Math 2.0

Geometry Foundations and axiom systems Problem

Trisecting the angle

Builds on Straightedge and compass construction

Problem

Given an arbitrary angle, construct with straightedge and compass 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∘30^\circ is constructible. The general problem asks for one method that works for every angle. The answer is no: the angle of 60∘60^\circ cannot be trisected. 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.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

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Straightedge and compass construction, concept, no evidence levelStraightedge and comp…conceptTrisecting the angle, problem, no evidence levelTrisecting the angleproblem
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Straightedge and compass construction concept
  2. Trisecting the angle problem

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Angle_trisection, Background and problem statement
About this page
Tag00J3DCCEK5
URIm2://00J3DCCEK5
Aliasesangle-trisection
Kindproblem
WritingW1 stated
MSC51M15
StatusThis copy of the site has no build data. Run m2 status 00J3DCCEK5.
UsesStraightedge and compass construction
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