History Of Mathematics: Greece Plato (427347); theaetetus of athens (c. 415-c. 369); Leodamas of Thasos (c. 380);Leon (fl. c. 375); Eudoxus of Cnidos (c. 400-c. 347); Callipus of Cyzicus (fl. http://aleph0.clarku.edu/~djoyce/mathhist/greece.html
Euclid - Introductory Comments By Proclus Euclid Introductory Comments by Proclus It is a difficult task in any science to select and arrange properly the elements out of which all other matters are produced and into which they can be resolved. time also lived Leodamas of Thasos, Archytas of Tarentum, and theaetetus of athens, by whom the theorems were increased http://www.headmap.com/book/mm/people/proclus.htm
Extractions: Euclid - Introductory Comments by Proclus Proclus's summary Thales, who had travelled to Egypt, was the first to introduce this science into Greece. He made many discoveries himself and taught the principles for many others to his successors, attacking some problems in a general way and others more empirically. Next after him Mamercus, brother of the poet Stesichorus, is remembered as having applied himself to the study of geometry; and Hippias of Elis records that he acquired a reputation in it. Following upon these men, Pythagoras transformed mathematical philosophy into a scheme of liberal education, surveying its principles from the highest downwards and investigating its theorems in an immaterial and intellectual manner. He it was who discovered the doctrine of proportionals and the structure of the cosmic figures. After him Anaxagoras of Clazomenae applied himself to many questions in geometry, and so did Oenopides of Chios, who was a little younger than Anaxagoras. Both these men are mentioned by Plato in the Erastae as having got a reputation in mathematics. Following them Hippocrates of Chios, who invented the method of squaring lunules, and Theodorus of Cyrene became eminent in geometry. For Hippocrates wrote a book on elements, the first of whom we have any record who did so.
Theaetetus theaetetus of athens. The first states (see for example 1). Theaetetus, ofAthens, astronomer, philosopher, disciple of Socrates, taught at Heraclea. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Theaetetus.html
Extractions: Most of what we know of Theaetetus 's life comes from the writing of Plato . It is clear that Plato held Theaetetus in the highest regard and he wrote two dialogues which had Theaetetus as the principal character, one of the dialogues being Theaetetus while the other is the Sophist In Theaetetus a discussion between Socrates , Theaetetus and his teacher Theodorus of Cyrene is recorded. This conversation took place in 399 BC and Theaetetus is described as a youth at the time. This allows us to give a fairly accurate date for Theaetetus's birth (although some have claimed that the Greek word could describe a man of up to 21 years old). Again from Plato we learn that Theaetetus's father, Euphronius of Sunium, was a wealthy man and left a large fortune. However, the money was squandered by the trustees of the will but despite this Theaetetus was generous to all around him. In appearance Theaetetus had a snub nose and protruding eyes but he is described by Plato as having a beautiful mind and he is also described as being the perfect gentleman.
Theaetetus Biography of Theaetetus (417BC369BC) theaetetus of athens. Born about 417 BC in Athens, Greece http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Theaetetus.html
Extractions: Most of what we know of Theaetetus 's life comes from the writing of Plato . It is clear that Plato held Theaetetus in the highest regard and he wrote two dialogues which had Theaetetus as the principal character, one of the dialogues being Theaetetus while the other is the Sophist In Theaetetus a discussion between Socrates , Theaetetus and his teacher Theodorus of Cyrene is recorded. This conversation took place in 399 BC and Theaetetus is described as a youth at the time. This allows us to give a fairly accurate date for Theaetetus's birth (although some have claimed that the Greek word could describe a man of up to 21 years old). Again from Plato we learn that Theaetetus's father, Euphronius of Sunium, was a wealthy man and left a large fortune. However, the money was squandered by the trustees of the will but despite this Theaetetus was generous to all around him. In appearance Theaetetus had a snub nose and protruding eyes but he is described by Plato as having a beautiful mind and he is also described as being the perfect gentleman.
T Index Thales of Miletus (2091*). theaetetus of athens (1320). Theodorus of Cyrene (673) http://www-groups.dcs.st-and.ac.uk/~history/Indexes/T.html
History Of Mathematics: Chronology Of Mathematicians A list of all of the important mathematicians working in a given century.Category Science Math Mathematicians Directories 347) *SB *MT; Plato (427347) *SB *MT; theaetetus of athens (c. 415-c.369) *MT; Leodamas of Thasos (fl. c. 380) *SB; Leon (fl. c. 375 http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html
Extractions: Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below Ahmes (c. 1650 B.C.E.) *MT Baudhayana (c. 700) Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB
Title theaetetus of athens Ca. 415 BCE to 369 BCE Theaetetus was one of the greatmathematicians to work in Athens during the time of Plato. http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/theattext.html
Extractions: In Euclid 's Elements , Theaetetus is credited with discovering the octahedron and icosahedron. Theaetetus also proved the existence of irrational numbers, a discovery that rendered many Pythagorean proofs as invalid and threw the Greek mathematical community into a crisis. This problem was soon solved by Eudoxus . It is not entirely clear if Eudoxus ' theory of proportions, which allowed him to solve the irrationality crisis actually came from Theaetetus but as we have no evidence to the contrary, Eudoxus has generally been given that credit.
History Of Geometry Mathematics of Plato's Academy . theaetetus of athens (417369 BC) wasa student of Plato's, and the creator of solid geometry. He was the http://geometryalgorithms.com/history.htm
Extractions: A Short History of Geometry Ancient This page gives a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland). Also, Click these links for our recommended: Greek Medieval Modern History Books ... History Web Sites The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs India (1500 BC - 200 BC)
Jays Web Magazine 5th century), the theoretical form of geometry was advanced by others, most prominentlythe Pythagorean Archytas of Tarentum, theaetetus of athens, and Eudoxus http://www.jaysnet.com/666revelation2.html
Extractions: In Christianity, the first and last letters of the Greek alphabet, used to designate the comprehensiveness of God, implying that God includes all that can be. In the New Testament Revelation to John, the term is used as the self-designation of God and of Christ. The reference in Revelation likely had a Jewish origin, based on such Old Testament passages as Isa. 44:6 ("I am the first and the last"), and Ps. 90:2 ("from everlasting to everlasting thou art God"). In rabbinic literature, the word emet ("truth"), composed of the first and last letters of the Hebrew alphabet, is "the seal of God," and in Judaic tradition it carries somewhat the same connotation as Alpha and Omega. Such hints about the nature of early Greek practical mathematics are confirmed in later sources, for example, in the arithmetic problems in papyrus texts from Ptolemaic Egypt (from the 3rd century BC onward) and the geometric manuals by Hero of Alexandria (1st century AD). In its basic manner this Greek tradition was much like the earlier traditions in Egypt and Mesopotamia. Indeed, it is likely that the Greeks borrowed from such older sources to some extent. Before the discovery of the celebrated Dead Sea Scrolls, several Square Hebrew inscriptions belonging mainly to the 1st century BC and the succeeding centuries were known; they were found on rocks, tombs, or ossuaries (depositories for the bones of the dead) and in synagogues and catacombs in Palestine, Syria, North Africa, and Italy. The biblical manuscripts, except for some fragments written on papyrus, belong to a much later date. The earliest fragment is the Nash papyrus of approximately the 1st century BC, now in the University of Cambridge Library. Many thousands of fragments of Hebrew biblical and other manuscripts, partly of the 7th and 8th centuries AD, were discovered in the Geniza, an archive in the old synagogue in Cairo.
Chapter 16: Archimedes many of the irrationals. In Plato's own time, the two greatest weretheaetetus of athens and Eudoxus of Cnidus. And at the Lyceum http://www.anselm.edu/homepage/dbanach/arch.htm
Extractions: During the 4th century B.C., Greek geometry burst its bonds and went on to the tremendous discoveries of the "age of giants." And Greek culture, too, burst from the mainland of Hellas and spread to most of the eastern Mediterranean. Both developments were connected with the romantic figure of Alexander the Great. After Plato's time, teachers and alumni from the Academy had gone on to found schools of their own. In particular, Plato's most famous associate, the great philosopher Aristotle, had set up the Lyceum in Athens, and started the systematic classification of human knowledge. And Aristotle's most renowned pupil was the warrior king Alexander of Macedon, who tried to conquer the world. In thirteen years, Alexander extended his rule over Greece proper, and Ionia, Phoenicia, Egypt, and the vast Persian domains as far as India. Then he died, and his empire broke up. But throughout those far-flung lands, he had founded Greek cities and planted the seeds of Greek civilization-the Greek language, Greek art, and, of course, Greek mathematics. Mathematicians traveled with his armies. And there is even a
Www.math.niu.edu/~rusin/known-math/98/sqrt_irrat theaetetus of athens, a student of Theodorus, may have had a lot to do with provingthat sqrt(n) is irrational whenever the natural number n is not a perfect http://www.math.niu.edu/~rusin/known-math/98/sqrt_irrat
Extractions: From: Ken.Pledger@vuw.ac.nz (Ken Pledger) Newsgroups: sci.math Subject: Irrationals (was Re: please don't laugh...) Date: Wed, 09 Dec 1998 15:05:55 +1200 In article Newsgroups: sci.math Subject: Re: how to prove: if x is not a perfect square, sqr (x) is irrational, x positive integer Date: Sat, 12 Dec 1998 23:12:34 -0500 On Sat, 12 Dec 1998, TS wrote: :Date: Sat, 12 Dec 1998 20:40:37 GMT :From: TS
Biography-center - Letter T myths/bios/medusa.html; theaetetus of athens, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Theaetetus.html;Theiler, Max www http://www.biography-center.com/t.html
Extractions: random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish 340 biographies Tabern, Donalee L.
Theaetetus theaetetus of athens. The first states (see for example 1) Theaetetus, ofAthens, astronomer, philosopher, disciple of Socrates, taught at Heraclea. http://math.ichb.ro/History/Mathematicians/Theaetetus.html
Combinatorial Tiling Theory results in mathematics is the enumeration of all regular polyhedra, the five Platonicsolids, which were treated mathematically by theaetetus of athens and in http://www.mathematik.uni-bielefeld.de/~huson/approach.html
Extractions: Clearly, the art of designing tilings and patterns is very old and well developed. But also the science of tilings and patterns, i.e. the study of their mathematical properties, has its roots in antiquity. One of the earliest known results in mathematics is the enumeration of all regular polyhedra, the five Platonic solids, which were treated mathematically by Theaetetus of Athens and in Euclid's Elements over 2000 years ago. The classification of all 13 semi-regular polyhedra goes back to Archimedes and earlier. A further milestone is Kepler's work (1571-1630) on 2- and 3-dimensional packings and tilings, such as the classification of all Archimedian tilings of the plane. Let be an index set. Recall that a Coxeter matrix M:IxI -> N is a map with Mii=1 and Mij>1 (if i not equal to j), that is often depicted as a graph with vertex set I, in which any two vertices i,j with are connected by an edge labeled Mij. Interpreting each i in I as a mirror and Mij as the angle between two such mirrors, Coxeter (1934) used these matrices (or graphs) to systematically investigate d-dimensional symmetry groups generated by reflections. In their comprehensive book, Gruenbaum and Shephard survey the work devoted to the classification of periodic patterns and tilings (1987). Many papers have been written on the subject, especially in the two-dimensional case. For example, the classification of all tile-transitive tilings of the plane is treated in (Delone 1959, Delone et al. 1978, Heesch 1968, Gruenbaum and Shephard 1979). Later, this classification was again derived as a simple and paradigmatic application of Delaney symbols in (Dress and Scharlau 1984). Similarly, all tile-transitive tilings of the sphere are classified in (Gruenbaum and Shephard 1981). However, for all the problems solved, the book also showed that a systematic approach to the classification of two- and higher-dimensional periodic tilings was missing.
Henry Mendell Articles on Theodorus of Cyrene and theaetetus of athens, Aristarchus of Samos , Nicomachus of Gerasa in The Encyclopedia of Classical Philosophy (ed. D http://www.ceu.hu/sun/sun 2003 modmod/CV/henry_mendell_2003.htm
Extractions: Central European University A Program for University Teachers, Researchers and Professionals in the Social Sciences and Humanities Summer University you are visitor no. Henry Mendell Philosophy Department, California State University, Los Angeles5151 State U. Dr. Education 1977-85: Stanford University (Ph.D. Jan., 1986) AOC: Philosophy of Science, Metaphysics Publications Book with Pat Suppesand Julius Moravcsik (eds.). Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr. Stanford: CSLI (distr. University of Chicago Press), 2001. Articles "The Trouble withEudoxus". In Pat Suppes, Julius Moravcsik, and Henry Mendell (eds.), Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr (Stanford: CSLI (distr. University of Chicago Press), 2001), 59-138 "Making Sense of Aristotelian Demonstration". Oxford Studies in Ancient Philosophy, 16 (1998), 160-225.
Mathematicians Archytas of Tarentum (of Taras) (c. 428c. 347) *SB *mt. Plato (427-347) *SB *MT.theaetetus of athens (c. 415-c. 369) *mt. Leodamas of Thasos (fl. c. 380) *SB. http://www.chill.org/csss/mathcsss/mathematicians.html
Extractions: List of Mathematicians printed from: http://aleph0.clarku.edu:80/~djoyce/mathhist/mathhist.html 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *mt 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *mt Zeno of Elea (c. 490-c. 430) *mt Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *mt Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *mt Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB Hippias of Elis (fl. c. 425) *SB *mt Theodorus of Cyrene (c. 425) Socrates (469-399) Philolaus of Croton (d. c. 390) *SB Democritus of Abdera (c. 460-370) *SB *mt 400 B.C.E. Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?) Archytas of Tarentum (of Taras) (c. 428-c. 347) *SB *mt Plato (427-347) *SB *MT Theaetetus of Athens (c. 415-c. 369) *mt Leodamas of Thasos (fl. c. 380) *SB
LookSmart - Other Mathematicians S-V MacTutor History of Mathematics theaetetus of athens Resource describes what isknown of the life of Theaetetus, the mathematician who is also a character in http://canada.looksmart.com/eus1/eus302562/eus317836/eus317914/eus328800/eus5187
Mid Sessional Project Report theaetetus of athens began work into the science of tiling over 2000 years ago.Other famous mathematicians in this field include Archimedes and Kepler. http://rockall.mech.kcl.ac.uk/flyeye/tiling.htm
Extractions: 1.2 Tiling and Patterns The art of tiling and patterns has been developed over the millennia, with ancient tillings and mosaics found, for example, in ancient Roman mosaics, such as the one on the left . This mosaic displays the classic properties of any tiling, with shapes repeating to from a tightly packed planar surface with no apparent gaps. The drosophila eye can be viewed as a tiling of perfectly hexagonal tiles. To accurately study this one must look at the science of tilings. Tilings can be viewed not simply as works of art, but as mathematically and scientifically intriguing complex field. This field has existed for almost as long as the tilings themselves. Theaetetus of Athens began work into the science of tiling over 2000 years ago. Other famous mathematicians in this field include Archimedes and Kepler. An example of Keplers work is shown to the right. To evaluate the implications on fly eye growth using this science, an assessment of similar tilings, consisting of regular polygons must be carried out. As was known back in Archimedes time, there are only three regular polygons, (angles and side lengths uniform) that will tessellate. These are the triangle, square and regular hexagon. Tilings of these are shown below
Mathem_abbrev Tusi, Nasir al Tusi, Sharaf al Tartaglia, Nicolo Taylor, Geoffrey Temple, GeorgeThabit ibn Qurra, Abu'l Thales of Miletus theaetetus of athens, Theodosius of http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm
Extractions: Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive.
