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Dinostratus: more detail

320 Bc: 320 Bc Births, 320 Bc Deaths, Perdiccas, Timon of Phlius, Menaechmus, Timocharis, Gongsun Long, Dinostratus, Alcetas, Zoilus
Dinostratus: An entry from Gale's <i>Science and Its Times</i> by Judson Knight, 2001
390 Bc: 390 Bc Births, 390 Bc Deaths, Tollund Man, Andocides, Heraclides Ponticus, Mozi, Battle of the Allia, Dinostratus, Attalus, Amadocus I

lists with details

Academia
THE ACADEMY 1, History. 1. dinostratus THE SQUARING OF THE CIRCLE.dinostratus proved that the trisectrix of Hippias could be used
http://descartes.cnice.mecd.es/ingles/maths_workshop/A_history_of_Mathematics/Gr

Extractions: THE ACADEMY 1 History DINOSTRATUS THE SQUARING OF THE CIRCLE Dinostratus proved that the trisectrix of Hippias could be used to solve this problem after discovering that the side of the square is the mean proportional between the arc of the quarter circle AC and the segment DQ. There are various stages to the reductio ad absurdum proof which are illustrated in the following windows: Let the circle with centre D and radius DR intersect the trisectrix at S and the side of the square at T. Draw the perpendicular SU to side DC from point S. As the arcs are proportional to the radii then AC/AB=TR/DR (2) From (1) and (2) it must follow that TR=AB (3) S is the point on the trisectrix which satisfies TR/SR=AB/SU (4) From (3) and (4) it follows that SR=SU However, this is absurd as the perpendicular is the shortest distance between a point and a line. Therefore, DR cannot be longer than DQ. 2.- We repeat this way of reasoning with the hypothesis
ACADEMIA_INDICE
and the parabola. This discovery allowed the duplication of the cubeto be calculated. dinostratus (350 BC), He proved the squaring
http://descartes.cnice.mecd.es/ingles/maths_workshop/A_history_of_Mathematics/Gr

Extractions: PLATO: THE ACADEMY History 1. BACKGROUND TO THE PERIOD Aristotle and Plato in the centre of Raphael's painting "The School in Athens". The Vatican Museum. The Peloponnesian Wars took place in the IVth century B.C. Sparta fought against Athens and behind them other Greek towns followed them into warfare. Sparta called on Persia to help them keep control of the towns they had occupied. Athens and Thebes became allies and together managed to defeat Sparta. King Philip of Macedon took advantage of the situation and became ruler of Greece. His reign lasted from 360 B.C. to 336 B.C. when, upon his death, his son Alexander took the throne. Alexander the Great was responsible for the invasion of the Persian empire, which included Syria, Palestine, Egypt, Mesopotamia and Iran. This century began with the death of Socrates (399 B.C.) The two great philosophers Aristotle and Plato , one of Socrates students and admirers also belonged to this period along with Archytas. Aristotle was Alexander the Great's private tutor and instilled in him the superiority of the Hellenic culture and encouraged him to go East and extend his empire. Plato managed to bring the greatest thinkers of the time together at his Academy in Athens. His contributions to mathematics include his rigorous method of justifying solutions through logical reasoning, his
Footnotes
. . . . .dinostratus dinostratus showed how to square the circleusing the trisectrix . . . . .
http://www.math.tamu.edu/~don.allen/history/greekorg/footnode.html

Extractions: Theodorus proved the incommensurability of , , , ...,. Archytas solved the duplication of the cube problem at the intersection of a cone, a torus, and a cylinder. ...histories Here the most remarkable fact must be that knowledge at that time must have been sufficiently broad and extensive to warrant histories ...Anaximander Anaximander further developed the air, water, fire theory as the original and primary form of the body, arguing that it was unnecessary to fix upon any one of them. He preferred the boundless as the source and destiny of all things. ...Anaximenes Anaximenes was actually a student of Anaximander. He regarded air as the origin and used the term 'air' as god ...proofs. It is doubtful that proofs provided by Thales match the rigor of logic based on the principles set out by Aristotle found in later periods. ...incommensurables. The discovery of incommensurables brought to a fore one of the principle difficulties in all of mathematics - the nature of infinity. ...discovered as attested by Archimedes. However, he did not rigorously prove these results. Recall that the formula for the volume pyramid was know to the Egyptians and the Babylonians. ...Persians. This was the time of Pericles. Athens became a rich trading center with a true democratic tradition. All citizens met annually to discuss the current affairs of state and to vote for leaders. Ionians and Pythagorean s were attracted to Athens. This was also the time of the conquest of Athens by Sparta.
Quadratrix Of Hippias -- From MathWorld
The quadratrix was discovered by Hippias of Elias in 430 BC, and laterstudied by dinostratus in 350 BC (MacTutor Archive). It can
http://mathworld.wolfram.com/QuadratrixofHippias.html
Dinostratus
turnbull.mcs.stand.ac.uk/history/References/dinostratus.html dire quelle na pas été visible, mais ce ne serait toujours quun faux
http://turnbull.mcs.st-and.ac.uk/history/Mathematicians/Dinostratus.html

Extractions: 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
Quadratrix - Definition Of Quadratrix By Webster Dictionary
of dinostratus, or of Tschirnhausen . Advertisement. Search. Word Browse.
http://www.webster-dictionary.net/definition/Quadratrix
CHRONOLOGY OF MATHEMATICIANS
420 HIPPIAS TRISECTRIX. 360 EUDOXUS PROPORTION AND EXHAUSTION. -350 MENAECHMUSCONIC SECTIONS. -350 dinostratus QUADRATRIX. -335 EUDEMUS HISTORY OF GEOMETRY.
http://users.adelphia.net/~mathhomeworkhelp/timeline.html

Extractions: CHRONOLOGY OF MATHEMATICIANS -1100 CHOU-PEI -585 THALES OF MILETUS: DEDUCTIVE GEOMETRY PYTHAGORAS : ARITHMETIC AND GEOMETRY -450 PARMENIDES: SPHERICAL EARTH -430 DEMOCRITUS -430 PHILOLAUS: ASTRONOMY -430 HIPPOCRATES OF CHIOS: ELEMENTS -428 ARCHYTAS -420 HIPPIAS: TRISECTRIX -360 EUDOXUS: PROPORTION AND EXHAUSTION -350 MENAECHMUS: CONIC SECTIONS -350 DINOSTRATUS: QUADRATRIX -335 EUDEMUS: HISTORY OF GEOMETRY -330 AUTOLYCUS: ON THE MOVING SPHERE -320 ARISTAEUS: CONICS EUCLID : THE ELEMENTS -260 ARISTARCHUS: HELIOCENTRIC ASTRONOMY -230 ERATOSTHENES: SIEVE -225 APOLLONIUS: CONICS -212 DEATH OF ARCHIMEDES -180 DIOCLES: CISSOID -180 NICOMEDES: CONCHOID -180 HYPSICLES: 360 DEGREE CIRCLE -150 PERSEUS: SPIRES -140 HIPPARCHUS: TRIGONOMETRY -60 GEMINUS: ON THE PARALLEL POSTULATE +75 HERON OF ALEXANDRIA 100 NICOMACHUS: ARITHMETICA 100 MENELAUS: SPHERICS 125 THEON OF SMYRNA: PLATONIC MATHEMATICS PTOLEMY : THE ALMAGEST 250 DIOPHANTUS: ARITHMETICA 320 PAPPUS: MATHEMATICAL COLLECTIONS 390 THEON OF ALEXANDRIA 415 DEATH OF HYPATIA 470 TSU CH'UNG-CHI: VALUE OF PI 476 ARYABHATA 485 DEATH OF PROCLUS 520 ANTHEMIUS OF TRALLES AND ISIDORE OF MILETUS 524 DEATH OF BOETHIUS 560 EUTOCIUS: COMMENTARIES ON ARCHIMEDES 628 BRAHMA-SPHUTA-SIDDHANTA 662 BISHOP SEBOKHT: HINDU NUMERALS 735 DEATH OF BEDE 775 HINDU WORKS TRANSLATED INTO ARABIC 830 AL-KHWARIZMI: ALGEBRA 901 DEATH OF THABIT IBN - QURRA 998 DEATH OF ABU'L - WEFA 1037 DEATH OF AVICENNA 1039 DEATH OF ALHAZEN
Mathematic Historic Style % % This File Is Based On A Table Of
1908, \died 1974} } \newcommand{\Dini}{{\sc Dini}\footnote{{\sc Ulisse Dini}, \born14.11.1845, \died 28.10.1918} } \newcommand{\dinostratus}{{\sc dinostratus
http://www.tug.org/tex-archive/macros/latex/contrib/mhs/mhs.sty
Definition Of Zylonite - BrainyDictionary
Definition of Quadratrix (n.) A curve made use of in the quadrature of othercurves; as the quadratrix, of dinostratus, or of Tschirnhausen.
http://www.brainydictionary.com/words/zy/zylonite241343.html
The Quadratrix
The curve already appears in ancient Greek geometry. It s named afterHippias of Elis and was used by dinostratus and Nicomedes.
http://cage.rug.ac.be/~hs/quadratrix/quadratrix.html

Extractions: 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
JMM HM DICIONÁRIO
Translate this page de Alexandria (c. 250) Diócles (c. -100) Diógenes Laércio, Diophantus, DemocritosDinostratos Diophantos Diocles, Democritos dinostratus Diophantus Diocles
http://phoenix.sce.fct.unl.pt/jmmatos/HISTMAT/HMHTM/HMDIC.HTM
ALC III,2: The Science Of Magnitudes
science. Menaechmus, dinostratus, Athenaeus, Helicon, and especiallyEudoxs made very important mathematical discoveries. Their
http://www.domcentral.org/study/ashley/arts/arts302.htm

Extractions: BENEDICT M. ASHLEY, O.P.: THE ARTS OF LEARNING AND COMMUNICATION CHAPTER II The Science of Magnitudes THE BEGINNINGS THE GREEKS, SCIENTISTS AND ARTISTS In the last chapter we indicated that, while mathematical calculation was developed in a practical way by the people of Mesopotamia and Egypt, and carried still further by the Hindus and Chinese, it was the Greeks who made it a theoretical study. They transformed it into a true science, rigorously logical in structure, and a model for all other sciences. It was these same scientifically minded Greeks who first arrived at a perfect conception of the fine arts. The art of Mesopotamia was strong and grandiose, but without grace or subtlety. The art of Egypt was subtle and mysterious, but strangely static and without inner thought or feeling. Only in the art of Greece is there achieved a living balance of all the elements of beauty. Their art was classical (from Latin classicus ,meaning "first class"), and became a standard for all later art. Not, indeed, that art of later ages need confine itself to copying the style and subject-matter of Greek art, as some people have thought but that we can learn from Greek literature, sculpture, and architecture a true conception of the elements that go into a work of art and of the harmony with which they should be united. Today we are inclined to think of science and art as unrelated fields. The artist seems to be all imagination and emotion, living in a subjective world of free fancy. The scientist seems to be all facts and abstract theories, living in the objective world of experiment and measurement. Yet the Greeks excelled both in art and science. In order to learn something of this lesson from the Greeks in this chapter we are going to try to get clearer notions of two questions:
Archimedes (287 B.C. - 212 B.C.)
dinostratus discovered the quadratrix resulting from the intersectionof a rotating line with another moving parallel to itself.
http://www.usefultrivia.com/biographies/archimedes_001.html

Extractions: ARCHIMEDES ARCHIMEDES was a native of Syracuse, one of the greatest cities of the West Grecian world. His letters to Dositheus of Alexandria show him to have been in constant communication with the students of geometry in that city. Plutarch, in his life of Marcellus, speaks of his intimate friendship with King Hiero of Syracuse, who induced him to apply his mechanical principles to the construction of military engines; though the time thus withdrawn from his theoretical researches was most unwillingly given. During the second Punic War Hiero had been in close alliance with Rome. But after his death, Hippocrates, an ambitious general, enlisted the city on the side of Carthage, and a Roman force, under the command of Marcellus, besieged it by sea and land. The fleet, equipped with the usual engines of war, especially the sambuca Cicero . It bore the image of a cylinder circumscribing a sphere, with a verse indicating, what Archimedes had held to be his greatest achievement, the measurement and mutual proportion of these two bodies. Dramatic, surely, was the contrast offered by the siege of Syracuse between the scientific intellect of Greece and the disciplined force of Rome; and not less remarkable is the admiration of the conqueror for the conquered, which, in a few generations, would weld the Greco-Roman world into one. Geometry, when Archimedes began his career, had made more progress than is shown by the thirteen books of Euclid's
Pappus (4th Century A.D.)
There are special studies on various curves; as the spirals of Archimedes,the quadratix of dinostratus, and the conchoid of Nicomedes.
http://www.usefultrivia.com/biographies/pappus_001.html

Extractions: PAPPUS PAPPUS was a contemporary of Theon of Alexandria, and taught mathematics in that city during the reign of Theodosius I. He wrote a commentary on the Great Syntaxis Almagest ] of Ptolemy, which has not come down to us. He is known to us by the work entitled Synagoge or Assemblage ; a collection in eight books of mathematical papers having no very distinct connection, and consisting of commentaries on the geometrical work of the previous six centuries, enriched by very fruitful additions of his own. For the history of ancient mathematics this work, of which the last six books and part of the second have been preserved, is invaluable. Already in the third century B.C. the filiation of discovery, so evident in this science, had been traced by Eudemus, a pupil of Aristotle, parts of whose work have been preserved by Proclus. Pappus supplies many details of Apollonius and of later writers who would otherwise have been unknown to us. Special studies on isolated problems occupy the greater part of his attention. Various modes of inserting two mean geometrical proportionals are discussed; new methods of inscribing the five regular solids in a sphere are put forward, (book iii). There are special studies on various curves; as the spirals of Archimedes , the quadratix of Dinostratus, and the conchoid of Nicomedes. Much attention is given to the work of Zenodorus on isoperimetry; and new problems on this subject are solved (book v). In the 6th book the earlier astronomers are spoken of.
ThinkQuest : Library : A Taste Of Mathematic
350?); Thymaridas (c. 350); dinostratus (c. 350); Speusippus (d. 339);Aristotle (384322); Aristaeus the Elder (fl. c. 350-330); Eudemus
http://library.thinkquest.org/C006364/ENGLISH/history/historygreece.htm

Extractions: Index Math Welcome to A Taste of Mathematics.You will find the taste of mathematics here.The history of Mathematics,famous mathematicians,cxciting knowledge,the world difficult problems and also mathematics in our life... Browsing,thinking,enjoying,and have a good time here! Visit Site 2000 ThinkQuest Internet Challenge Languages English Chinese Students fangfei Beijing No.4 High School, Beijing, China ziyan Beijing No.4 High School, Beijing, China Coaches Tife Zesps3 Szks3 Ogslnokszta3c9cych Numer 1, Beijing, China xueshun Beijing No.4 High School, Beijing, China Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy
ThinkQuest : Library : The Gift Of Prometheus
dinostratus, his brother, succeeded in using Hippias quadratrix to squarethe circle; that is, to construct a square equal in area to a circle.
http://library.thinkquest.org/C0122667/greece/maths.html

Extractions: Index Visit Site 2001 ThinkQuest Internet Challenge Students Jayson Victoria Junior College, Singapore, Singapore Wei-Ern Victoria Institution, Johor, Malaysia Durgesh The Woodlands, Mississauga, Canada Coaches Soong-Chee Victoria Junior College, Singapore, Singapore Ming Chun Samuel Tanjong Katong Secondary School, Singapore, Singapore Abiola University of Richmond, Palmgrove, Nigeria Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy
Hippias2.html
square making . dinostratus (circa 350 BC) was the first to use itfor this purpose, according to Pappus (circa 300 AD). . What
http://www.ms.uky.edu/~carl/ma330/hippias/hippias21.html

Extractions: Hippias and his quadratrix Hippias of Elis (430 BC) was a sophist who invented the quadratrix curve to trisect an angle. The problem of trisecting a given angle was one of the problems that generated a lot of mathematics during this period, and several mathematicians devised methods for solving this problem. Like many other sophists, Hippias was an itinerant teacher who made his living wowing the locals with his knowledge. Apparently, he did alright, but didn't leave much of a legacy except for the quadratrix. Definition of the curve The curve can be described in a few sentences. Let ABCD denote a square. Over a unit time period, allow the top segment of the square to fall at a uniform speed to the bottom of the square. During the same time, allow the left side of the square to rotate clockwise at a uniform speed to the bottom of the square. At each time, the two segments will intersect in a point P. The totality of all these points P is defined as the quadratrix. Drawing the quadratrix One can imagine how Hippias might have sketched the quadratrix in the sand, but one can hardly image how he would have made an accurate sketch of it.
Jooned
juures. Aastal 350 uuris seda dinostratus ringi kvadratuuri probleemijuures. Kapajoont tuntakse ka kui Gutshoveni kõverat. Esimesena
http://www.art.tartu.ee/~illi/kunstigeomeetria/koverad/jooned7.htm
OPTED V0.03 Letter Q
trices (pl. ) of Quadratrix. Quadratrix (n.) A curve made use of in the quadratureof other curves; as the quadratrix, of dinostratus, or of Tschirnhausen.
http://www.phy.hr/~matko/DICTIONARY/v003/wb1913_q.html

Extractions: Q ) the seventeenth letter of the English alphabet, has but one sound (that of k), and is always followed by u, the two letters together being sounded like kw, except in some words in which the u is silent. See Guide to Pronunciation, / 249. Q is not found in Anglo-Saxon, cw being used instead of qu; as in cwic, quick; cwen, queen. The name (k/) is from the French ku, which is from the Latin name of the same letter; its form is from the Latin, which derived it, through a Greek alphabet, from the Ph/nician, the ultimate origin being Egyptian. Qua conj. ) In so far as; in the capacity or character of; as. Quab n. ) An unfledged bird; hence, something immature or unfinished. Quab v. i. ) See Quob, v. i. Qua-bird n. ) The American night heron. See under Night. Quacha n. ) The quagga. Qvacked ) of Quack Quacking ) of Quack Quack v. i. ) To utter a sound like the cry of a duck. Quack v. i. ) To make vain and loud pretensions; to boast. Quack v. i. ) To act the part of a quack, or pretender. Quack n. ) The cry of the duck, or a sound in imitation of it; a hoarse, quacking noise. Quack n.
Assignment 19
mathematics. Great mathematicians whose works were revived by Pappus includeEuclid, Archimedes, Apollonius, Nicomedes, and dinostratus.
http://www.herkimershideaway.org/algebra2/doc_page27.html

Extractions: Assignment 19 Obvious is the most dangerous word in mathematics." (Eric Temple Bell ) PAPPUS (ca 300): An excellent mathematician who lived in Alexandria, Pappus attempted to rekindle interest in the mathematical works of the Greeks. This was not an easy task, since Christians had destroyed much of the ancient Greek documents, but Pappus managed to create his Mathematical Collection which cites or references over thirty different ancient mathematicians. Much of our knowledge of Greek mathematics has been derived from the works of Pappus. His work is often called the requiem of Greek mathematics. Great mathematicians whose works were revived by Pappus include Euclid Archimedes Apollonius Nicomedes , and Dinostratus Why did Herkimer have trouble making a phone call to the zoo? Answer : Because the lion was busy. Herky s friends JUSTIN TIME ...this guy always arrives at the very last minute. LEE KEEROOF ... a repairman who prevents rain water from dripping into your house. Reading : Section 3.4, pages 163-166. Written: Page 166-167/9, 13, 15, 17

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