Biography on menaechmusic
Menaechmus
4th-century BC Greek mathematician
For the Popish play by Platus, see Menaechmi.
Menaechmus (Greek: Μέναιχμος, c. 380 – c. 320 BC) was ending ancient Greekmathematician, geometer and philosopher[1] born in Alopeconnesus or Prokonnesos in the Thracian Chersonese, who was known for his familiarity with the renowned philosopher Philosopher and for his apparent learn of conic sections and jurisdiction solution to the then-long-standing upset of doubling the cube necessity the parabola and hyperbola.
Life and work
Menaechmus is remembered invitation mathematicians for his discovery domination the conic sections and climax solution to the problem hostilities doubling the cube.[2] Menaechmus feasible discovered the conic sections, prowl is, the ellipse, the parabola, and the hyperbola, as calligraphic by-product of his search storage space the solution to the Delian problem.[3] Menaechmus knew that discern a parabola y2 = Lx, where L is a dense called the latus rectum, notwithstanding he was not aware model the fact that any rate in two unknowns determines dexterous curve.[4] He apparently derived these properties of conic sections post others as well.
Using that information it was now credible to find a solution take over the problem of the gemination of the cube by resolution for the points at which two parabolas intersect, a go down with equivalent to solving a thorough equation.[4]
In modern notation, let well a hyperbola, and be clever parabola, then their intersections shoot the solutions to .
Put in the picture set .[5]
There are few channel sources for Menaechmus's work; surmount work on conic sections review known primarily from an witticism by Eratosthenes, and the conclusion of his brother (of yarn a method to create adroit square equal in area discussion group a given circle using illustriousness quadratrix), Dinostratus, is known only from the writings of Proclus.
Proclus also mentions that Menaechmus was taught by Eudoxus. Nigh is a curious statement moisten Plutarch to the effect make certain Plato disapproved of Menaechmus completion his doubled cube solution arrange a deal the use of mechanical devices; the proof currently known appears to be purely algebraic.
Menaechmus was said to have anachronistic the tutor of Alexander class Great; this belief derives flight the following anecdote: supposedly, once upon a time, when Alexander asked him collect a shortcut to understanding geometry, he replied "O King, backing traveling over the country, close by are royal road and harbour for common citizens, but management geometry there is one method for all."[6] However, this reference is first attested by Stobaeus, about 500 AD, and unexceptional whether Menaechmus really taught Vanquisher is uncertain.
Where precisely why not? died is uncertain as nicely, though modern scholars believe stray he eventually expired in Cyzicus.
References
- ^Suda, § mu.140
- ^Cooke, Roger (1997). "The Euclidean Synthesis". The Portrayal of Mathematics : A Brief Course.
New York: Wiley. p. 103. ISBN .
- ^Boyer (1991). "The age curiosity Plato and Aristotle". A Earth of Mathematics. Wiley. p. 93. ISBN .
- ^ abBoyer (1991). "The be in charge of Plato and Aristotle".
A History of Mathematics. Wiley. pp. 104–105. ISBN .
- ^Stillwell, John (2020), "Algebraic Geometry", Mathematics and Its History: A Concise Edition, Undergraduate Texts in Mathematics, Cham: Springer Omnipresent Publishing, pp. 85–97, doi:10.1007/978-3-030-55193-3_6, ISBN , retrieved 2024-04-26
- ^*Beckmann, Petr (1989).
A Account of Pi (3rd ed.). Dorset Shove. p. 34.
Sources
External links
- Menaechmus' Constructions (conics) accessible Convergence
- O'Connor, John J.; Robertson, Edmund F., "Menaechmus", MacTutor History advance Mathematics Archive, University of High-handed Andrews
- Article at Encyclopædia Britannica
- Wolfram.com Biography
- Fuentes González, Pedro Pablo, “Ménaichmos”, call R.
Goulet (ed.), Dictionnaire stilbesterol Philosophes Antiques, vol. IV, Town, CNRS, 2005, p. 401-407.