:''There is also a Menaechmus in

Plautus Titus Maccius Plautus (; c. 254 – 184 BC), commonly known as Plautus, was a Roman playwright of the Old Latin period. His comedies are the earliest Latin literary works to have survived in their entirety. He wrote Palliata comoedia, the gen ...

' play, ''

The Menaechmi ''Menaechmi'', a Latin-language play, is often considered Plautus' greatest play. The title is sometimes translated as ''The Brothers Menaechmus'' or ''The Two Menaechmuses''. The ''Menaechmi'' is a comedy about mistaken identity, involving a se ...

''.'' Menaechmus ( el, Μέναιχμος, 380–320 BC) was an

ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

geometer A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

and philosopher born in

Alopeconnesus Alopeconnesus or Alopekonnesos ( grc, Ἀλωπεκόννησος, "fox island") was an ancient Greek city located on the western coast of ancient Thrace, located in the region of the Thracian Chersonesus. It was an Aeolian colony, and was belie ...

Prokonnesos Marmara Island ( ) is a Turkish island in the Sea of Marmara. With an area of it is the largest island in the Sea of Marmara and is the second largest island of Turkey after Gökçeada (older name in Turkish: ; el, Ίμβρος, links=no ''Im ...

in the

Thracian Chersonese The Thracians (; grc, Θρᾷκες ''Thrāikes''; la, Thraci) were an Indo-European speaking people who inhabited large parts of Eastern and Southeastern Europe in ancient history.. "The Thracians were an Indo-European people who occupied t ...

, who was known for his friendship with the renowned philosopher

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...

and for his apparent discovery of

conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a specia ...

s and his solution to the then-long-standing problem of

doubling the cube Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related pro ...

using the

parabola In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One descript ...

and

hyperbola In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, cal ...

Life and work

Menaechmus is remembered by mathematicians for his discovery of the

conic sections In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special ...

and his solution to the problem of doubling the cube. Menaechmus likely discovered the conic sections, that is, the

ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

, the

, and the

, as a by-product of his search for the solution to the

Delian problem Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related probl ...

. Menaechmus knew that in a parabola y² = ''L''x, where ''L'' is a constant called the ''

latus rectum In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a speci ...

'', although he was not aware of the fact that any equation in two unknowns determines a curve. 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 Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related probl ...

by solving for the points at which two parabolas intersect, a solution equivalent to solving a cubic equation. There are few direct sources for Menaechmus's work; his work on conic sections is known primarily from an

epigram An epigram is a brief, interesting, memorable, and sometimes surprising or satirical statement. The word is derived from the Greek "inscription" from "to write on, to inscribe", and the literary device has been employed for over two mille ...

Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria ...

, and the accomplishment of his brother (of devising a method to create a square equal in area to a given circle using the

quadratrix In geometry, a quadratrix () is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and Ehrenfried Walther von Tschirnhaus, E. W. Tschirnhaus, ...

Dinostratus Dinostratus ( el, Δεινόστρατος; c. 390 – c. 320 BCE) was a Greece, Greek mathematician and geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle. Life and work Di ...

, is known solely from the writings of

Proclus Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers ...

. Proclus also mentions that Menaechmus was taught by Eudoxus. There is a curious statement by

Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...

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 Alexander III of Macedon ( grc, wikt:Ἀλέξανδρος, Ἀλέξανδρος, Alexandros; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king of the Ancient Greece, ancient Greek kingdom of Maced ...

; 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 Joannes Stobaeus (; grc-gre, Ἰωάννης ὁ Στοβαῖος; fl. 5th-century AD), from Stobi in Macedonia, was the compiler of a valuable series of extracts from Greek authors. The work was originally divided into two volumes containin ...

, 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 Cyzicus (; grc, Κύζικος ''Kúzikos''; ota, آیدینجق, ''Aydıncıḳ'') was an ancient Greek town in Mysia in Anatolia in the current Balıkesir Province of Turkey. It was located on the shoreward side of the present Kapıdağ Peni ...

References

Sources

* * *

External links

Menaechmus' Constructions (conics)
a
Convergence
*
Article
at

Encyclopædia Britannica The (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various time ...

Wolfram.com Biography
* Fuentes González, Pedro Pablo, �
Ménaichmos
��, in R. Goulet (ed.), ''Dictionnaire des Philosophes Antiques'', vol. IV, Paris, CNRS, 2005, p. 401-407. {{Authority control Ancient Greek mathematicians 4th-century BC Greek people History of geometry 380 BC births 320 BC deaths Philosophers and tutors of Alexander the Great 4th-century BC mathematicians