Ptolemy's Inequality · 1 Theorem · 2 Proof for Coplanar Case · 3 Outline for 3-D Case · 4 Proof for All Dimensions? · 5 Note about Higher Dimensions · 6 See Also ... Proof for Coplanar Case · Proof for All Dimensions? |
In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to ... |
In (*) and its proof, 3 can be replaced by any positive integer n and that gives Ptolemy's inequality in n-dimensional space. The following are some exercises. |
24 мая 2015 г. · Here we collect some proofs of the following nice geometric result. If ABCD is a quadrilateral, then AB.CD + BC.DA \geq AC.BD with equality if ABCD is cyclic. |
4 сент. 2021 г. · Theorem 6.4.1 Ptolemy's inequality. In any quadrangle, the product of diagonals cannot exceed the sum of the products of its opposite sides; ... |
The theorem says that if the quadrilateral can be inscribed in a circle then Ptolemy's condition is satisfied. |
Ptolemy's theorem states the relationship between the diagonals and the sides of a cyclic quadrilateral. It is a powerful tool to apply to problems about ... |
Ptolemy's theorem gives a relationship between the side lengths and the diagonals of a cyclic quadrilateral; it is the equality case of Ptolemy's Inequality. ... |
There are elegant proofs to Ptolemy, as well as instructive ones that explain the method being used very well. Exercise 2.1. Prove Ptolemy's Inequality with ... |
16 мая 2014 г. · ABCD is a convex quadrilateral in which AB2+CD2=BC2+AD2. Prove by vectors that diagonals AC and BD are orthogonal to each other. linear algebra - Explanation for the proof of Ptolemy-inequality geometry - Proof of Ptolemy's inequality using $z \mapsto \frac1z Does the Ptolemy's inequality hold for concave quadrilaterals? geometry - Ptolemy's inequality and Pompeiu's theorem Другие результаты с сайта math.stackexchange.com |
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