81. Kalendarium Matematyczne 360 pne Grek dinostratus za pomoca kwadratrysy (krzywej Hippiasza) rozwiazalzadanie kwadratury kola. 320 pne Arystarch z Samos i Euklides opisali krzywe http://gamma.im.uj.edu.pl/complex2001/cd2005mat/mat/ciekawostki/kalend/mat/khm2.

Kalendarium historii matematyki Okres antyczny od 500 r. p.n.e. do 400 r. n.e. 420 p.n.e. Grek Hippiasz z Elidy odkry³ kwadratrysê - now¹ krzyw¹ oprócz znanych ju¿ wczeœniej okrêgu i linii prostej. 420 p.n.e. Grecy odkrywaj¹ odcinki niewspó³mierne (liczby niewymierne). 414 p.n.e. Urodzi³ siê grecki matematyk Teataesz (zmar³ w 369 p.n.e.). Bada³ wieloœciany foremne i stwierdzi³, ¿e istnieje piêæ i tylko piêæ wieloœcianów foremnych. 408 p.n.e. Urodzi³ siê grecki filozof Eudoksos z Knidos (zmar³ w 355 p.n.e.). Opracowa³ model ruchu cia³ niebieskich ze skomplikowan¹ kombinacj¹ obracaj¹cych siê sfer. Stworzy³ teoriê proporcji, zajmowa³ siê (ok. 360 p.n.e.) z³otym podzia³em. Poda³ sposoby obliczania objêtoœci pewnych bry³ metod¹ wyczerpywania. 400 p.n.e. Grecy sformu³owali trzy s³ynne zadania, które przez wieki bêd¹ stanowi³y zagadkê dla matematyków: kwadratura ko³a, podwojenie szeœcianu i trysekcja kata. Dopiero w XIX wieku udowodniono, ¿e ¿adne z tych zadañ nie jest wykonalne za pomoc¹ cyrkla i linijki (bez podzia³ki). 360 p.n.e. Grecki matematyk Menechemus odkry³ krzywe sto¿kowe, nazwane póŸniej elips¹, parabol¹, hiperbol¹. Rozwi¹za³ zadanie podwojenia szeœcianu.

82. The Quadratrix It s named after Hippias of Elis and was used by dinostratus and Nicomedes.The curve is defined in a dynamical way. Consider the square ABDC. http://cage.rug.ac.be/~hs/quadratrix/quadratrix.html

THE QUADRATRIX Trisecting an angle - Squaring the circle Introduction Three famous geometrical construction problems, originating from ancient Greek mathematics occupied many mathematicians until modern times. These problems are the duplication of the cube: construct (the edge of) a cube whose volume is double the volume of a given cube, angle trisection: construct an angle that equals one third of a given angle, the squaring of a circle: given (the radius of) a circle, construct (the side of) a square whose area equals the area of the circle. In the ancient Greek tradition the only tools that are available for these constructions are a ruler and a compass . During the 19th century the French mathematician Pierre Wantzel proved that under these circumstances the first two of those constructions are impossible and for the squaring of the circle it lasted until 1882 before a proof had been given by Ferdinand von Lindemann If we extend the range of tools the problems can be solved. New tools can be material tools (ex. a "marked ruler", that's a ruler with two marks on it, a "double ruler", that's a ruler with two parallel sides,...), or

83. The Most Complete Listing Of Library Reference Recources, Including Books, Dicti Dihigo, Martin. Diller, Phyllis. DiMaggio, Joe. Dinghas, Alexander. Dini, Ulisse.dinostratus. Diocles. Diogenes. Dion, Céline. Dion, Celine. Dione. Dionis du Séjour http://www.infolinks.us/index.cfm?page=Lib.Biographies&cat=People&scat=D

84. Dinostratus PDF A List of Mathematicians http://www.gap-system.org/~history/Mathematicians/Dinostratus.html

Dinostratus Born: about 390 BC in Greece Died: about 320 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Dinostratus is mentioned by Proclus who says (see for example [1] or [3]):- Amyclas of Heraclea, one of the associates of Plato , and Menaechmus , a pupil of Eudoxus who had studied with Plato , and his brother Dinostratus made the whole of geometry still more perfect. It is usually claimed that Dinostratus used the quadratrix, discovered by Hippias , to solve the problem of squaring the circle Pappus tells us (see for example [1] or [3]):- For the squaring of the circle there was used by Dinostratus, Nicomedes and certain other later persons a certain curve which took its name from this property, for it is called by them square-forming in other words the quadratrix It appears from this quote that Hippias discovered the curve but that it was Dinostratus who was the first to use it to find a square equal in area to a given circle. Proclus , who claims to be quoting from Eudemus , writes (see [1]):- Nicomedes trisected any rectilinear angle by means of the conchoidal curves, of which he had handed down the origin, order, and properties, being himself the discoverer of their special characteristic. Others have done the same thing by means of the quadratrices of

85. QUADRATRIX Definition QUADRATRIX. QUADRATRIX. Noun. 1. A curve made use of in the quadratureof other curves; as the quadratrix, of dinostratus, or of Tschirnhausen. http://www.websters-dictionary-online.org/definition/english/QU/QUADRATRIX.html

Philip M. Parker, INSEAD. QUADRATRIX Definition: QUADRATRIX QUADRATRIX Noun . A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen. Source: Etymology: Websters 1913 Crosswords: QUADRATRIX English words defined with "QUADRATRIX" -trices -trixes references Top Rhyming with "QUADRATRIX" Words rhyming with "QUADRATRIX" (pronounced 'Quad*ra"trix'): Adjutrix, Administratrix, Bisectrix, Cicatrix, Conservatrix, Creatrix, Curatrix, Generatrix, matrix, Negotiatrix, Osculatrix, Rectrix, Rixatrix, separatrix, testatrix, tortrix, Tutrix, Victrix. ( additional references Top Anagrams: QUADRATRIX Words within the letters "a-a-d-i-q-r-r-t-u-x" -3 letters : quadrat. -4 letters : datura, diquat, ritard. -5 letters : atria, audit, aurar, durra, quart, quirt, radar, radix, riata, tiara, triad, urari. Source: compiled by the editor from various references ; see credits. SCRABBLE Top Alternative Orthography: QUADRATRIX Hexadecimal (or equivalents, 770AD-1900s) references Leonardo da Vinci (1452-1519; backwards)

86. Dinostratus - Definition Of Dinostratus By Webster's Online Dictionary dinostratus explanation. Definition of dinostratus California Dinumeration.dinostratus not found in the Dictionary. Advertisement. Close. Real http://www.webster-dictionary.org/definition/Dinostratus

Word: Browse dinnerware DINO Dino Paul Crocetti Dinoceras ... Dioecia Dinostratus not found in the Dictionary Advertisement Search results none found Online Dictionary Home

87. Lebensdaten Von Mathematikern Translate this page dinostratus (um 390 - um 320 v. Chr.) Diokles (um 240 - um 180 v. Chr.) Dionis duSejour, Achille Pierre (11.1.1734 - 22.8.1794) http://www.mathe.tu-freiberg.de/~hebisch/cafe/lebensdaten.html

Diese Seite ist dem Andenken meines Vaters Otto Hebisch (1917 - 1998) gewidmet. By our fathers and their fathers in some old and distant town from places no one here remembers come the things we've handed down. Marc Cohn Dies ist eine Sammlung, die aus verschiedenen Quellen stammt, u. a. aus Jean Dieudonne, Geschichte der Mathematik, 1700 - 1900, VEB Deutscher Verlag der Wissenschaften, Berlin 1985. Helmut Gericke, Mathematik in Antike und Orient - Mathematik im Abendland, Fourier Verlag, Wiesbaden 1992. Otto Toeplitz, Die Entwicklung der Infinitesimalrechnung, Springer, Berlin 1949. MacTutor History of Mathematics archive A B C ... Z Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843)

88. QUADRATRIX - LoveToKnow Article On QUADRATRIX of this class are those of dinostratus and EW Tschirnhausen, which are both The quadratrix of dinostratus was well known to the ancient jreek geometers, http://99.1911encyclopedia.org/Q/QU/QUADRATRIX.htm

QUADRATRIX QUADRATRIX (from Lat. quadrator, squarer), in mathe matics, a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves FIG. i. ;/ i / FIG. 2. of this class are those of Dinostratus and E. W. Tschirnhausen, which are both related to the circle. The cartesian equation to the curve is y = x cot . which shows that the curve is symmetrical about the axis of y, and that it consists of a central portion flanked by infinite branches (fig. 2). The asymptotes are *= *=2na, n being an integer. The intercept on the axis of y is 2a/x; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected. The curve also permits the solution of the problems of duplicating a cube (q.v.) and trisecting an angle. The quadratrix of Tschirnhausen is constructed by dividing the arc and radius of a quadrant in the same number of equal parts as before. The mutual intersections of the lines drawn from the points of division of the arc parallel to AB, and the lines drawn parallel to BC through the points of division of AB, are points on the quadratrix (fig. 3). The cartesian equation is y a cos Trx/2a. The curve is periodic, and cuts the axis of x at the points #= =*=(2n-i)a, n being an integer; the maximum values of y are =*=a. Its properties are similar to those of the quadratrix of Dinostratus. QUACK QUADRATURE To properly cite this QUADRATRIX article in your work, copy the complete reference below:

89. References For Dinostratus Anciens D Translate this page dinostratus, math.. - Frère de Ménechme, il serait né vers 375 av. J.-C. Cf. F.Lasserre, De Léodamas de Thasos , référencé dans ce répertoire, p. 561 http://www-gap.dcs.st-and.ac.uk/~history/References/Dinostratus.html

References for Dinostratus Version for printing Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: G J Allman, Greek geometry from Thales to Euclid (Dublin, 1889). T L Heath, A History of Greek Mathematics I (Oxford, 1921). B L van der Waerden, Science awakening (Groningen, 1954). Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR April 1999 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Dinostratus.html

90. Categorized Entries Abantiades A patronymic applied to Perseus (qv), Acrisius, and other descendantsof Abas (qv). Abderites. ( *)abdhri/ths ) and Abder imacr;ta. http://test.perseus.tufts.edu/cgi-bin/showcategory.pl?category=2

91. Tom.com http://www.scitom.com.cn/history/landmark/ldm146.html

92. ”ŠwŽj Translate this page The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www2m.biglobe.ne.jp/~m-souda/mysouda/math/smith/chapter3/math7.htm

”ŠwŽj [ƒtƒBƒƒ‰ƒIƒX] [ƒGƒŠƒX‚̃qƒbƒsƒAƒX] [ƒƒgƒ“Aƒtƒ@ƒGƒCƒmƒXAƒGƒEƒNƒeƒ‚ƒ“] [Exhaustion‚Ì•û–@] ... [ƒAƒeƒl‚̃eƒAƒCƒeƒgƒX] ƒtƒBƒƒ‰ƒIƒX A”ނ̊֐S‚͐”Šw‚Æ‚¢‚¤‚æ‚è“NŠw‚É‚ ‚Á‚½BƒOƒmƒ‚ƒ“‚ð•`ŽÊ‚µ‚Đ”Šw‚Ì•ª–ì‚ɐG‚ê‚Ä‚Í‚¢‚邪B ƒGƒŠƒX‚̃qƒbƒsƒAƒX ƒƒgƒ“Aƒtƒ@ƒGƒCƒmƒXAƒGƒEƒNƒeƒ‚ƒ“ @ƒsƒ^ƒSƒ‰ƒX‚ƃvƒ‰ƒgƒ“‚ÌŠÔ‚ÌŽž‘ãAƒAƒeƒl‚ł͐”Šw“I“V•¶Šw‚É”ñí‚Ȋ֐S‚ª‚ ‚Á‚½‚±‚Æ‚ªAŽOl‚Ì“V•¶ŠwŽÒAƒƒgƒ“Aƒtƒ@ƒGƒCƒmƒXAƒGƒEƒNƒeƒ‚ƒ“ ‚Ì’˜ì‚Ì’†‚ÉŒ©o‚¹‚éB‚µ‚©‚µA”Þ‚ç‚̍vŒ£‚ð‹æ•Ê‚·‚邱‚Æ‚Í‚Å‚«‚È‚¢B“NŠwŽÒ‚̃eƒIƒtƒ‰ƒXƒgƒX‚Í ƒGƒOƒ][ƒXƒ`ƒ‡ƒ“‚Ì•û–@ ƒAƒ“ƒeƒBƒtƒHƒ“‚ƃGƒOƒ][ƒXƒ`ƒ‡ƒ“‚Ì•û–@ @ƒAƒŠƒXƒgƒeƒŒƒX‚́AƒAƒ“ƒeƒBƒtƒHƒ“ ƒAƒ‹ƒLƒ ƒ^ƒX @ƒvƒ‰ƒgƒ“‚ÌŽž‘ãA’˜–¼‚ȃsƒ^ƒSƒ‰ƒX”h‚Ì“NŠwŽÒAƒAƒ‹ƒLƒ ƒ^ƒX ‚́A”ŠwŽÒA«ŒRA­Ž¡‰ÆA”Žˆ¤Žå‹`ŽÒA‹³ˆçŽÒ‚Æ‚µ‚Ä–¼º‚ðŸ‚¿“¾‚Ä‚¢‚½BƒLƒPƒ(BC106-43)‚́A”Þ‚Ì‚±‚Æ‚ðˆÌ‘å‚ÈŽt‚Ì—F‚Æ‚µ‚ÄŒê‚Á‚Ä‚¢‚éBƒzƒ‰ƒeƒBƒEƒX(BC65-8)‚́AƒAƒhƒŠƒAŠC‚Å“ï”j‚µÀ‚Á‚½”Þ‚ÉŒ¾‹y‚µ‚āAŽŸ‚̂悤‚ÈŒ¾—t‚ðŽc‚µ‚Ä‚¢‚éB @ƒGƒEƒfƒ‚ƒX(Eudemus)(c.335BC)‚́AŽ©‚ç‚ÌŠô‰½Šw‚Ì’˜ì‚ɂ‚¢‚ÄŒê‚èAŽ„‚½‚¿‚Ɂu“ÆŽ©‚ÌŒö—‚ÅŠw–â‚ð–L‚©‚É‚µAŒ’‘S‚È‘ÌŒn‰»‚ð‚¨‚±‚È‚Á‚½vl‚½‚¿‚̈êl‚Å‚ ‚Á‚½‚ÆŒ¾‚Á‚Ä‚¢‚éB•Ê‚̒q‚©‚çAŽ„‚½‚¿‚́A”ނ́AŽŸ‚̂悤‚È–½‘è‚ð’m‚Á‚Ä‚¢‚āA‹^‚¢‚È‚­Ø–¾‚µ‚½‚Ɛ„˜_‚µ‚Ä‚¢‚éB @‚PD’¼ŠpŽOŠpŒ`‚Ì’¼Šp‚Ì’¸“_‚©‚çAŽÎ•Ó‚ɐ‚ü‚ðˆø‚­‚ƁA‚»‚ꂼ‚ê‚̕ӂ́AŽÎ•Ó‚Æ‚»‚ê‚ɗאڂ·‚éü•ª‚Æ‚Ì‘Šæ•½‹Ï‚Å‚ ‚éB @‚QD‚ü‚́AŽÎ•Ó‚É‚Å‚«‚½“ñ‚‚̐ü•ª‚Ì‘Šæ•½‹Ï‚Å‚ ‚éB @‚RDŽOŠpŒ`‚Ì’¸“_‚©‚ç~‚낵‚½‚ü‚ªA‘Εӂ̓ñ‚‚̐ü•ª‚Ì‘Šæ•½‹Ï‚Å‚ ‚é‚È‚çA‚»‚Ì’¸“_‚ÌŠp‚Í’¼Šp‚Å‚ ‚éB @‚UD“ñ‚‚̕½–Ê‚ªA‘æŽO‚Ì•½–ʂƐ‚’¼‚Å‚ ‚é‚È‚çA“ñ‚‚̕½–Ê‚ÌŒðü‚à‚»‚Ì•½–ʂɐ‚’¼‚Å‚ ‚邵A‚Ü‚½A‚»‚Ì•½–Ê‚ª‘æŽO‚Ì•½–Ê‚ÆŒð‚í‚é’¼ü‚Æ‚à‚’¼‚Å‚ ‚éB

93. Textes D témoignages. Dio Chrysostomus Fragments et témoignages http://callimac.vjf.cnrs.fr/RSPA/Textes/Textes_D.html

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