Ruler map /2902 194

■ Make a regular polygon.

Use only rulers and compasses to make regular pentagons.

Use only rulers and compasses to make a regular hexagon.

Making a regular heptagon with a ruler and compasses is a seemingly simple problem, but many famous mathematicians are at a loss, because a ruler can't make a regular heptagon.

It's impossible to make a correct nonagon only by using rulers and compasses, because it's not enough to divide an angle into three equal parts by using rulers and compasses.

Solution to the problem: In his sophomore year, Gauss obtained the regular drawing method of regular heptagon, and gave the condition that regular polygon can be drawn by rules: the number of sides of regular polygon drawn by rules must be the product of non-negative integer power of 2 and different Fermat prime numbers, which solved the problem that has not been solved for two thousand years.

Fermat prime number