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Inspiration ........................................................................................................................................... 122020 SMPF - Vivianis Theorem and Related Problems
Inspiration ........................................................................................................................................... 12
Methodology ........................................................................................................................................ 12
Results .................................................................................................................................................. 13
I.
Viviani’s Theorem and its Extensions ......................................................................... 13
1. Vectors approach ................................................................................................................ 13
Theorem 1.1 ................................................................................................................ 13
Theorem 1.2 ................................................................................................................ 17
Theorem 1.3 ................................................................................................................ 17
2. Corollaries .......................................................................................................................... 18
Corollary 1 ................................................................................................................... 18
Corollary 2 – Unsolved challenge ................................................................................ 19
II.
Carnot’s Theorem ....................................................................................................... 20
1. Extended Carnot’s Theorem and its Converse ................................................................... 20
Theorem 2.1 ................................................................................................................ 20
Theorem 2.2 ................................................................................................................ 21
2. The link between extended Carnot’s Theorem and extended Viviani’s Theorem ................ 22
Linked problem 1 ........................................................................................................ 22
Linked problem 2 ........................................................................................................ 23
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