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dbr:Braikenridge–Maclaurin_theorem
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Braikenridge–Maclaurin theorem Teorema de Braikenridge-Maclaurin
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In geometry, the Braikenridge–Maclaurin theorem, named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's theorem. En geometria, el teorema de Braikenridge–Maclaurin, anomenat així pels matemàtics escocesos del segle XVIII William Braikenridge i Colin Maclaurin, és l'invers del teorema de Pascal. Diu que si els tres punts d'intersecció dels tres parells de rectes prolongació dels costats oposats d'un hexàgon estan en una mateixa recta , aleshores els sis vèrtexs de l'hexàgon estan en un cònica .
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En geometria, el teorema de Braikenridge–Maclaurin, anomenat així pels matemàtics escocesos del segle XVIII William Braikenridge i Colin Maclaurin, és l'invers del teorema de Pascal. Diu que si els tres punts d'intersecció dels tres parells de rectes prolongació dels costats oposats d'un hexàgon estan en una mateixa recta , aleshores els sis vèrtexs de l'hexàgon estan en un cònica . El teorema es pot aplicar a la construcció de Braikenridge-Maclaurin que és una construcció sintètica d'una cònica definida per cinc punts, variant el sisè punt. El teorema de Pascal afirma que, donats sis punts d'una cònica (els vèrtex d'un hexàgon), les tres línies definides per les seves cares oposades s'intersecaran en tres punts colineals. In geometry, the Braikenridge–Maclaurin theorem, named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's theorem. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a synthetic construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three collinear points. This can be reversed to construct the possible locations for a sixth point, given five existing ones.
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1997