---
tag: 00J3DCCEK5
kind: problem
name: Trisecting the angle
aliases: [angle-trisection]
msc: [51M15]
uses: [0DAECMZVRT]
sources:
  - url: https://en.wikipedia.org/wiki/Angle_trisection
    locator: Background and problem statement
same_as:
  wikidata: Q733081
  wikipedia: Angle trisection
---

## Problem

Given an arbitrary angle, construct with [[straightedge and compass|0DAECMZVRT]] alone an angle one third as large.

## Remarks

Some angles can be trisected. For example, a right angle can be trisected, because an angle of $30^\circ$ is constructible.
The general problem asks for one method that works for every angle.
The answer is no: [[the angle of $60^\circ$ cannot be trisected|0EWXPZCSZ0]].
The problem has solutions with other tools, such as a marked ruler or origami.

## History

The problem comes from ancient Greek geometry.
Pierre Wantzel proved in 1837 that it has no solution for arbitrary angles.

## Explanations

### L1 human

Bisecting an angle is easy with a compass.
Trisecting it, that is, dividing it into three equal parts, is not possible in general with straightedge and compass alone.