1. History Of Mathematics: Greece Apameia Posidonius. Athens Aristotle, Plato, Ptolemy, Socrates, Theaetetus. Byzantium (Constantinople) Philon, Proclus Plato (427347) theaetetus of athens (c. 415-c http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

2. Regular Convex Polytopes A Short Historical Overview, Regular Polytopes And N-di Plato founded a school in Athens "the Academy". In his work Pytagoreans (scholars of phytagoras), the octahedron and icosahedron are due to theaetetus of athens, a friend of Plato http://presh.com/hovinga/regularandsemiregularconvexpolytopesashorthistoricalove

Regular and semi-regular convex polytopes a short historical overview: Dating back from about 500 BC and most likely much earlier a lot of research on the properties of regular polytopes has been carried out. For those who are unfamiliar with this topic an outline of major discoveries is given below in chronological order: Phytagoras born about 569 BC in Samos, Ionia Greece, died about 475 BC. Although early findings acknowledged by mathematicians and historians date back before the time of Phytagoras like the Babylonians who were aquainted with the famous Pythagoras's theorem c^2=a^2+b^2 as early as 3750 BC, this was not discoverd until 1962. Some of the first basic geometric theorems are credited to Phytagoras. Phytagoras is often called the first pure mathematician; he founded a school "the semicircle" and many pupils elaborated on his findings and thoughts. Besides his famous theorem some basic polygon theorems are credited to Phytagoras and his pupils: A polygon with n sides has sum of interior angles 2*n - 4 right angles (90 degrees) and sum of exterior angles equal to four right angles (360 degrees). This was later described in more detail by Euclid.

3. Chapter 16: Archimedes Aristotle, had set up the Lyceum in Athens, and started the systematic classification of human knowledge time, the two greatest were theaetetus of athens and Eudoxus of Cnidus http://www.anselm.edu/homepage/dbanach/arch.htm

Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell) 16. A ROYAL ROAD, AFTER ALL 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

4. Biography-center - Letter T .com/myths/bios/medusa.html. theaetetus of athens, wwwhistory.mcs.st-and.ac.uk/~history/ Mathematicians/Theaetetus.html. Theiler, Max http://www.biography-center.com/t.html

Visit a 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 T 361 biographies Tabern, Donalee L. www.invent.org/hall_of_fame/142.html Tacca, Ferdinand www.getty.edu/art/collections/bio/a451-1.html Tacquet, Andrea www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tacquet.html Taft, Helen Herron www.whitehouse.gov/WH/glimpse/firstladies/html/ht27.html Taft, William Howard odur.let.rug.nl/~usa/P/wt27/about/taftbio.htm Tagore, Rabindranath www.nobel.se/literature/laureates/1913/tagore-bio.html Tahir, ibn www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Baghdadi.html Taiga, Marton www.kirjasto.sci.fi/taiga.htm Taillandier, Vincent www.getty.edu/art/collections/bio/a1075-1.html Tait, Peter Guthrie www-history.mcs.st-and.ac.uk/~history/Mathematicians/Tait.html Takacs, Karoly

5. History Of Mathematics: Chronology Of Mathematicians 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

Chronological List of Mathematicians 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 Table of Contents 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 List of Mathematicians 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

6. 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

Theaetetus of Athens Born: about 417 BC in Athens, Greece Died: about 369 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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.

7. Theaetetus Biography of Theaetetus (417BC369BC) theaetetus of athens. Born about 417 BC in Athens, Greece so then he would have been born when theaetetus of athens was teaching in Heraclea and would http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Theaetetus.html

Theaetetus of Athens Born: about 417 BC in Athens, Greece Died: about 369 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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.

8. Theaetetus theaetetus of athens. Born about 415 BC in Athens, Greece Diedabout 369 BC in Athens, Greece. Show birthplace location http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Thtts.htm

Theaetetus of Athens Born: about 415 BC in Athens, Greece Died: about 369 BC in Athens, Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Theaetetus studied with Theodorus of Cyrene and at the Academy with Plato Theaetetus was the first to study the octahedron and the icosahedron. Euclid 's 10th and 13th books are almost certainly a description of Theaetetus's work. This means that it was Theaetetus's work on irrational lengths which is described in the 10th book, thought by many to be the finest work of the Elements. Theaetetus is also thought to be the author of the theory of proportion which appears in Eudoxus 's work. References (7 books/articles) References elsewhere in this archive: There is a Crater Theaetetus on the moon. You can see a list of lunar features named after mathematicians. Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Theaetetus.html

9. History Of Geometry This page has a short history of geometry and the people who created it. book The Mathematics of Plato's Academy . theaetetus of athens ( 417369 BC BC), collecting the theorems of Pythagoras, Hippocrates, Theaetetus, Eudoxus and other predecessors http://www.geometryalgorithms.com/history.htm

History Home Overview [History] Algorithms Books Gifts Web Sites A Short History of Geometry Ancient This is 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 recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt 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) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

10. 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

THEAETETUS OF ATHENS Ca. 415 BCE to 369 BCE Theaetetus was one of the great mathematicians to work in Athens during the time of Plato . He was considered by his contemporaries as having a unique way of looking at mathematical problems, thus giving him an excellent insight, and was held in the highest esteem by Plato himself. 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. Theaetetus' work with irrationals did not survive, but books X and XIII of Euclid 's Elements are suspected to be based directly on his theories. Theaetetus died in -369 from an infection resulting from injuries that he sustained in a battle against Corinth.

11. 8th Grade Archytas of Tarentum (of Taras) (c. 428c. 347) *SB *MT ·. Plato (427-347) *SB *MT ·. theaetetus of athens (c. 415-c http://mslombardo.freehosting.net/catalog.html

Free Web site hosting - Freeservers.com Web Hosting - GlobalServers.com Choose an ISP NetZero High Speed Internet ... Dial up $14.95 or NetZero Internet Service $9.95 8th Grade Info Home Page 5th Grade 6th Grade 7th Grade ... Guest Book Page Your project You need to hand me a 2 page paper on the mathematician of your choice by May 31st. You must have 3 sources. I have compiled a list of "MaThMaGiCiAnS" you can choose from. Mathmaticians List of Mathematicians 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

12. Mathematicians Archytas of Tarentum (of Taras) (c. 428c. 347) *SB *mt. Plato (427-347) *SB *MT. theaetetus of athens (c. 415-c http://www.chill.org/csss/mathcsss/mathematicians.html

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

13. 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

History Home Overview [History] Algorithms Books Gifts Web Sites A Short History of Geometry Ancient This is 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 recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt 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) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

14. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï BC in Miletus, Asia Minor (now Turkey) Died about 546 BC in Miletos, Turkey Theaetetus,theaetetus of athens Born about 415 BC in Athens, Greece Died about http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=T

15. LookSmart - Directory - 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://search.looksmart.com/p/browse/us1/us317914/us328800/us518756/us549013/

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Mathematicians Other Mathematicians S-V - Read about the lives and works of mathematicians with surnames beginning in the letters S through V. Directory Listings About allRefer Reference - Alfred North Whitehead, Mathematics, Bio Dig into details on life, works, achievements, and background of the English mathematician and philosopher. Link to related terms and browse the bibliography. allRefer Reference - John Von Neumann, 1903-57 Discover details on achievements, background, life, and works of the American mathematician. Find personal memories of this mathematician, who died in 2001 and made many key breakthroughs in the early days of the Internet. Forbes.com - God, Stephen Wolfram, and Everything Else Michael Malone's November, 2000, article profiles the mathematician Stephen Wolfram and his ideas on complexity and order in the universe. MacTutor History of Mathematics - Theaetetus of Athens Resource describes what is known of the life of Theaetetus, the mathematician who is also a character in one of Plato's best known dialogues. MacTutor History of Mathematics Archive - Alfred N. Whitehead

16. Untitled Document results in mathematics is the enumeration of all regular polyhedra, the five Platonicsolids, which were treated mathematically by theaetetus of athens and in http://euch3i.chem.emory.edu/proposal/www.mathematik.uni-bielefeld.de/~huson/edi

Introduction 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. The theory of Delaney symbols, introduced by Andreas Dress (1984, 1987) and inspired by Mathew Delaney (1980), provides a suitable combinatorial framework for formulating, studying and solving classification problems concerning periodic tilings of simply connected manifolds. In this approach, any given d-dimensional periodic tiling is described in terms of its Delaney symbol (D,m), which can also be interpreted as a finite, connected edge- -colored graph with maps defined on its vertices. Based on all this, it seems natural to attempt to develop a computational approach to the theory of tilings, the fundamental idea being to transform problems concerning periodic tilings, symmetric polytopes and symmetry groups into combinatorial problems in terms of Delaney symbols which one then can address and solve using methods of symbolic calculation from combinatorics, algebra and geometry.

17. From Ken.Pledger@vuw.ac.nz (Ken Pledger) Newsgroups Sci.math 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

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

18. 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

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. Some suggestions on the historical perspective might be: (a) Any wars etc. (b) Scientific breakthroughs of the time (c) Major discoveries of the time (d) How did this mathematician change history etc.

19. 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

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 Kepler’s 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 To understand this, one must look at the fact that for any plane tiling

20. Re Leodamas Of Thasos By William C Waterhouse on the First Book of Euclid s Elements, 66 At this time Plato s time also livedLeodamas of Thasos, Archytas of Tarentum, and theaetetus of athens, by whom http://mathforum.org/epigone/math-history-list/frunclypru/199709101926.PAA04076@

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