1. 化圆为方。
2. 倍立方。
3. 三等分角。
直到现代，在这些问题被提出两千多年后，才证明所有这三个古代问题都无法仅用圆规和直尺解决。
另一个直到 1997 年才被证明无解的古代几何问题是海什木的双曲线镜问题。正如奥吉尔维 (1990) 指出的那样，构造一般的正多面体实际上是古代的“第四个”未解决问题。
古代几何问题
另请参阅
海什木的双曲线镜问题, 三等分角, 化圆为方, 圆规, 可构造数, 可构造多边形, 倍立方, 几何作图, 正多面体, 直尺使用 Wolfram|Alpha 探索
参考文献
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.在 Wolfram|Alpha 中被引用
古代几何问题请引用为
Weisstein, Eric W. "古代几何问题。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/GeometricProblemsofAntiquity.html