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 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 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 Web 资源。 https://mathworld.net.cn/GeometricProblemsofAntiquity.html