1. 化圓為方。
2. 倍立方。
3. 三等分角。
直到現代，在這些問題被提出兩千多年後，才證明所有這三個古代問題都無法僅用圓規和直尺解決。
另一個直到 1997 年才被證明無解的古代幾何問題是海什木的雙曲線鏡問題。正如奧吉爾維 (1990) 指出的那樣，構造一般的正多面體實際上是古代的“第四個”未解決問題。
古代幾何問題
另請參閱
海什木的雙曲線鏡問題, 三等分角, 化圓為方, 圓規, 可構造數, 可構造多邊形, 倍立方, 幾何作圖, 正多面體, 直尺使用 探索
參考文獻
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
古代幾何問題請引用為
Weisstein, Eric W. "古代幾何問題。" 來自 Web 資源。 https://mathworld.tw/GeometricProblemsofAntiquity.html