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Geometric Problems of Antiquity


The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge:

1. circle squaring.

2. cube duplication.

3. angle trisection.

Only in modern times, more than 2000 years after they were formulated, were all three ancient problems proved insoluble using only compass and straightedge.

Another ancient geometric problem not proved impossible until 1997 is Alhazen's billiard problem. As Ogilvy (1990) points out, constructing the general regular polyhedron was really a "fourth" unsolved problem of antiquity.


See also

Alhazen's Billiard Problem, Angle Trisection, Circle Squaring, Compass, Constructible Number, Constructible Polygon, Cube Duplication, Geometric Construction, Regular Polyhedron, Straightedge

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References

Conway, J. H. and Guy, R. K. "Three Greek Problems." In The Book of Numbers. New York: Springer-Verlag, pp. 190-191, 1996.Courant, R. and Robbins, H. "The Unsolvability of the Three Greek Problems." §3.3 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 117-118 and 134-140, 1996.Loomis, E. S. "The Famous Three." §1.1 in The Pythagorean Proposition: Its Demonstrations Analyzed and Classified and Bibliography of Sources for Data of the Four Kinds of "Proofs," 2nd ed. Reston, VA: National Council of Teachers of Mathematics, pp. 5-6, 1968.Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 135-138, 1990.Pappas, T. "The Impossible Trio." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 130-132, 1989.Jones, A.; Morris, S.; and Pearson, K. Abstract Algebra and Famous Impossibilities. New York: Springer-Verlag, 1991.Stoschek, E. "Modul 41 Literatur." http://marvin.sn.schule.de/~inftreff/modul41/lit41.htm.Stoschek, E. "Modul 41. Three Geometric Problems of Antiquity: Their Approximate Solutions in Automata Representation--Integrated Control Processors for Nanotechnology." http://marvin.sn.schule.de/~inftreff/modul41/task41.htm.

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Geometric Problems of Antiquity

Cite this as:

Weisstein, Eric W. "Geometric Problems of Antiquity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeometricProblemsofAntiquity.html

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