Inappropriate tone date February 2008 A porism is a mathematical proposition or corollary . In particular, the term porism has been used to refer to a direct result of a proof, analogous to how a corollary ... to constructing what is proposed, and finally a porism as directed to finding what is proposed ... was changed by certain later geometers, who defined a porism on the ground of an accidental characteristic ..., as a result unsought, as it were, but seen to follow from a theorem. On the porism ... measure are porisms Proclus , ed. Friedlein, p. 301 . Pappus on Euclid s porism Pappus gives a complete enunciation of a porism derived from Euclid, and an extension of it to a more general case. This porism, expressed in modern language, asserts that &mdash given four straight lines of which three ... 2 in number, describes a straight line. Pappus gives also a complete enunciation of one porism ..., De porismatibus , begins with definitions of theorem, problem, datum, porism and locus. Respecting the porism Simson says that Pappus s definition is too general, and therefore he will substitute for it the following ... demonstranda aunt, invenienda proponantur. blockquote A locus says Simson is a species of porism ... defined a porism thus A proposition affirming the possibility of finding such conditions as will render ... of a porism appears to be most favoured in England, Simson s view has been most generally accepted ... to base thereon a view of the nature of a porism more closely conforming to the definitions in Pappus ... he gives the name of porism to one section. According to Frans van Schooten , if the various ... of the four line Porism begin the book, instead of the intercept Porism fully enunciated by Pappus, to which the lemma to the first Porism relates intelligibly, being a particular case of it. An interesting ... Lehre von den Kegelschnitten im Altertum , 1886, ch. viii. . Observing, e.g., that the intercept Porism ... therefore to the geometrical porism as defined in Pappus and Proclus . See also Poncelet s porism ... more details
Image PonceletPorism.gif thumb right Illustration of Poncelet s porism for n 3, a triangle that is inscribed in one circle and circumscribes another. In geometry , Poncelet s porism , named after French engineer and mathematician Jean Victor Poncelet , states the following Let C and D be two plane conic s. If it is possible to find, for a given n 2, one n sided polygon that is simultaneously inscribed in C and circumscribed around D , then it is possible to find infinitely many of them. Poncelet s porism can be proved via elliptic curve s geometrically this depends on the representation of an elliptic curve as the Double cover topology double cover of C with four ramification point s. Note that C is isomorphic to the complex projective line . The relevant ramification is over the four points of C where the conics intersect. There are four such points by B zout s theorem . One can also describe the elliptic curve as a double cover of D in this case, the ramification is over the contact points of the four bitangents. Proof Let p be a point of P sup 2 sup and a line of the dual projective plane. The key tool is the curve X given by the set of pairs p , where p is on the conic C and is tangent to the conic D . Then X is smooth more specifically ... Steiner s porism External links http sbseminar.wordpress.com 2007 07 16 poncelets porism David Speyer on Poncelet s Porism D. Fuchs, S. Tabachnikov, Mathematical Omnibus Thirty Lectures on Classic ... s Porism for a general Ellipse and a Parabola made using http www.geogebra.org webstart GeoGebra ... showing Poncelet s Porism for 2 general ellipses order 3 made using http www.geogebra.org webstart ... Borcherds showing Poncelet s Porism for 2 general ellipses order 5 made using http www.geogebra.org ... Java applet by Michael Borcherds showing Poncelet s Porism for 2 general ellipses order 6 made using ... mathworld.wolfram.com PonceletsPorism.html Article on Poncelet s Porism at Mathworld. Category Conic ... more details
Image Pivot theorem.svg thumb right 300px Image Pivot theorem 3d.png thumb right 300px The three dimensional case the four spheres intercepts other spheres on black circles. In geometry , the pivot theorem states that, given any three points P, Q, and R on each respective side of a triangle ABC, the three circles through the points AQR, BPR and CPQ share a common point M. Conversely, this is equivalent to a porism given any three circles sharing a common point M, there are an infinite number of triangles such that one point lies on each circle and the sides of the triangle pass through the intersection points of the circles. There is also a three dimensional analog, in which the four spheres passing through a point of a tetrahedron and points on the edges of the tetrahedron intersect in a common point. See also Miquel s theorem Bibliography cite book author Wells D year 1991 title The Penguin Dictionary of Curious and Interesting Geometry publisher Penguin Books location New York isbn 0 14 011813 6 pages pp. 227&ndash 228 External links MathWorld title Pivot theorem urlname PivotTheorem Category Circles Category Mathematical theorems ... more details
About the Scottish mathematician other people with a similar name Robert Simpson disambiguation File Robert Simson memorial.jpg thumb Memorial to Robert Simson in West Kilbride cemetery. The memorial plate reads To Dr. Robert Simson of the University of Glasgow, the Restorer of Grecian Geometry and by his works, the great promoter of its study in the Schools. A Native of this Parish. Robert Simson 14 October 1687 &ndash 1 October 1768 was a Scotland Scottish mathematics mathematician and Professor of Mathematics, Glasgow professor of mathematics at the University of Glasgow . The pedal line of a triangle is sometimes called the Simson line after him. Life The eldest son of John Simson of Kirktonhall, West Kilbride in Ayrshire , Robert Simson was intended for the Church, but the bent of his mind was towards mathematics. He was educated at the University of Glasgow and graduated M.A. When the prospect opened of his succeeding to the Professor of Mathematics, Glasgow mathematical chair at the University of Glasgow , Simson proceeded to London for further study. After a year in London, he returned to Glasgow and, in 1711, was appointed by the university to the professorship of mathematics, an office which he retained until 1761. Works Simson s contributions to mathematical knowledge took the form of critical editions and commentaries on the works of the ancient geometer s. The first of his published writings is a paper in the Philosophical Transactions 1723, vol. xl. p. 330 on Euclid s Porism s . Then followed Sectionum conicarum libri V. Edinburgh, 1735 , a second edition of which, with additions, appeared in 1750. The first three books of this treatise were translated into English and, several times, printed as The Elements of the Conic section Conic Sections . In 1749, was published Apollonii Pergaei locorum planorum libri II. , a restoration of Apollonius of Perga Apollonius s lost treatise, founded on the lemma mathematics lemma s given in the seventh book of ... more details
wikify date November 2010 Henry Martyn Taylor , Fellow of the Royal Society F.R.S. , Fellow of the Royal Astronomical Society F.R.A.S. 6 June 1842, Bristol &ndash 16 October 1927, Cambridge , was an England English mathematician and barrister . ref cite journal last1 F. first1 A. R. title Mr. H. M. Taylor, F.R.S. journal Nature date 1927 11 05 volume 120 issue 3027 pages 664&ndash 665 doi 10.1038 120664a0 ref ref cite journal title sc Henry Martyn Taylor journal Monthly Notices of the Royal Astronomical Society year 1929 volume 89 pages 324&ndash 325 bibcode 1929MNRAS..89..324. ref ref cite journal author1 Addison, Henry Robert author2 Oakes, Charles Henry author3 Lawson, William John author4 Sladen, Douglas Brooke Wheelton title TAYLOR, Henry Martyn journal Who s Who, year 1907 volume 59 pages p. 1723 url http books.google.com books?id yEcuAAAAYAAJ&pg PA1723 ref Henry Martyn Taylor was the second son of the Rev. James Taylor and Eliza Johnson. He was educated in Wakefield and at Trinity College, Cambridge , where he graduated B.A. as 3rd Wrangler University of Cambridge Wrangler in 1865. ref Venn id TLR861HM name Taylor, Henry Martyn ref He was elected a Fellow of the Royal Society in Jun 1898. His candidacy citation read that he was Barrister at Law. Fellow of Trinity College, Cambridge. Ex Tutor of Trinity College, Cambridge. Third Wrangler and Second Smith s Prizeman in 1865. Author of papers in the Mathematical Messenger, as follows Vol iii, p 189, Geometrical Explanation of the Equations for the Longitude of the Node and the Inclination of the Orbit vol v, p 1, 1876, On the Generation of Developable Surface through Two given Curves vol vii, p 22, 1877, On Certain Series in Trigonometry vol vii, p 145, 1877, On the Porism of the Ring of Circles touching Two Circles vol xi, p 177, On a Six point Circle connected with a Triangle vol xiii, p 145, On a Cubic Surface vol xvi, p 39, On a Geometrical Interpretation of the Algebraic Expression which, equated to Zero, r ... more details
work refers to this result as a Porism or self evident corollary Furthermore it is clear ... were calculated using the Porism now referred to as Pythagoras Theorem. No doubt the great astronomer ... and ED are known along with diagonals CE and BD by application of the Porism Pythagoras Thm . Then math ... corresponding to sin 30 6 is then calculated by application of the Porism . http articles.adsabs.harvard.edu ... Coelestium , Copernicus does not refer to Pythagoras Theorem by name but uses the term Porism a word ... of another existing theorem. The Porism can be viewed on pages http articles.adsabs.harvard.edu cgi ... more details
Poncelet s porism Talk Poncelet s porism Pons asinorum Talk Pons asinorum Ponte del Diavolo game ... Population viability analysis Talk Population viability analysis Porism Talk Porism Porous set Talk ... more details
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