Braikenridge–maclaurin construction
WebDec 13, 2024 · Abstract. We prove a generalization of both Pascal's Theorem and its converse, the Braikenridge–Maclaurin Theorem: If two sets of k lines meet in k 2 distinct points, and if dk of those points lie on an irreducible curve C of degree d, then the remaining k(k − d) points lie on a unique curve S of degree k − d.If S is a curve of degree k − d … Webwhere is a line through the point .. See also Pascal's Theorem. © 1996-9 Eric W. Weisstein 1999-05-26
Braikenridge–maclaurin construction
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WebMay 5, 2012 · You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate … WebMar 24, 2024 · The geometric construction of a conic section from five points lying on it is called the Braikenridge-Maclaurin Construction. The explicit equation for this conic is given by the equation (8) The general …
WebProposition 3 (Braikenridge-Maclaurin) If three lines meet three other lines in nine points, and three of these points lie on a line, then the remaining six points lie on a conic. Of interest here is that these theorems extend in the case of parallel lines when one adds a point at in nity. We are really working in the projective plane RP2 ... WebBraikenridge-Maclaurin Construction 2 Parabola Laurence D. Finston This document is part of GNU 3DLDF, a package for three-dimensional drawing. Copyright c 2007, 2008, …
WebThe Braikenridge-Maclaurin Construction Let AC and BD meet in X. Draw any line L through meeting BE and AE. Suppose L cuts BE at Y and AE at Z. Let CY and DZ meet at F. By the Converse of Pascal's Theorem, F lies on the conic. Of course the conic is the locus of points F so obtained. The Cabri figure conpascal2.fig illustrates this. Synthetically, the conic can be constructed by the Braikenridge–Maclaurin construction, by applying the Braikenridge–Maclaurin theorem, which is the converse of Pascal's theorem. Pascal's theorem states that given 6 points on a conic (a hexagon), the lines defined by opposite sides intersect in … See more In Euclidean and projective geometry, five points determine a conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve). There are additional subtleties for conics that do not exist for … See more This result can be proven numerous different ways; the dimension counting argument is most direct, and generalizes to higher degree, while other proofs are special to conics. Dimension counting Intuitively, passing … See more The natural generalization is to ask for what value of k a configuration of k points (in general position) in n-space determines a variety of degree d and dimension m, which is a fundamental question in enumerative geometry. A simple case of … See more • Five Points Determine a Conic Section, Wolfram interactive demonstration See more Given five points, one can construct the conic containing them in various ways. Analytically, given the coordinates $${\displaystyle (x_{i},y_{i})_{i=1,2,3,4,5}}$$ of the five points, the equation for the conic can be found by See more While five points determine a conic, sets of six or more points on a conic are not in general position, that is, they are constrained as is … See more • Cramer's theorem (algebraic curves), for a generalization to n-th degree planar curves See more
WebA conic matrix M can be computed using a matrix form of the Braikenridge-Maclaurin construction, [CG67] (Figure 3) which we review here for completeness. This construction is based on Pascal’s theorem. Construct three pairs of lines, each pair passing through opposing sides of the hexagon (x,w 1,...w 5). Each pair of lines will intersect at ...
WebThe Braikenridge-Maclaurin Construction. Pascal's Theorem and its Converse lead to an interesting construction for points on the conic determined by five points with no three collinear. This appears to have been discovered independently by Braikenridge and Maclaurin. There was a dispute between the two over priority. the soul keeper seriesWebBraikenridge-MacLaurin Theorem (Cont’d) LetAQand CPmeetin R(which is, of course, the center of the circle), let a variable diam- ... Braikenridge-MacLaurin construction, the locus of X is the conic APBQC. Hence the conic coincides with the circle. George Voutsadakis (LSSU) Projective Geometry August 2024 5 / 30 ... the soul king brookWebMay 5, 2012 · You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or … the soul keeper torrenthttp://www.brackenridgeconstruction.com/ myrtle beach sc dealsWeb(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID ... myrtle beach sc distanceWebThe Braikenridge– Maclaurin Theorem is just the instance k= 3 of Theorem 4. The case where k= 4 is illustrated in Figure 4. Figure 4: An illustration of Theorem 4 when k = 4. We use the Cayley-Bacharach Theorem to prove Theorem 4 in Section 3. In Sec-tion 4 we consider the kinds of curves produced by the construction in Theorem 4. myrtle beach sc cruisehttp://www.brackenridgeconstruction.com/our-company/ the soul kingdom