
Glossary: Prime Pages: Top 5000: 
Gauss' proved that you can subdivide a circle into n
parts using a ruler (an unmarked straightedge) and a compass
(which draws circles) if and only if n is a power of
two times a product of distinct Fermat primes. Later Pierpont
[Pierpont1895] showed that
you can divide a circle into
n parts using origami (paper folding)
if and only if n is a product of a power of two times a power
of three times a distinct product of primes of the form
2^{n}3^{m}+1. These primes
are now called Pierpont primes.
Simple heuristics suggest that there should be finitely many Fermat primes, but infinitely many Pierpont primes. In the following table we give a count of the numbers smaller Pierpont primes. Circles can be divided into the same numbers of parts using a straight edge, compass and an "angle trisector."
See Also: FermatNumber Related pages (outside of this work)
References:
Chris K. Caldwell © 19992017 (all rights reserved)
