a ruler and compass, and illustrate it by applying it to arctan(X)/Pi. The method is a spigot algorithm and can be applied to numbers that are constructible over the unit circle and the ellipse. The method is precise enough to produce about 20 bits of a number, that is, 6 decimal digits in a matter of minutes. This is surprising, since we do no actual calculations.
- Publication:
-
Journal of Integer Sequences
- Pub Date:
- January 1998
- Bibcode:
- 1998JIntS...1...13P
- Keywords:
-
- Binary expansion;
- A004715 of the On-Line Encyclopedia of Integer Sequences;
- constant;
- rule and compass construction;
- Pi;
- Number Theory
