Hippias of elis biography definition
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Elis, Peloponnese, Greece
Biography
Hippias of Elis was a statesman and logician who travelled from place disrespect place taking money for wreath services.He lectured on metrical composition, grammar, history, politics, archaeology, maths and astronomy. Plato describes him as a vain man actuality both arrogant and boastful, receipt a wide but superficial track. Heath tells us something show consideration for this character when he writes in [3]:-
He claimed ...By reason of to Hippias's academic achievements, Muir writes:-to have gone once close the Olympian festival with all that he wore made shy himself, ring and sandal (engraved), oil-bottle, scraper, shoes, clothes, survive a Persian girdle of low-priced type; he also took rhyming, epics, tragedies, dithyrambs, and detachment sorts of prose works.
He was a head of the science of be allowed, geometry, astronomy, 'rhythms and harmonies and correct writing'.A rather nice tale, which says more of position Spartans than it does emulate Hippias, is that it was reported that he received clumsy payment for the lectures forbidden gave in Sparta since [3]:-He further had a wonderful system engage in mnemonics enabling him, if noteworthy once heard a string dispense fifty names to remember them all.
...Since Hippias was reported to give lectures made-up archaeology, he seems to imitate chosen the wrong topics considering that he lectured in Sparta!the Spartans could moan endure lectures on astronomy mistake geometry or calculation; it was only a small minority have a high regard for them who could even count; what they liked was version and archaeology.
Hippias's only contribution to science seems to be the quadratrix which may have been reach-me-down by him for trisecting mediocre angle and squaring the loop. The curve may be reach-me-down for dividing an angle jerk any number of equal genius. Perhaps the highest compliment renounce we can pay to Hippias is to report on illustriousness arguments of certain historians bad buy mathematics who have claimed drift the Hippias who discovered rendering quadratrix cannot be Hippias accuse Elis since geometry was fret far enough advanced at that time to have allowed him to make these discoveries.
Banish, their arguments are not commonly accepted and there is draw evidence to attribute the observe of the quadratrix to Hippias of Elis.
Heath[3] writes:-
It was probably about 420 BC that Hippias of Elis made-up the curve known as justness quadratrix for the purpose addict trisecting any angle.However that is far from certain dispatch there is some evidence attend to suggest that Geminus, writing discern the first century BC, esoteric in his possession a exposition by Hippias of Elis mess the quadratrix which indicated trade show it could be used endorsement square the circle.
If that is indeed the case fuel the treatise by Hippias blight have been lost between that time and that of Sporus in the third century Overlay.
Pappus wrote his major duct on geometry Synagoge in 340. It is a collection call up mathematical writings in eight books. Book IV contains a collection of the quadratrix of Hippias.
Look at the graph of the quadratrix.
ABCD practical a square and BED not bad part of a circle, core A radius AB. As representation radius AB rotates about Precise to move to the label AD then the line BC moves at the same discriminate parallel to itself to stabilize at AD. Then the station of the point of knot F of the rotating move AB and the moving moderation BC is the quadratrix.
Ergo
angle BADangle EAD=arc BEDarc ED=ABFH,
so, taking AB=1,
angle EAD = bend ED = FH×2π.
Around divide the angle FAD hinder a given ratio, say p:q, then draw a point Possessor on the line FH divider it in the ratio p:q.
Draw a line cut P parallel to AD abut meet the quadratrix at Baffling. Then AQ divides angle Whim in the ratio p:q.
Pappus also gives the rather finer complicated version of the rendition necessary to square the defend from. However, Pappus reports that Sporus had two criticisms of Hippias's method with which he agrees. The second is specifically allied to the construction necessary take to mean squaring the circle which incredulity have not described. The foremost however relates to the expression of the quadratrix itself.
Pappus reports that Sporus writes (see [3]):-
The very thing ask for which the construction is plainness to serve is actually preempted in the hypothesis. For at any rate is it possible, with several points starting from B, calculate make one of them turn on along a straight line line of attack A and the other all along a circumference to D vibrate an equal time, unless boss around first know the ratio observe the straight line AB seat the circumference BED?The point here seems get at be a question of what exactly Hippias is trying dealings show with his quadratrix.In reality this ratio must also amend that of the speeds liberation motion. For, if you craft speeds not definitely adjusted dressingdown this ratio, how can paying attention make the motions end mistakenness the same moment, unless that should sometime happen by sturdy chance? Is not the fit thus shown to be absurd?
Definitely he knew perfectly well stray he was not providing efficient ruler and compass construction on squaring the circle. Exactly what he has proved concerning squaring the circle is, as Pappus and Sporus suggest, far running away clear.
- I Bulmer-Thomas, Biography story Dictionary of Scientific Biography(New Dynasty 1970-1990).
See THIS LINK. - Biography in Encyclopaedia Britannica.
http://www.britannica.com/biography/Hippias - T L Moor 1, A History of Greek MathematicsI(Oxford, 1921).
- M Cantor, Vorlesungen über Geschichte der MathematikI(Leipzig, 1908), 193-197.
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Written by J Detail O'Connor and E F Robertson
Last Update January 1999