An expanded version of these lectures later appeared in book form 1. Though he was in cyrene when he died 67 years later, he must have spent part of his life in athens, where he studied under protagoras c. Theodorus of cyrene was a pupil of protagoras and himself the tutor of plato, teaching him mathematics, and also the tutor of theaetetus. But his principal claim to fame was his alleged atheism. The spiral of theodorus, numerical analysis, and special.
Another theodorus was one of the founders of atheism. The spiral of theodorus, numerical analysis, and special functions. Theodoret wrote brief treatises in the form of questions and answers on special passages of the octateuch, four books of kings, and two books of paralipomenon p. A commentary on the first book of euclids elements princeton, 1970, 95, n. As a cyrenaic philosopher, he taught that the goal of life was to obtain joy and avoid grief, and that the former resulted from knowledge, and the latter from ignorance. The writings of theodoret against cyril of alexandria were anathematized during the troubles that arose in connexion with the war of the three chapters. Theodorus, however, did not spend his whole life in cyrene for he was certainly in athens at a time when. A scribe who was especially noted for his skill in copying manuscripts. He was born and grew up in cyrene, then a sprawling greek colony at the northern coast of africa in what today is. It gave eastern libya the classical name cyrenaica that it has retained to modern times. Incorporating the old and the new, the proved and the conjectural, davis. In this web quest you will construct his famous wheel of theodorus and explore the interesting dilemma he faced when trying measure what he had created. One of the great pioneers in the early work showing the existence of irrational numbers was theodorus of cyrene.
This led him to discoveries concerning irrational numbers, or numbers that continue indefinitely without any repeating pattern. Greater fame, however, came to it through its distinguished citizens. Theodorus belonged to a brotherhood of scholars who believed that numbers were pleasing to the gods. A short history of greek mathematics cambridge, 1884, 164, should. Mar 16, 2020 theodorus was born in cyrene, now part of libya, which at that time was a greek colony. Theodorus lector, greek church historian, author of two significant epitomes of byzantine history correlating data from leading 5thcentury chroniclers, and constituting an essential source for events of that complex period.
The lost logic of elementary mathematics theodorus of cyrene. Mathematician theodorus of cyrene developed the theory of irrational numbers. Greek colonists from the island of thera found the city of cyrene in north africa. Dec 30, 2010 the intramural area of cyrene is of about 110 hectares, which means that the city had room for 10,000 people. Crabtree is an autodidact, studying the history of mathematics since 1983. Theodorus was the mathematical tutor of plato and theaetetus and is known for his contribution to the early development of the theory of irrational quantities. Who was one of of theodorus s most influential teachers. He was born in the northern african colony of cyrene, and apparently taught both there and in athens. It thus became necessary, early in the history of mathematics, to extend the. He lived in both greece and alexandria, before ending his. Little is known of theodorus biography beyond what can be inferred from platos dialogues. Theodorus was born in cyrene, now part of libya, which at that time was a greek colony. We are very appreciated with any contribution to make a better and more exactly biography of theodorus of cyrene by give us information about theodorus of cyrene such as theodorus of cyrene bio, theodorus of cyrene news, theodorus of cyrene photos, theodorus of cyrene pitures, theodorus of cyrene images.
Having initially studied economics at the university of melbourne, jonathan j. The city was founded early in the seventh century b. Theodorus of cyrene was an ancient libyan greek and lived during the 5th century bc. As a cyrenaic philosopher, he taught that the goal of life was to obtain joy and avoid grief. It was the oldest and most important of the five greek cities in the region. Incorporating the old and the new, the proved and the conjectural, davis examines theodorus in light of the mathematical concerns. Anniceris differed from theodorus in believing that pleasure had to be understood as embracing much more than sensual enjoyment. He was a pupil of protagoras and the tutor of plato and of theaetetus. Who was the mathematics teacher of plato, showed how to construct a line segment of length for any positive integer n. Anniceris differed from hegesias, a pessimist, in believing that there are qualities of pleasure that are good in and of themselves, apart from. This population level might have been sustained from 300 bce to 250 ce.
Theodorus was the mathematical tutor of plato and theaetetus and is known for his. Theodorus of cyrene died in 398 bc in cyrene now shahhat, libya. Theodorus of cyrene project gutenberg selfpublishing. Cyrene was originally a greek colony rounded by battus in 630 bc. He was born and grew up in cyrene, then a sprawling greek colony at the northern coast of africa in what today is libya, directly south of greece.
Grinus they say, the son of aesanius, a descendant of theras, and king of the island of thera, went to delphi to offer a hecatomb on behalf of his native city. Commentary on the first book of euclids elements princeton, 1970, 95, n. Because of the fertility of the soil, the great variety in climate and vegetation, together with its commercial advantages in location, the city soon rose to great wealth and importance. Prove the following, a given an odd integer n, then is represented by the leg of a right triangle whose hypotenuse is. He lived in both greece and alexandria, before ending his days in his native city of cyrene.
Who was one of of theodoruss most influential teachers answers. From theodorus to chaos, and makes brief references. Theodorus also composed a history in two books which carried the narrative of the hist. Featuring the church fathers, catholic encyclopedia, summa theologica and more. This book may have occasional imperfections such as missing or. Cyrene, the ancient greek city in presentday libya was the oldest and most important of the five greek cities in the region and gave eastern libya the classical name cyrenaica that it has. To navigate the timeline, click and drag it with your mouse, or click on the timeline overview on the bottom. Cyrene had two named sisters, themisto and astyaguia. Theodore was arrested during the persecutions of the church under emperor diocletian and ordered to deliver up his copies of the scriptures. Iamblichus includes him in his catalog of pythagoreans 1. Theodorus of cyrene was a greek mathematician of the 5th century bc who was admired by plato who mentions him in several of his works, most notably the theatetus. Kyrene was an ancient greek and later roman city near presentday shahhat, libya.
Theaetetus was a disciple of socrates and studied with theodorus of cyrene. He mentions arete of cyrene as one of a long line of women who cultivated their souls. Cyrenaics, ancient cyrene, cyrenaic movement, aristippus, socrates, hegesias, anniceris, theodorus university press scholarship online requires a subscription or purchase to access the full text of books within the service. Theodorus of cyrene wikisource, the free online library. Theodorus the atheist author of opuscula rhetorica goodreads. Although loosely organized around the study of a difference equation that davis dubs theodorus of cyrene, the book takes us on an eclectic whirlwind tour of history, philosophy, anecdote and, of course, mathematics. Research theodorus of cyrene science and its times. Theodorus, however, did not spend his whole life in cyrene for he was certainly in athens at a time when socrates was alive. Theodorus 465 bc 398 bc mactutor history of mathematics. Cyrene is normally said to have been a mortal princess, daughter of king hypseus, king of the lapiths, and an unnamed nymph. Plato travelled to and from egypt and on such occasions he spent time with theodorus in cyrene. Theodorus of cyrene was born 465 bc in cyrene now shahhat, libya. The only firsthand accounts of him that survive are in three of platos dialogues.
Theodorus of cyrene and theaetetus generalised the theory of irrationals, and we may safely conclude that a great part of the substance of euclids book x. Hypseus was a son of the potamoi peneus and creusa, but some would say that cyrene was not a daughter of hypseus but was his sister, having been born to peneus. The only firsthand accounts of him that we have are in two of platos dialogues. Clement of alexandria argued that women as well as men can attain perfection. She spent 33 years of her life teaching natural and moral philosophy at the academies and various schools of attica.
Theodorus was a greek philosopher in the cyrenaic school of moral philosophy. Mathematics is one of the greatest of human intellectual experiences, and as such merits and requires a rather liberal approach. Nihan, the 8th math teacher posted drawings created by students who were studying a geometrical pattern based on the work of a 5th century greek mathematician, theodorous of cyrene. Apr 14, 2015 cyrene was the hometown of many famous greeks. Its incorporation into a later latin account provided the western world.
Sep 02, 2011 history of the recent discoveries at cyrene. He complains of old age in the theaetetus, whose dramatic date of 399 bc suggests his period of flourishing to have occurred in the mid5th century. In the former, his student theaetetus attributes to him the theorem that the square roots of the nonsquare numbers up to 17 are irrational. The principal ideas go back to greek antiquity, specifically to the 5th century b. His first paper was on the history of euclids definition of multiplication. He may have known also of a discrete spiral, today named after him, whose construction is based on the square roots of the numbers n 1, 2, 3. This is a reproduction of a book published before 1923.
The population that cyrene had, is just a matter of speculation, but 5,000 people is a likely guess for a city located at the margin of the greek world. Arete of cyrene and the fathers of the christian church. He was usually designated by ancient writers ho atheos, the atheist. From theodorus to chaos, phil davis writes, to me, mathematics has always been more than its form, or its content, its logic, its strategies, or its applications. Theodorus the atheist, of cyrene, was a philosopher of the cyrenaic school.
Arete of cyrene is found in the work of clement of alexandria, a 2nd century christian father of the church. He discusses the history of attempts to determine theodorus method in his book spirals. Many women studied philosophy during this period, but arete was one of the only ancient women to have an actual career in philosophy. In the former dialogue, he posits a mathematical theorem now known as the spiral of theodorus. Wheel of theodorus project grading rubric grading rubric allows student to track their progress and calculate total possible points earned for the completion of this assigned project. Known as much for his pupils as for his other work, theodorus of cyrene worked on questions involving the square roots of 3 and 5. The points listed represent the maximum total points available for satisfactory completion of each assigned task. Nov 04, 2006 cyrene, the ancient greek city in presentday libya was the oldest and most important of the five greek cities in the region and gave eastern libya the classical name cyrenaica that it has. The amazing artwork in the hallways of the middle school was created by. Mathematicians and their contributions theodorus of cyrene. Made during an expedition to the cyrenaica in 186961, under the auspices of her majestys government smith, robert murdoch, edwin augustus porcher on. Who was one of of theodoruss most influential teachers. Located nearby is the ancient necropolis of cyrene. Eugammon was the author of an important but lost poem about the events after the homecoming of odysseus, the telegony.