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	Menaechmus Summary
		It was actually more important in terms of mathematical discovery that Menaechmus was the first to show that hyperbolas, parabolas, and can be obtained by cutting a cone in a plane that is not parallel to the base of the cone.
		There are few direct sources for Menaechmus' work- his work on conic sections is known primarily from a 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.
		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 solely algebraic.
	www.bookrags.com /Menaechmus (1161 words)

	Menaechmus
		Some have inferred from this (see for example [4]) that Menaechmus acted as a tutor to Alexander the Great, and indeed this is not impossible to imagine since as Allman suggests Aristotle may have provided the link between the two.
		Proclus that Menaechmus was the head of a School and this is argued convincingly by Allman in [4].
		Allman [4] suggests that Menaechmus might have drawn the curves by finding many points on them and that this might be considered as a mechanical device.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Menaechmus.htm (885 words)

	Menaechmus (print-only)
		Menaechmus is famed for his discovery of the conic sections and he was the first to show that ellipses, parabolas, and hyperbolas are obtained by cutting a cone in a plane not parallel to the base.
		Menaechmus made his discoveries on conic sections while he was attempting to solve the problem of duplicating the cube.
		Other references to Menaechmus include one by Theon of Smyrna who suggests that he was a supporter of Eudoxus's theory of the heavenly bodies based on concentric spheres.
	www-groups.dcs.st-and.ac.uk /history/Printonly/Menaechmus.html (1014 words)

	Duplication of the Cube
		In contrast to analysis, this reversed procedure is called "synthesis." Menaechmus' cube duplication is an example of analysis: he assumed the mean proportionals x and y and then discovered them to be equivalent to the result of intersecting the three curves whose construction he could take as known.
		Menaechmus' solution is probably the first one using the conic sections and their properties.
		It may have been evolved in the Academy by some one contemporary with or junior to Menaechmus, for the arrangement in the figure of the two given straight lin segments and the two means between them is exactly the same as in Menaeucmus' figure.
	www.cs.mcgill.ca /~cs507/projects/1998/zafiroff (3282 words)

	Menaechmus biography
		Menaechmus is famed for his discovery of the
		Menaechmus made his discoveries on conic sections while he was attempting to solve the problem of
		Other references to Menaechmus include one by Theon of Smyrna who suggests that he was a supporter of Eudoxus's theory of the heavenly bodies based on
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Menaechmus.html (1170 words)

	Untitled Document
		For Riemann, as for Pythagoras, Archytas, Menaechmus, Plato, et al., each increase of degree of extension, from "n" to "n+1", occurs by the addition of a new principle, not a new independent "dimension".
		Menaechmus demonstrated that the magnitude that doubles the cube is formed by the intersection of a parabola and an hyperbola.
		As Menaechmus demonstrates, when the hyperbola and parabola are combined, a power is expressed by the resulting proportionality, which is higher than exists in either curve independently.
	www.wlym.com /antidummies/part35.html (1975 words)

	Menaechmi home Plautus (Dramata)
		Menaechmus enters talking about what has happened to him and says that he is a wretched man. The doctor approaches and questions him.
		Menaechmus says that he is not his master but as far as he is concerned he is free.
		Menaechmus and Menaechmus Sosicles see each other and realize they have the same name, and they discover that they are twin brothers.
	home.att.net /~c.c.major/pla/menaechmi.html (993 words)

	Schiller Institute -Pedagogy - Hyberbolic Functions- A Fugue Across 25 Centuries!
		Embedded in the discoveries of Archytas and Menaechmus was a principle that would not fully blossom until 2,200 years later, with the discoveries of Riemann and Gauss.
		His insight was based on the same principle recognized by Menaechmus, that the hyperbola, when projected onto a plane, was formed by a series of rectangles whose area was always equal.
		The principle underlying the constructions of Archytas and Menaechmus; the discontinuity expressed by the infinite boundary between the hyperbola and parabola; the inversion of the geometric and arithmetic in the hyperbola: From Gauss' perspective, these all reflect a transformation between negative and positive curvature.
	www.schillerinstitute.org /educ/pedagogy/hyperbolic_bmd3.html (2408 words)

	StudyGuide
		The name Menaechmus, although not a Roman name, was probably familiar to the Roman audiences.
		Menaechmus was a Greek mathematician who solved the problem of how to double the size of a cube.
		The young Menaechmus in Plautus' comedy is kidnapped in the city of Tarentum while he and his father are visiting the ludi.
	www.homestead.com /ludicrum/studyguide~NS4.HTML (2734 words)

	Menaechmi or The Twin Brothers
		Just prior to their appearance on the street where Menaechmus of Epidamnus lives, the latter has as usual been quarreling with his wife.
		When she sees Menaechmus Sosicles, Erotium insists that he come in and eat the feast she has prepared.
		Meanwhile, the wife of Menaechmus of Epidamnus discovers the loss of the mantle and makes such a scene that her husband attempts to recover the mantle from Erotium.
	www.theatrehistory.com /ancient/plautus003.html (531 words)

	Conic Sections: Apollonius and Menaechmus
		Menaechmus (Μέναιχμος) (from Alopeconnesus or Proconnesus) earlier (about 380 BC- about 320 BC) showed that circle, ellipses, parabolas, and hyperbolas are obtained by cutting a cone with a plane.
		Probably they were discovered from the work of Greeks with sundials, considering for example the problem of the intersection of a light cone with a plane.
		The work of Menaechmus and Apollonius was quite theoretical although we have seen that there was a specific problem to be solved.
	www.mlahanas.de /Greeks/Conics.htm (1771 words)

	Kakiseni.com - The Menaechmi
		Menaechmus I quarrels with his wife and threatens divorce, steals a dress from her, and gives it to his mistress Erotium, who offers to make dinner for him and his parasitic companion Peniculus.
		While Menaechmus is busy in town with the legal problems of his clients, Sosicles is taken for his brother by Erotium and handsomely entertained.
		A doctor gets four slaves to arrest Menaechmus for treatment, but the slave Messenio rescues him from them and is granted his freedom for it by Menaechmus, who does not even know him.
	www.kakiseni.com /events/theatre/NzQ1OA.html (350 words)

	TMTh:: MENAECHMCUS OF THRACE
		Menaechmus was the first to describe and study conic sections (the ellipse, the parabola and the hyperbola): these are the curves that result from plane intersections of a cone (the "triad", or three conic sections, of Menaechmus).
		He studied the problem of the duplication of the cube, and proved that the point demanded is a function of the intersection of two parabolas or of a parabola and a hyperbola.
		Menaechmus was the first to solve equations in the third degree.
	www.tmth.edu.gr /en/aet/1/67.html (219 words)

	Section 1.c Why Do Menaechmus' Constructions Work? (Site not responding. Last check: 2007-10-20)
		In the same work by Eutocius we have a description of Eratosthenes' (3rd century B.C.) (pronunciation) solution to the problem of finding two mean proportionals.
		Based on this quote, it would seem that the "triads of Menaechmus" refers to the three conic sections (we have not yet discussed the ellipse at this point).
		Because of this Menaechmus is given credit for discovering all three conic sections.
	nsm1.nsm.iup.edu /gsstoudt/conics/section_1_c.html (252 words)

	Chapter 16: Archimedes
		Menaechmus, who had studied with Plato and Eudoxus, was trying to teach Alexander some geometric proofs.
		And attempts to solve them led to the invention of new curves that broke the rules-they were made by a variety of mechanical or three-dimensional means.
		Menaechmus himself, struggling with the problem of doubling the cube, dreamed up the idea of cutting a cone with a plane.
	www.anselm.edu /homepage/dbanach/arch.htm (1819 words)

	Conic Sections in Ancient Greece
		Menaechmus is credited with the discovery of conic sections around the years 360-350 B.C.; it is reported that he used them in his two solutions to the problem of "doubling the cube".
		Following the work of Menaechmus, these curves were investigated by Aristaeus and of Euclid.
		Menaechmus was a pupil of Eudoxus, a contemporary of Plato (Heath, 1921, p.
	www.math.rutgers.edu /~cherlin/History/Papers1999/schmarge.html (5833 words)

	Convergence \| Can You Really Derive Conic Formulae from a Cone?
		The problem is the problem of doubling the cube, one of the three famous problems of antiquity.
		While we are not certain as to the exact moment of discovery, most authors attribute it to Menaechmus (4th century B.C.) [8, pp.
		What follows is Menaechmus' construction, according to Euctocius, of the two mean proportionals between two given lengths.
	mathdl.maa.org /convergence/1?pa=content&sa=viewDocument&nodeId=196&pf=1 (4094 words)

	Rudens
		Menaechmus 2, twin brother of Menaechmus I, from Syracuse
		Act I, scene 1: Menaechmus 1 enters form SR house and Peniculus who, at first, is unseen by Menaechmus I, enters form the Forum, SL.
		Menaechmus wears his wife's dress under his tunic.
	www.homestead.com /ludicrum/Rudens.html (721 words)

	Italian Institute of Culture in Sydney
		The Menaechmi is a play about mistaken identity, involving a set of twins, Menaechmus of Epidamnus and Menaechmus of Syracuse.
		After being separated from him, Menaechmus was adopted by a businessman who lived in Epidamnus.
		His original father died of grief, and his twin brother was renamed Menaechmus after his long-lost brother.
	www.iicsydney.esteri.it /IIC_Sydney/webform/SchedaEvento.aspx?id=47 (209 words)

	Archimedes of Syracuse: Introduction
		The curve is therefore identified as a cross section of a right-angled cone (right-angled because one side of the cone is at right angles with its base), or simply a conic section.
		(Menaechmus would not have used the term 'parabola', for this word was coined centuries later by Apollonius.)
		While it is possible to use a straightedge and compass to determine any number of points on this conic section, as is done above, the entire curve is not constructible.
	cerebro.xu.edu /math/math147/02f/archimedes/archintro.html (1546 words)

	World and Nation-State
		As the accompanying diagrams illustrate, the parabola possesses the characteristic of one mean between two extremes, while the hyperbola embraces two (see Figures 2a and Animation 1a and 2b and Animation 1b).
		Menaechmus showed that the intersection of an hyperbola and a parabola produces the result of placing two means between two extremes (Figure 3).
		Surfaces that contained curves with the characteristics of the hyperbola or catenary, Gauss called ``negatively'' curved, while surfaces that were formed by curves with the characteristics of circles and ellipses, he called ``positively'' curved
	www.larouchepub.com /eiw/public/2002-33/bruce3/gauss3.html (2368 words)

	Plautus' Menaechmi
		Menaechmus I asks Erotium for dress back, but she doesn’t have it and says that he has dress and bracelet.
		When Menaechmus II denies that he has ever been in the wife’s house, the Old Man thinks he is insane, so again Menaechmus II decides to play along for his own benefit.
		Menaechmus II promises freedom to Messenio if he can prove that Menaechmus I is his twin brother.
	depthome.brooklyn.cuny.edu /classics/course/twins.html (1096 words)

	Dictionary of Greek and Roman Biography and Mythology, page 1029 (v. 2) (Site not responding. Last check: 2007-10-20)
		[gallon, canachus.] Pliny quotes among the authorities for his 33d and 34th books, Menaechmus, a writer on the toreutic art, under which designation the chryselephantine statues were included.
		§ 18) a group by Menaechmus, of a calf pressed down by the knee, and with the neck doubled back (no doubt by some one about to sacrifice it, but this Pliny _ omits) ; and he adds that Menaechmus wrote upon his art.
		202) are therefore almost certainly wrong in identifying Pliny's Menaechmus with the Me^ naechmus or Manaechmus of Sicyon, who wrote a work ire pi rexvtruv (which means here actors, not artists, as Harduin and the rest evidently thought: see Meinejce, Hist.
	www.ancientlibrary.com /smith-bio/2137.html (984 words)

	Menaechmus (c.380-c.320 BC)
		A Greek mathematician, thought to have been a pupil of Eudoxus, who is famed for his discovery of the conic sections and for being the first to show that ellipses, parabolas, and hyperbolas are formed by cutting a cone in a plane that is not parallel to the base.
		Menaechmus made his discoveries on conic sections while attempting, unsuccessfully, to solve the problem of duplicating the cube.
		It has also been suggested that he served as a tutor to Alexander the Great.
	www.daviddarling.info /encyclopedia/M/Menaechmus.html (152 words)

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	a-plus-researchpapers.com /term-papers/4261/research-paper-menaechmus-play.html (410 words)

	Sept17 (Site not responding. Last check: 2007-10-20)
		He is a creature of someone’s imagination, specifically Menaechmus 1’s”.
		That is, he does everything Menaechmus 1 would like to do (visit Erotium, steal the palla and get away with it, insult his wife, get rid of his parasite).
		The 'search' is long and arduous (Menaechmus 2 is out of money, exhausted) because it is a process of self-discovery.
	www.classics.uiuc.edu /clciv120a/Oct24.htm (396 words)

	Untitled Document
		Menaechmi or The Menaechmus Twins inspired, among others, Shakespeare's The Comedy of Errors and Rodgers' and Hart's The Boys from Syracuse.
		MENAECHMUS: If you weren't mean, if you weren't stupid, if you weren't a violent virago, what you see displeases your husband would be displeasing to you, too.
		Now mark my words, if you act like this toward me after today, you shall hie yourself home to your father as a divorcee.
	www.comp.dit.ie /dgordon/Lectures/Hum1/040310/040310hum.htm (1428 words)

	CLAS 3330: 9/8/04. Notes for9/10 (Site not responding. Last check: 2007-10-20)
		Menaechmus I's wife meets Menaechmus II, mistaking him for her husband.
		How does Menaechmus II finally decide to deal with her and her father?
		Which Menaechmus does Messenio rescue from being beaten up and hauled away by the intervening slaves?
	www2.tltc.ttu.edu /george/CLAS3330/333098for91004.htm (286 words)

	Untitled (Site not responding. Last check: 2007-10-20)
		Joseph Furnari's recent adaptation welcomed Plautus's Menaechmus Brothers into the millennium in the intimate environment of West Side Rep.
		The two Menaechmus brothers were separated in infancy back home in Syracuse and are unwittingly reunited as adults with predictably hilarious results.
		Like a favorite old sitcom, which we have seen a dozen times but laugh at all the same things time after time, the twins' exploits are a permanent fixture in the fabric of the theatre.
	www.oobr.com /top/volFive/five/ten/mena.html (409 words)

	Section 1.b Menaechmus' Constructions
		Let us consider how Menaechmus constructed the two mean proportionals.
		In this manner, Menaechmus constructed the mean proportionals to a and b.
		This solution cannot be completed with ruler and compass only, and hence is not a solution.
	nsm1.nsm.iup.edu /gsstoudt/conics/section_1_b.html (411 words)

	Plautus and Segal (1998) Four comedies: The braggart soldier, The brothers Menaechmus, The haunted house, The pot of ... (Site not responding. Last check: 2007-10-20)
		Plautus and Segal (1998) Four comedies: The braggart soldier, The brothers Menaechmus, The haunted house, The pot of goldm
		Four comedies: The braggart soldier, The brothers Menaechmus, The haunted house, The pot of goldm
		To view the the latter's ratings, click on Chapters/Papers/Articles in the STATISTICS box, select a publication from the list that appears, and then click on either Quality or Interest in that publication's STATISTICS box.
	www.getcited.org /?PUB=100458916&showStat=Ratings (99 words)

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