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 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. 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. 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. Ogilvy,
C. S. Excursions
in Geometry. Pappas,
T. "The Impossible Trio." The
Joy of Mathematics. Jones, A.; Morris, S.; and Pearson, K. Abstract
Algebra and Famous Impossibilities. 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 . Referenced
on Wolfram|Alpha Geometric Problems of Antiquity
Cite this as:
Weisstein, Eric W. "Geometric Problems of Antiquity."
From MathWorld https://mathworld.wolfram.com/GeometricProblemsofAntiquity.html
Subject classifications
years after they were formulated, were all three ancient
problems proved insoluble using only compass and straightedge.
