Subject: [HM] Caratheodory Biography
From: Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Date: Fri Mar 17 2000 - 13:15:16 EST
A biography of the great C.Caratheodory was recently published in Athens.
Bibliographic details:
Evangelos Spandagos: The Life and the Work of C. Caratheodory. [In Greek]
Athens: Aithra, 2000. 446 pages. ISBN 960-7007-84-0
In the page 134 we read:
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The following theorem, due to Caratheodory, is known as "Caratheodory
Relation": A triangle ABC is given. Consider a point O inside the triangle.
Then:
--> --> -->
E_A * OA + E_B * OB + E_C * OC = 0,
where E_A, E_B, E_C are the areas of the triangles BOC, COB, and AOB resp.
This theorem was given as a problem in the first National [Greek] Mathematical
Olympiad in Athens 1985 by the Greek Mathematical Sosiety.
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Unfortunately, the author doesn't give a reference.
Is it in fact a Caratheodory theorem, or a misattribution?
Antreas
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