Math 2.0

Geometry Foundations and axiom systems Problem

Doubling the cube

Builds on Straightedge and compass construction

Problem

Given the edge of a cube, construct with straightedge and compass alone the edge of a cube with twice the volume.

Remarks

For an edge of length 11, the new edge has length 23\sqrt[3]{2}. So the problem asks whether 23\sqrt[3]{2} is a constructible number. The answer is no: doubling the cube is impossible. The problem has solutions with other tools, such as a marked ruler or conic sections.

History

The problem is also called the Delian problem, after a legend about an oracle on the island of Delos. Hippocrates of Chios showed that it is equivalent to finding two mean proportionals between a segment and a segment twice as long. Pierre Wantzel proved in 1837 that no straightedge and compass solution exists.

Reading path

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

Show the path as a graph
Straightedge and compass construction, concept, no evidence levelStraightedge and comp…conceptDoubling the cube, problem, no evidence levelDoubling the cubeproblem
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.
  • no evidence level
  1. Straightedge and compass construction concept
  2. Doubling the cube problem

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Doubling_the_cube, lead section
  2. Web https://en.wikipedia.org/wiki/Doubling_the_cube, History
About this page
Tag04SD3F4FCR
URIm2://04SD3F4FCR
Aliasesdelian-problem, duplication-of-the-cube
Kindproblem
WritingW1 stated
MSC51M15
StatusThis copy of the site has no build data. Run m2 status 04SD3F4FCR.
UsesStraightedge and compass construction
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What this page needs for W2

  • edge bounds both (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

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