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Encyclopedia > Hippocrates of Chios

Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c. 470 - c. 400 BCE. A geometer is a mathematician whose area of study is geometry. ... Era Vulgaris redirects here. ...

He was born on the isle of Chios, where he originally was a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, possibly for litigation. There he grew into a leading mathematician. Chios (Greek: , alternative transliterations Khios and Hios, see also List of traditional Greek place names; Ottoman Turkish: صاقيز Sakız; Genoese: Scio) is a Greek island in the Aegean Sea five miles off the Turkish coasts. ... Athens (Greek: Αθήνα - Athína) is the largest city and capital of Greece, located in the Attica periphery of central Greece. ...

On Chios Hippocrates may have been a pupil of the mathematician and astronomer Oenopides of Chios. In his mathematical work there probably was some Pythagorean influence too, perhaps via contacts between Chios and the neighbouring island of Samos, a center of Pythagorean thinking: Hippocrates has been described as a 'para-Pythagorean', a philosophical 'fellow traveler'. The Reductio ad absurdum argument (or proof by contradiction) has been traced to him. Oenopides of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived around 450 BCE. He was born shortly after 500 BC on the island of Chios, but mostly worked in Athens. ... This article or section does not cite any references or sources. ...



The major accomplishment of Hippocrates is that he was the first to write a systematically organized geometry textbook, called Stoicheia (= Elements, that is, basic theorems, or building blocks of mathematical theory). This was an important step because from now on mathematicians from all over the ancient world could, at least in principle, build on a common framework of basic concepts, methods, and theorems, which stimulated the scientific progress of mathematics. Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ...

Only a single, and famous, fragment of Hippocrates' Elements is existent, embedded in the work of Simplicius. In this fragment the area is calculated of some so-called 'Hippocratic lunes' (crescent-shaped areas, bounded by two concave circular arcs). This was part of a research programme to achieve the "quadrature of the circle", that is, to calculate the area of the circle, or, equivalently, to construct a square with the same area as a circle. The strategy apparently was to divide a circle into a number of crescent-shaped parts. If it were possible to calculate the area of each of those parts, then the area of the circle as a whole would be known too. Only much later was it proven (by Ferdinand von Lindemann, in 1882) that this approach had no chance of success, because the factor pi (π) is transcendental. The number π is the ratio of the circumference to the diameter of a circle, and also the ratio of the area to the square on the radius. Alternate meaning: Pope Simplicius Simplicius, a native of Cilicia, a disciple of Ammonius and of Damascius, was one of the last of the Neoplatonists. ... This square and circle have the same area. ... Carl Louis Ferdinand von Lindemann (April 12, 1852 - March 6, 1939) was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i. ... When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ... In mathematics, a transcendental number is any complex number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. ...

In the century after Hippocrates at least four other mathematicians wrote their own Elements, steadily improving terminology and logical structure. In this way Hippocrates' pioneering work laid the foundation for Euclid's Elements (c. 325 BC) that was to remain the standard geometry textbook for many centuries. Euclid (Greek: ), also known as Euclid of Alexandria, was a Hellenistic mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BC). ...

Two other contributions by Hippocrates in the field of mathematics are noteworthy. He found a way to tackle the problem of 'duplication of the cube', that is, the problem of how to construct a cube root. Like the quadrature of the circle this was another of the so-called three great mathematical problems of Antiquity. Hippocrates also invented the technique of 'reduction', that is, to transform specific mathematical problems into a more general problem that is more easy to solve. The solution to the more general problem then automatically gives a solution to the original problem. Doubling the cube is one of the three most famous geometric problems unsolvable by straightedge and compass alone. ...


In the field of astronomy Hippocrates tried to explain the phenomena of comets and the Milky Way. His ideas have not been handed down very clearly, but probably he thought both were optical illusions, the result of refraction of solar light by moisture that was exhaled by, respectively, a putative planet near the sun, and the stars. The fact that Hippocrates thought that light rays originated in our eyes instead of in the object that is seen, adds to the unfamiliar character of his ideas, which belong to the realm of speculative philosophy. Comet Hale-Bopp Comet McNaught as seen from Swifts Creek, Victoria, Australia on 23 January 2007 For other uses, see Comet (disambiguation). ... It has been suggested that Andromeda-Milky Way collision be merged into this article or section. ...


Under the name of Isicrate, Alfred Jarry attributed to him the origins of ’Pataphysics. Alfred Jarry Alfred Jarry (September 8, 1873 – November 1, 1907) was a French writer born in Laval, Mayenne, France, not far from the border of Brittany; he was of Breton descent on his mothers side. ... Pataphysics, a term coined by the French writer Alfred Jarry, is a philosophy dedicated to studying what lies beyond the realm of metaphysics. ...


  • Ivor Bulmer-Thomas, 'Hippocrates of Chios', in: Dictionary of Scientific Biography, Charles Coulston Gillispie, ed. (18 Volumes, New York 1970-1990) pp. 410-418.
  • [Axel Anthon] Björnbo, 'Hippokrates', in: Paulys Realencyclopädie der Classischen Altertumswissenschaft, G. Wissowa, ed. (51 Volumes; 1894-1980) Vol. 8 (1913) col. 1780-1801.

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NAME Hippocrates of Chios
SHORT DESCRIPTION Greek geometer and astronomer

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