Topology Atlas | Conferences
Conference on Knot Theory and Its Applications to Physics and Quantum Computing; 60th birthday of Jozef H. Przytycki
January 6-9, 2015
University of Texas at Dallas
Richardson, TX, USA |
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Organizers
Mieczyslaw K. Dabkowski (UTD) Tobias Hagge (UTD) Valentina S. Harizanov (GWU) Viswanath Ramakrishna (UTD) Radmila Sazdanovic (NCSU) Adam S. Sikora (SUNYUB)
Conference Homepage |
Heron's Formula from a 4-dimensional point of view
by
J. Scott Carter
University of South Alabama
Coauthors: David Mullens
Let a triangle with edge lengths a, b, and c, with a ≤ b ≤ c be given. Let A denote the area of the triangle.
Heron's formula states that
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16 A2 = (a+b+c)(a+b-c)(a-b+c)(-a+b+c). |
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As such it is a formula that relates 4-dimensional volumes.
In this talk we show how to provide a scissor's congruence between the related volumes. The proof will involve some very elementary
decompositions of a variety of 4-dimensional cubes.
Date received: December 7, 2014
Copyright © 2014 by the author(s).
The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas.
Document # cbjz-41.