# Constructing a Regular Heptagon Using Plemelj's Method

Constructing a Regular Heptagon Using Plemelj's Method

This Demonstration shows Plemelj's method for constructing a regular heptagon, using the following steps:

1. Draw a circle with center and radius .

σ

O

1

2. Draw an equilateral triangle with on .

OAB

AB

σ

3. Let be the midpoint of .

C

OB

4. Construct a point on so that .

D

OB

OD=1/3OB

5. Construct a point on so that .

E

DC

∠EAC=1/3∠DAC

6. Successively measure out points on at distance starting with .

σ

AE

A

Verification

Suppose . Then

∠CAD=3γ

tan(3γ)===

CD

AC

1

6

3

2

1

3

3

Since ,

cosγ=AC/AE

AE===

AC

cosγ

3

2cosγ

s

7