1. Hippocrates Of Chios --  Encyclopædia Britannica MLA style " hippocrates of chios." Encyclopædia Britannica. 2004 APA style hippocrates of chios. Encyclopædia Britannica. Retrieved April 27, 2004, from Encyclopædia Britannica http://www.britannica.com/eb/article?eu=41418

2. Hippocrates Of Chios (ca. 450 BC) -- From Eric Weisstein's World Of Scientific B Mathematicians. Nationality. Greek. hippocrates of chios (ca. 450 BC) Dunham, W. " Hippocrates' Quadrature of the Lune." Ch. 1 in Journey Through Genius The Great Theorems of Mathematics. New York http://scienceworld.wolfram.com/biography/HippocratesofChios.html

Branch of Science Mathematicians Nationality Greek Hippocrates of Chios (ca. 450 BC) Greek mathematician who squared lunes in the 5th century B. C. Additional biographies: Greek and Roman Science and Technology References Dunham, W. "Hippocrates' Quadrature of the Lune." Ch. 1 in Journey Through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 1-20, 1990. Heath, T. L. A History of Greek Mathematics, Vol. 1: From Thales to Euclid. New York: Dover, p. 185, 1981.

3. Hippocrates, Part 1 Four Areal Views. Introduction. The story of mathematics, and the achievements and biographies of its practitioners, is intriguing in every way. read in a book of mathematical history that hippocrates of chios, contemporary of Plato in 5th century B as a center of learning. hippocrates of chios, the lunesquarer, was http://doe.ncia.net/~bobmead/hippoc1.htm

Home Math History Articles Graduate Projects ... Other GSP Sketchpads Four Areal Views Introduction The story of mathematics, and the achievements and biographies of its practitioners, is intriguing in every way. This series of articles will trace one concept, that of the area of planar figures, through four eras in history. We will see those particular problems and applications of area measurement that faced mathematicians in each era. We will examine the strengths and weaknesses of various approaches. We will see evidence of startling creativity in the solutions, and what is more, we will see the "look" and substance of mathematics change forever. In Part One we visit ancient Greece and witness their best minds struggle with making geometry a logical system. We will see their attempts to create a basis of comparison for all planar areas in a topic known as quadrature. Each achievement gave rise to many new questions. An important one to keep in mind as you read is: could Euclidian geometry ever reach the degree of comprehensiveness and efficiency needed to solve all the quantitative problems of our universe? In Part Two we will see the achievements of ancient cultures, both Eastern and Western, congregate and synthesize in the Arabian Empire after the fall of Rome. A system to be known as algebra will unify much of Greek geometry, Hindu number theory, and application problems from the earliest civilizations. Area will be a key link in the theory of quadratics.

4. Famous Mathematician - Hippocrates Hippocrates. Full Name hippocrates of chios. Lived Between 470410 BC. Nationality Greek. Primary Occupation Geometer. Claim to Fame Hippocrates worked on the problems of squaring the circle duplicating the cube. http://www.famousmathematician.com/profiles/hippocrates.htm

Hippocrates Full Name: Hippocrates of Chios Lived Between: 470-410 BC Nationality: Greek Primary Occupation: Geometer Claim to Fame: Hippocrates worked on the problems of squaring the circle duplicating the cube. Hippocrates was the first to square three of the four lunes, Quadrature of the circle was the prominent problem of Greek mathematics. Recommended Book: Journey Through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 1-20, 1990. Recommended Link: Hippocrates Quadrature of the Lune Send mail to webmaster@famousmathematician.com with questions or comments about this web site. www.famousmathematician.com Last modified: January 23, 2003

5. Hippocrates hippocrates of chios. hippocrates of chios taught in Athens and worked on theclassical problems of squaring the circle and duplicating the cube. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hippocrates.html

Hippocrates of Chios Born: about 470 BC in Chios (now Khios), Greece Died: about 410 BC Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating the cube Iamblichus [4] writes:- One of the Pythagoreans Hippocrates lost his property, and when this misfortune befell him he was allowed to make money by teaching geometry. Heath [6] recounts two versions of this story:- One version of the story is that Hippocrates was a merchant, but lost all his property through being captured by a pirate vessel. He then came to Athens to persecute the offenders and, during a long stay, attended lectures, finally attaining such proficiency in geometry that he tried to square the circle. Heath also recounts a different version of the story as told by Aristotle ... he allowed himself to be defrauded of a large sum by custom-house officers at Byzantium, thereby proving, in Aristotle 's opinion, that, though a good geometer, he was stupid and incompetent in the business of ordinary life.

6. Hippocrates Biography of Hippocrates (470BC410BC) hippocrates of chios. Born about 470 BC in Chios (now Khios), Greece hippocrates of chios taught in Athens and worked on the classical problems of squaring the circle and http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hippocrates.html

Hippocrates of Chios Born: about 470 BC in Chios (now Khios), Greece Died: about 410 BC Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating the cube Iamblichus [4] writes:- One of the Pythagoreans Hippocrates lost his property, and when this misfortune befell him he was allowed to make money by teaching geometry. Heath [6] recounts two versions of this story:- One version of the story is that Hippocrates was a merchant, but lost all his property through being captured by a pirate vessel. He then came to Athens to persecute the offenders and, during a long stay, attended lectures, finally attaining such proficiency in geometry that he tried to square the circle. Heath also recounts a different version of the story as told by Aristotle ... he allowed himself to be defrauded of a large sum by custom-house officers at Byzantium, thereby proving, in Aristotle 's opinion, that, though a good geometer, he was stupid and incompetent in the business of ordinary life.

7. H Index 1657*) Hill, George (514*) Hille, Einar (1295*) Hindenburg, Carl (512) Hipparchusof Rhodes (2557*) Hippias of Elis (904) hippocrates of chios (1282*) Hire http://www-gap.dcs.st-and.ac.uk/~history/Indexes/H.html

Names beginning with H The number of words in the biography is given in brackets. A * indicates that there is a portrait. Haar Hachette , Jean (944*) Hadamard , Jacques (2759*) Hadley , John (191*) Hahn , Hans (138*) , Jaroslav (907*) Haitam , Abu Ali al- (2490*) Hall, Marshall Jr. Hall, Philip Halley , Edmond (2532*) Halmos , Paul (1328*) Halphen , George (872*) Halsted , George (299*) Hamill , Christine (445) Hamilton, William Hamilton, William R Hamming , Richard W (582*) Hankel , Hermann (546*) Hardy, Claude Hardy, G H Harish-Chandra Harriot , Thomas (3306*) Hartley , Brian (466*) Hartree , Douglas (696*) Hasib Abu Kamil al (1012) Hasse , Helmut (1189*) Hatvani Hau , Lene (1018*) Hausdorff , Felix (345*) Hawking , Stephen (1282*) Hay , Louise (2037*) Hayes , Ellen (1060*) Hazlett , Olive (1345*) Haytham , Abu Ali al (2490*) Heath , Thomas (822*) Heaviside , Oliver (1270*) Heawood , Percy (730*) Hecht , Daniel (117) Hecke , Erich (730*) Hedrick , Earle (501*) Heegaard , Poul (380*) Heilbronn , Hans (2122*) Heine , Eduard (268*) Heisenberg , Werner (2631*) Hellinger , Ernst (1233*) Helly , Eduard (909*) Helmholtz , Hermann von (2214*) Heng , Zhang (1481*) Henrici , Olaus (117*) Hensel , Kurt (252*) Heraclides of Pontus (773*) Herbrand , Jacques (376*) , Pierre (148) Hermann , Jakob (267*) Hermann of Reichenau Hermite , Charles (1849*) Heron of Alexandria (2275) Herschel, Caroline

8. Hippocrates Of Chios hippocrates of chios (ca. 470ca. 410 BC). Greek mathematician Hippocratesworked in classic problems of geometry, such as squaring the circle. http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib

Hippocrates of Chios (ca. 470ca. 410 B.C. Greek mathematician Hippocrates worked in classic problems of geometry, such as squaring the circle. He taught in Athens. Much of his geometry was contained in his lost work entitled Elements of Geometry . That work is contained in the first two books of Euclid's Elements . His book also contained solutions to quadratic equations and rudimentary methods of integration

9. Hippocrates Of Chios © 1998 Bernard SUZANNE. Last updated December 5, 1998. Plato and his dialogues Home Biography - Works - History of interpretation - New hypotheses - Map of dialogues table version or non tabular version. Hippocrates, born in the island of Chios, in Ionia, started, according to a tradition to square the circle, Hippocrates adressed the problem of the surface of lunes, figures http://www.dialogues-de-platon.org/tools/char/hipchios.htm

Bernard SUZANNE Last updated December 5, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations Hippocrates, born in the island of Chios , in Ionia, started, according to a tradition recorded in Philoponus' Commentary on Aristotle's Physics , as a merchant and came to Athens to prosecute pirates who had robbed him of all his goods. Required to stay there for a while to settle his case, he consorted with philosophers and became interested in mathematics, so that in the end, he stayed in Athens from about 450 to 430 B. C. He was, according to Proclus ( Commentary on Euclid , I), the first to write Elements (possibly around B. C.), more than one century before those of Euclid (usually dated from around 300 B. C.), but his works are no longer extant and are known only from references by later commentators. In trying to square the circle, Hippocrates adressed the problem of the surface of lunes, figures included between two intersecting arcs of circles.

10. Hippocrates Of Chios hippocrates of chios. mid fifth century BCE. One of the greatest geometersof antiquity, Hippocrates, started out as a merchant. Aside http://www.math.sfu.ca/histmath/Europe/Euclid300BC/HIPPOCRATES.HTML

Hippocrates of Chios mid fifth century B.C.E. One of the greatest geometers of antiquity, Hippocrates, started out as a merchant. Aside from being a brilliant mathematician, Aristotle said he was not a very clever merchant, since he was cheated of his money by crooked tax officials in Byzantium (some say he was robbed by pirates.) After moving to Athens around 430 B.C.E. to prosecute the offenders, he attended lectures in his leisure time and eventually became a teacher of geometry. One of Hippocrates achievements was that of the quadrature or squaring of the circle. Hippocrates also worked on the duplication of the cube and was the first to reduce the problem of doubling the cube of side a to the problem of discovering two mean proportionals b, c between a and 2a. For if a:b = b:c = c:2a then a :b = (a:b) = (a:b)(b:c)(c:2a)=a:2a and b . Hippocrates was unable to solve this proportion of finding two mean proportionals between one straight line and another line twice as long. The approach Hippocrates took to the problem simplified it from one of solid geometry to one of plane geometry. Hippocrates is said to be the first to have written an Elements of Geometry

11. Chios that island (area 7). Chios was a member city of the Ionian Confederacy I, 142148). Chios was he birthplace of the great mathematician hippocrates of chios ( not to be http://www.plato-dialogues.org/tools/loc/chios.htm

Bernard SUZANNE Last updated November 15, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. By clicking on the minimap at the beginning of the entry, you can go to a full size map in which the city or location appears. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations Large island off the coast of Asia Minor, south of Lesbos , and main city on that island (area 7) Chios was a member city of the Ionian Confederacy, the

12. Hippocrates Of Chios Hippocrates, born in the island of Chios, in Ionia, started, according to a traditionrecorded in Philoponus Commentary on Aristotle s Physics, as a merchant http://plato-dialogues.org/tools/char/hipchios.htm

Bernard SUZANNE Last updated December 5, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations Hippocrates, born in the island of Chios , in Ionia, started, according to a tradition recorded in Philoponus' Commentary on Aristotle's Physics , as a merchant and came to Athens to prosecute pirates who had robbed him of all his goods. Required to stay there for a while to settle his case, he consorted with philosophers and became interested in mathematics, so that in the end, he stayed in Athens from about 450 to 430 B. C. He was, according to Proclus ( Commentary on Euclid , I), the first to write Elements (possibly around B. C.), more than one century before those of Euclid (usually dated from around 300 B. C.), but his works are no longer extant and are known only from references by later commentators. In trying to square the circle, Hippocrates adressed the problem of the surface of lunes, figures included between two intersecting arcs of circles.

13. Search Results For Hippocrates - Encyclopædia Britannica hippocrates of chios. Greek geometer who compiled the first known work on the elements of Annotated biography of this ancient Greek geometer. hippocrates of chios. University of St http://www.britannica.com/search?query=Hippocrates&ct=&fuzzy=N

14. Chios Chios was he birthplace of the great mathematician hippocrates of chios (not tobe confused with the famous physician of the same name, Hippocrates of Cos http://plato-dialogues.org/tools/loc/chios.htm

Bernard SUZANNE Last updated November 15, 1998 Plato and his dialogues : Home Biography Works History of interpretation ... New hypotheses - Map of dialogues : table version or non tabular version . Tools : Index of persons and locations Detailed and synoptic chronologies - Maps of Ancient Greek World . Site information : About the author This page is part of the "tools" section of a site, Plato and his dialogues , dedicated to developing a new interpretation of Plato's dialogues. The "tools" section provides historical and geographical context (chronology, maps, entries on characters and locations) for Socrates, Plato and their time. By clicking on the minimap at the beginning of the entry, you can go to a full size map in which the city or location appears. For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations Large island off the coast of Asia Minor, south of Lesbos , and main city on that island (area 7) Chios was a member city of the Ionian Confederacy, the

15. Hippocrats' Quadrature Of The Lune hippocrates of chios. Math 7200 Project hippocrates of chios taught in Athens and worked on the classical problems of squaring the circle and duplicating http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Math 7200/Math 7200 projec

Hippocrates of Chios Math 7200 Project (Project proposal here by Samuel Obara Hippocrates' Quadrature of the lune Indroduction Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating Iamblichus [4] writes:- One of the Pythagorean [Hippocrates] lost his property, and when this misfortune befell him he was allowed to make money by teaching geometry. Heath [6] recounts two versions of this story:- One version of the story is that [Hippocrates] was a merchant, but lost all his property through being captured by a pirate vessel. He then came to Athens to persecute the offenders and, during a long stay, attended lectures, finally attaining such proficiency in geometry that he tried to square the circle. Heath also recounts a different version of the story as told by Aristotle:- ... he allowed himself to be defrauded of a large sum by custom-house officers at Byzantium, thereby proving, in Aristotle's opinion, that, though a good geometer, he was stupid and incompetent in the business of ordinary life. The suggestion is that this 'long stay' in Athens was between about 450 BC and 430 BC.

16. Hippocrates --  Britannica Student Encyclopedia Although he has been , hippocrates of chios Greek geometer who compiled thefirst known work on the elements of geometry nearly a century before Euclid. http://www.britannica.com/ebi/article?eu=296806&query=philetas of cos&ct=ebi

17. The Inscribed Circle of Hippocrates. hippocrates of chios lives in the second half of the fifth century hippocrates of chios is sometimes confused with the Father of Medicine, Hippocrates of Cos pictured http://web.pdx.edu/~marky/Assignment5/hippocrates.htm

The Lune of Hippocrates Hippocrates of Chios lives in the second half of the fifth century B.C.E. and is believed to have died in Athens. Although his original work was lost, it was referred to in detail by subsequent mathematicians such as Eudemus and Simplicius. Perhaps Hippocrates's greatest contribution to geometry dealt with the figure at the right. In a failed attempt to square a circle, he proved that certain regions between circles could be squared. Such regions resemble crescent moons and are called lunes. His result compares the areas of the red lune FBG and the area of triangle GOF. Hippocrates of Chios is sometimes confused with the Father of Medicine, Hippocrates of Cos pictured above. The Lune of Hippocrates Examining the Lune This is the same as the area of triangle FGO. It is amazing that the area of an object that is the intersection of two circles, can produce a triangle of exactly the same area. Hippocrates' discovery most likely came out of a failed attempt at one of the three great problems of antiquity. That given a circle, produce a square of exactly the same area. Sometimes this is referred to as "squaring the circle." Many people worked on this problem, until it was proven to impossible.

18. Hippoarea.html hippocrates of chios. Introduction the Area Problem. The Babylonians,the Egyptians, and indeed every ancient civilization had knowledge http://cerebro.xu.edu/math/math147/02f/hippocrates/hippoarea.html

Hippocrates of Chios Introduction: the Area Problem The Babylonians, the Egyptians, and indeed every ancient civilization had knowledge of basic geometric concepts like how to calculate the areas of simple plane figures (triangles, squares, rectangles, parallelograms, trapezoids, and the like) and the volumes of simple solid bodies (parallelopipeds and pyramids). The Greeks however turned geometry into a real science by applying to it the deductive methods they were systematizing through philosophy. For the first time, epistemological questions were being studied about mathematical ideas: how do we know that the results we have discovered are true? Are these ideas interrelated? Dialectical reasoning strove to find the first principles of mathematical knowledge as a foundation for understanding the real world. This created an architecture of logical structure for mathematical ideas based on cause and effect relationships: if a certain theorem was a consequence of another, then the second was given an a priori precedence over the first. It became standard for geometers to communicate in a very spare language, consisting of statements of theorems followed by their proofs followed the next theorem in the logical development, with little in the way of discussion or explanation. It may not have had the same emotive force as the epic poetry of Homer, but it was beautiful in its own abstract way, like music to the listener. Moreover it was seen as uncovering the secrets of the physical universe, since physical objects and phenomena like light and sound behaved according to geometric principles.

19. Hippotext.html hippocrates of chios the quadrature of a lune 1. hippocrates of chios wasa merchant who fell in with a pirate ship and lost all his possessions. http://cerebro.xu.edu/math/math147/02f/hippocrates/hippotext.html

Hippocrates of Chios: the quadrature of a lune From Philoponus Commentary on Aristotle's Physics Hippocrates of Chios was a merchant who fell in with a pirate ship and lost all his possessions. He came to Athens to prosecute the pirates and, staying a long time in Athens by reason of the indictment, consorted with philosophers, and reached such proficiency in geometry that he tried to affect the quadrature of the circle. He did not discover this, but having squared the lune he falsely thought from this that he could square the circle also. For he thought that from the quadrature of the lune the quadrature of the circle could also be calculated. From Simplicius Commentary on Aristotle's Physics Eudemus , however, in his History of Geometry says that Hippocrates did not demonstrate the quadrature of the lune on the side of a square but generally, as one might say. For every lune has an outer circumference equal to a semicircle or greater or less, and if Hippocrates squared the lune having an outer circumference equal to a semicircle and greater and less, the quadrature would appear to be proved generally. I shall set out what Eudemus wrote word for word, adding only for the sake of clearness a few things taken from Euclid's Elements on account of the summary style of Eudemus, who set out his proofs in abridged form in conformity with the ancient practice. He writes thus in the second book of the History of Geometry.

20. Quadrature Of A Convex Polygon The first who provided a step towards a possible solution was Hippocratesof Chios (not Kos!). BC.). hippocrates of chios, The area problem. http://www.mlahanas.de/Greeks/PolygonQuadrature.htm

Quadrature of a Convex Polygon Eves thinks that the Greeks knew a method for reducing a convex polygon of any number of sides to a triangle of equal area. In the figure below we consider a polygon ABCFGHJ. We take a side CF extended to meet a line GK from an adjacent vertex, running parallel to the diagonal FH in the polygon. We cut a corner by connecting H with K, while maintaining the same area. So we see a complex figure equated to a simpler one. The polygon with 7 vectices ABCFGHJ has the same area as the polygon with 6 vertices ABCKHJ. To see this we construct a parallel to FH at G. Extend CF that meets this parallel at K. FHK and FGH have the same height and base FH. A similar process can be continued with the polygon ABCKHJ again until we obtain a triangle. First Step: Construct a rectangle with an area equal to the triangle assumed to be ABC. For this bisect the height AD at E. Now the rectangle HJIG with width IJ = BC and height JH = ED has the same area as the triangle ABC. Now extend IJ marking a point K with KJ=JH. Draw a circle using L as midpoint of IK and radius LI = LK. Extend JH and take intersection point M on circle. Use JM as side and construct square JMPN. This has the same area as HJIG and thus the same area as the triangle ABC.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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