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         Bryson Of Heraclea:     more detail
  1. Bryson of Heraclea: An entry from Gale's <i>Science and Its Times</i>

1. Bryson Origins
Variations Bricen, Brison, Brisson, Bruson, Bryceson, Brydeson, Bryson. The earliest known bearer of the name was bryson of heraclea, a mathematician of ancient Greece around 350 BC, who devised a
http://www.brysonclan.net/old.htm
Variations: Bricen, Brison, Brisson, Bruson, Bryceson, Brydeson, Bryson
The earliest known bearer of the name was Bryson of Heraclea, a mathematician of ancient Greece around 350 BC, who devised a new way of squaring a circle. Naturally, no modern Bryson can trace their lineage back to the original Bryson, but our name is very old. Unfortunately that age also clouds its origin. However, we have several theories based on fragmentary records. One legend told in the family is that two missionaries were sent from Rome to both France and Scotland. The missionary to France became known as Brisson. The missionary to Scotland became known as Bryson. Legend fables that we are the descendants of that Bryson. One creditable theory has some similarity to the missionary legend. It links the family with the French Brissons but as ancestors not comrades. This theory holds that the family descended from French Huguenots named Brisson. Around the time of the Massacre on St. Bartholomew Day in 1512 they escaped from France to Scotland, Ireland, and England. Their name gradually changed to the more anglicized Bryson with each passing year. Another theory has the family originating from Ulster, particularly in Counties Donegal and Derry. The earlier spelling of the name was Mrieson with similar variants. The Bryson and Morrison names evolved from those earlier Gaelic names. This theory holds that at least some of the Irish Brysons developed independent of the Scot Brysons.

2. The Clan Bryson
earliest known bearer of the name was bryson of heraclea, a mathematician of ancient Greece Naturally, no modern Bryson can trace their lineage back to the original Bryson, but our
http://www.irishclans.com/cgi-bin/iclans.cgi/clandisplay/site/goti/iclans?alias=

3. ThinkQuest : Library : 3.14ever
Two of the first Greeks to discover Pi were Antiphon and bryson of heraclea. They tried finding people to follow in Antiphon and Bryson's footsteps. When Archimedes started studying
http://library.thinkquest.org/CR0213924/history.html
Index Math
The website 3.14ever is devoted to the teaching of Pi and Pi history. Visit Site 2002 ThinkQuest USA 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

4. The History Of ?
The History of Pi. David Wilson. History of Mathematics. Rutgers, Spring 2000 Antiphon and bryson of heraclea came up with the innovative idea of inscribing a polygon circle" (Blatner, 16) .
http://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html
The History of Pi
David Wilson
History of Mathematics
Rutgers, Spring 2000
Throughout the history of mathematics, one of the most enduring challenges has been the calculation of the ratio between a circle's circumference and diameter, which has come to be known by the Greek letter pi . From ancient Babylonia to the Middle Ages in Europe to the present day of supercomputers, mathematicians have been striving to calculate the mysterious number. They have searched for exact fractions, formulas, and, more recently, patterns in the long string of numbers starting with 3.14159 2653..., which is generally shortened to 3.14. William L. Schaaf once said, "Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi" (Blatner, 1). We will probably never know who first discovered that the ratio between a circle's circumference and diameter is constant, nor will we ever know who first tried to calculate this ratio. The people who initiated the hunt for pi were the Babylonians and Egyptians, nearly 4000 years ago. It is not clear how they found their approximation for pi, but one source (Beckman) makes the claim that they simply made a big circle, and then measured the circumference and diameter with a piece of rope. They used this method to find that

5. History Of Mathematics: Chronology Of Mathematicians
370) *SB. Xenocrates of Chalcedon (c. 396314) Heraclides of Pontus (c. 390-c. 322) bryson of heraclea (c 350
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. 8th Grade
Xenocrates of Chalcedon (c. 396314) ·. Heraclides of Pontus (c. 390-c. 322) ·. bryson of heraclea (c 350
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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

7. Bryson
bryson of heraclea. Born about 450 BC in Heraclea (now Taranto, Italy) Died ? Aristotlementions bryson of heraclea, who was the son of Herodorus of Heraclea.
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bryson.html
Bryson of Heraclea
Born: about 450 BC in Heraclea (now Taranto, Italy)
Died:
Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Plato
and Aristotle both mention a mathematician called Bryson, but as is often the case, there is not complete agreement among scholars as to whether these refer to the same person or to two different people. Aristotle mentions Bryson of Heraclea, who was the son of Herodorus of Heraclea. Bryson was a Sophist and Aristotle criticises him both for his assertion that there is no such thing as indecent language, and also for his method of squaring the circle . We do know some details of this methods of squaring the circle and, despite the criticisms of Aristotle , it was an important step forward in the development of mathematics. Aristotle 's criticism appears to have been based on the fact that Bryson's proof used general principles rather than on geometric ones, but it is somewhat unclear exactly what Aristotle meant by this. Diogenes Laertius gives some other biographical details of Bryson, but these cannot all be correct since Bryson's interaction with a number of philosophers is stated, yet certain of these are impossible due to the dates during which these men lived. Perhaps the most likely of the details preserved by Diogenes Laertius is that Bryson was either a pupil of Socrates or of Euclid of Megara It is a little difficult to reconstruct exactly what Bryson's method of squaring the circle was. According to Alexander Aphrodisiensis, writing in about 210 AD, Bryson

8. B Index
Filippo (1667*) Bruno, Francesco Faà di (521*) Bruno, Giuseppe (297) Bruno, Giordano(1891*), Bruns, Heinrich (90*) bryson of heraclea (527) Buckminster Fuller
http://www-gap.dcs.st-and.ac.uk/~history/Indexes/B.html
Names beginning with B
The number of words in the biography is given in brackets. A * indicates that there is a portrait. Babbage , Charles (2793*)
Bachelier
, Louis (1384*)
Bachet
, Claude (165)
Bachmann
, Paul (386*)
Backus
, John (542*)
Bacon
, Roger (657*)
Baer
, Reinhold (596*)
Baghdadi
, Abu al (947)
Baire

Baker
, Alan (647*)
Baker
, Henry (794*) Ball , Walter W Rouse (706) Balmer , Johann (601*) Banach , Stefan (2533*) Banneker , Benjamin (892*) Banna , al-Marrakushi al (861) Banu Musa brothers Banu Musa, al-Hasan Banu Musa, Ahmad Banu Musa, Jafar ... bar Hiyya , Abraham (641) Barbier , Joseph Emile (637) Bari , Nina (403*) Barlow , Peter (623) Barnes , Ernest (609*) Barocius , Franciscus (201) Barrow , Isaac (2332*) Barozzi , Francesco (201) Bartholin , Erasmus (189) Batchelor , George (1035*) Bateman , Harry (1651*) Battaglini , Guiseppe (102*) Baudhayana Battani , Abu al- (1333*) Baxter , Agnes (624*) Bayes , Thomas (538*) Beaugrand , Jean (222) Beaune , Florimond de (316) Beg , Ulugh (1219*) Bell, Eric Temple Bell, John Bellavitis , Giusto (762*) Beltrami , Eugenio (1057*) ben Ezra , Abraham (552) ben Gerson , Levi (268) ben Tibbon , Jacob (198) Bendixson , Ivar Otto (1208*) Benedetti , Giovanni (211) Bergman , Stefan (311*) Berkeley , George (239*) Bernays , Paul Isaac (772*) Bernoulli, Daniel

9. Bryson
Biography of Bryson (450BC390BC) bryson of heraclea. Born about 450 BC in Heraclea (now Taranto, Italy Aristotle mentions bryson of heraclea, who was the son of Herodorus of Heraclea. Bryson was a
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bryson.html
Bryson of Heraclea
Born: about 450 BC in Heraclea (now Taranto, Italy)
Died:
Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
Plato
and Aristotle both mention a mathematician called Bryson, but as is often the case, there is not complete agreement among scholars as to whether these refer to the same person or to two different people. Aristotle mentions Bryson of Heraclea, who was the son of Herodorus of Heraclea. Bryson was a Sophist and Aristotle criticises him both for his assertion that there is no such thing as indecent language, and also for his method of squaring the circle . We do know some details of this methods of squaring the circle and, despite the criticisms of Aristotle , it was an important step forward in the development of mathematics. Aristotle 's criticism appears to have been based on the fact that Bryson's proof used general principles rather than on geometric ones, but it is somewhat unclear exactly what Aristotle meant by this. Diogenes Laertius gives some other biographical details of Bryson, but these cannot all be correct since Bryson's interaction with a number of philosophers is stated, yet certain of these are impossible due to the dates during which these men lived. Perhaps the most likely of the details preserved by Diogenes Laertius is that Bryson was either a pupil of Socrates or of Euclid of Megara It is a little difficult to reconstruct exactly what Bryson's method of squaring the circle was. According to Alexander Aphrodisiensis, writing in about 210 AD, Bryson

10. ThinkQuest : Library : A Taste Of Mathematic
390c. 322); bryson of heraclea (c 350?); Menaechmus (c. 350); Theudiusof Magnesia (c. 350?); Thymaridas (c. 350); Dinostratus (c. 350
http://library.thinkquest.org/C006364/ENGLISH/history/historygreece.htm
Index Math
A Taste of Mathematic
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

11. Biography-center - Letter B
.com/doctor.cfm/2542.html. bryson of heraclea, wwwhistory.mcs.st-and.ac.uk/~history/ Mathematicians/Bryson.html. Buber, Martin
http://www.biography-center.com/b.html
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B
1183 biographies

12. GEOMETRY
bryson of heraclea took an important step when he circumscribed, in addition toinscribing, polygons to a circle, but he committed an error in treating the
http://18.1911encyclopedia.org/G/GE/GEOMETRY.htm
GEOMETRY
GEOMETRY It is convenient to discuss the subject-matter of geometry under the following headings: I. Euclidean Geometry: a discussion of the axioms of existent space and of the geometrical entities, followed by a synoptical account of Euclids Elements. II, Projective Geometry: primarily Euclidean, but differing from I. in employing the notion of geometrical continuity (q.v.) points and lines at infinity. III. Descriptive Geometry: the methods for representing upon planes figures placed in space of three dimensions. V. Line Geometry: an analytical treatment of the line regarded as the space element. VT. Non-Euclidean Geometry: a discussion of geometries other than that of the space of experience. VII. Axioms of Geometry: a critical analysis of the foundations of geometry. ~A fresh stimulus was given by, the succeeding Platonists, who, accepting in part the Pythagorean. cosmology, made the study of geometry preliminary to that of philosophy. The many discoveries made by this school were facilitated in no small measure by the clarification of the axioms and definitions, thc logical sequence of propositions which was adopted, and, mor especially, by the formulation of the analytic method, i,e. ol assuming the truth of a proposition and then reasoning to 1 i For Egyptian geometry see EGYPT. Science and Matherna~ics.

13. History Of Mathematics: Greece
370) Xenocrates of Chalcedon (c. 396314) Heraclides of Pontus (c. 390-c. 322) bryson of heraclea (c 350
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)

14. GottliebMath: Pi: History
bryson of heraclea was the first person to try to calculate pi using a valuegreater than that of pi and one below pi (by inscribing and circumscribing
http://www.joshgottlieb.net/gottliebmath/pi/history.html
GOTTLIEBMATH:PI:HISTORY History Page *Pi to 100 decimal places This page lists the main events in the history of, what is, in my opinion, the most important number that exists: the irrational, transcendental ratio of a circle's circumference to its diameter known to the world as Click here for the main page Click here for a list of formulas to calculate I would like to thank all of the references where I got much of the information for this page. Welcome to... THE PI HISTORY PAGE VERY EARLY PI (up to c. 500 BCE) THE GREEKS (c. 500 BCE to c. 0) PROGRESS IN ASIA (c. to c. 1000 CE) DIGITS GALORE! (c. 1000 CE to c. 1900 CE) ... THE ELECTRONIC AGE (1946 CE to present) VERY EARLY PI (up to c. 500 BCE) Back to Index of Time
  • The first known mention of the ratio of circumference to diameter was written by Ahmes, an Egyptian scribe around 1650 BCE on the Rhind Papyrus. He implied that pi=256/81=3.16049..., less than 1% greater than our current value of 3.141592...! Even though he figured out a value for pi, it is doubtful he knew how to use it for circumference: the Rhind Papyrus talks about making a square whose area is equal to a circle's by using 8/9 of the diameter as one side. But the rest of the world didn't learn of his discovery: By 650 BCE, the Babylonians and the Jews were still using 3 for pi. In fact, the bible declares that the value of pi is 3: "Also he made a molten sea of ten cubits from brim to brim [diameter], round in compass....and a line of thirty cubits did compass it round about [circumference]."

15. Full Alphabetical Index
Translate this page 300*) Brouwer, LEJ (419*) Brown, Ernest (470*) Bruno, Francesco Faà di (521*) Bruno,Giuseppe (294) Bruns, Heinrich (90*) bryson of heraclea (527) Budan de
http://alas.matf.bg.ac.yu/~mm97106/math/alphalist.htm
Full Alphabetical Index
The number of words in the biography is given in brackets. A * indicates that there is a portrait.
A
Abbe , Ernst (602*)
Abel
, Niels Henrik (2899*)
Abraham
bar Hiyya (641)
Abraham, Max

Abu Kamil
Shuja (1012)
Abu Jafar

Abu'l-Wafa
al-Buzjani (1115)
Ackermann
, Wilhelm (205)
Adams, John Couch

Adams, J Frank

Adelard
of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (12)

16. Table Of Contents
HIPPIAS OF ELIS. THE ODOROS OF CYRENE. ANTIPHON THE SOPHIST. bryson of heraclea.ASTRONOMY. PARMENIDES OF ELEA. PHILOLAOS OF CROTON. HICETAS OF SYRACUSE.
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Table of Contents for Ancient Science Through the Golden Age of Greece Introduction to the Dover Edition Acknowledgments The Meaning of Abstraction The Evolution of Abstraction Learning the Abstract Language Words vs. Images

17. Sci.math Message
The first ones I m aware of doing this are the Greek philosophers/mathematiciansAntiphon and bryson of heraclea (469399 BCE) who were trying to find the area
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18. Historyofpi
The Principle of exhaustion was developed in around 400BC by Antiphonand bryson of heraclea. This involved working out the area
http://students.bath.ac.uk/ns1pnb/historyofpi.htm
The Early History of Pi
was first calculated in about 1650BC by Ahmes who was an Egyptian scribe. His writings were known as the Rhind Papyrus. In his words "cut off 1/9 of a diameter and construct a square upon the remainder; this has the same area as the circle". These days, knowing that the area of a cirlce is r , if the area of a square is 8/9, then Ahmes' theory implies that the ratio of the circumference to the diameter is 3.16049 and therefore his prediction of . However, Ahmes' word did not spread far. The Rhind Papyrus is the first recording of a circle being squared. This technique is one of the oldest mathematical problems and still continues to appear through history. The Rhind Papyrus was translated and explained by Eisenlohr in 1877 in
Pi and the Greeks
The Greeks studied the idea of the measure of circles between 500BC and 200BC. Their main interest in was for exploring and expanding their minds - not the idea of measuring land and for buildings. Anaxagoras of Clazomenae tried to find a definite relationship between squares and circles and was able to invent a way of drawing a square which had an area equal to a circle. The Principle of exhaustion was developed in around 400BC by Antiphon and Bryson of Heraclea. This involved working out the area of a circle by doubling the sides of a hexagon and repeating this several times. The idea was that eventually, the polygon would have so many sides that it would now have become a circle.

19. Godlike Productions -- Forum Archives
c. 370) *SB Xenocrates of Chalcedon (c. 396314) Heraclides of Pontus (c. 390-c.322) bryson of heraclea (c 350?) Menaechmus (c. 350) *SB Theudius of Magnesia
http://godlikeproductions.com/bbs/message.php?page=64&topic=3&message=278278&mpa

20. Sci.math Message
The first ones I m aware of doing this are the Greek philosophers/mathematiciansAntiphon and bryson of heraclea (469399 BCE) who were trying to find the
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previous next Message: Re: Is this Pi formula of any worth?
Subject:
Re: Is this Pi formula of any worth?
Author: bobbysim2000@aol.comme
Date Posted: Sep 2 2003 3:30:17:000PM
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