World Library  
Flag as Inappropriate
Email this Article




There is also a Menaechmus in Plautus' play, The Menaechmi.

Menaechmus (Greek: Μέναιχμος, 380–320 BC) was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola.


  • Life and work 1
  • References 2
  • Sources 3
  • External links 4

Life and work

Menaechmus is remembered by mathematicians for his discovery of the conic sections and his solution to the problem of doubling the cube.[1] Menaechmus likely discovered the conic sections, that is, the ellipse, the parabola, and the hyperbola, as a by-product of his search for the solution to the Delian problem.[2] Menaechmus knew that in a parabola y² = Lx, where L is a constant called the latus rectum, although he was not aware of the fact that any equation in two unknowns determines a curve.[3] He apparently derived these properties of conic sections and others as well. Using this information it was now possible to find a solution to the problem of the duplication of the cube by solving for the points at which two parabolas intersect, a solution equivalent to solving a cubic equation.[3]

There are few direct sources for Menaechmus's work; his work on conic sections is known primarily from an epigram by Eratosthenes, and the accomplishment of his brother (of devising a method to create a square equal in area to a given circle using the quadratrix), Dinostratus, is known solely from the writings of Proclus. Proclus also mentions that Menaechmus was taught by Eudoxus. There is a curious statement by Plutarch to the effect that Plato disapproved of Menaechmus achieving his doubled cube solution with the use of mechanical devices; the proof currently known appears to be purely algebraic.

Menaechmus was said to have been the tutor of Alexander the Great; this belief derives from the following anecdote: supposedly, once, when Alexander asked him for a shortcut to understanding geometry, he replied "O King, for traveling over the country, there are royal road and roads for common citizens, but in geometry there is one road for all." (Beckmann, A History of Pi, 1989, p. 34) However, this quote is first attested by Stobaeus, about 500 AD, and so whether Menaechmus really taught Alexander is uncertain.

Where precisely he died is uncertain as well, though modern scholars believe that he eventually expired in Cyzicus.


  1. ^ Cooke, Roger (1997). "The Euclidean Synthesis". The History of Mathematics : A Brief Course. New York: Wiley. p. 103. Eutocius and Proclus both attribute the discovery of the conic sections to Menaechmus, who lived in Athens in the late fourth century B.C.E. Proclus, quoting Eratosthenes, refers to "the conic section triads of Menaechmus." Since this quotation comes just after a discussion of "the section of a right-angled cone" and "the section of an acute-angled cone", it is inferred that the conic sections were produced by cutting a cone with a plane perpendicular to one of its elements. Then if the vertex angle of the cone is acute, the resulting section (calledoxytome) is an ellipse. If the angle is right, the section (orthotome) is a parabola, and if the angle is obtuse, the section (amblytome) is a hyperbola (see Fig. 5.7). 
  2. ^  
  3. ^ a b  


  • Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience.  

External links

  • Menaechmus' Constructions (conics) at Convergence
  • .  
  • Article at Encyclopædia Britannica
  • Biography
  • Fuentes González, Pedro Pablo, “Ménaichmos”, in R. Goulet (ed.), Dictionnaire des Philosophes Antiques, vol. IV, Paris, CNRS, 2005, p. 401-407.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.