TY - JOUR
T1 - Associative Binary Operations and the Pythagorean Theorem
AU - Bell, Denis
N1 - Bell, D. Associative Binary Operations and the Pythagorean Theorem. Math Intelligencer 33, 92–95 (2011). https://doi.org/10.1007/s00283-010-9171-6
PY - 2011/3
Y1 - 2011/3
N2 - In a recent article [2], L. Berrone presented a new approach to the Pythagorean Theorem (PT). The idea is to derive the geometric theorem from analytic and algebraic properties, by methods of functional equations. (So we are not dealing with a method that was an option for the ancients!) I thought about Berrone’s ideas, within his context of functional equations. Some pleasant surprises fell out. Then a surprising gift of functional equations back to geometry closed the circle for me – and will close this article.
AB - In a recent article [2], L. Berrone presented a new approach to the Pythagorean Theorem (PT). The idea is to derive the geometric theorem from analytic and algebraic properties, by methods of functional equations. (So we are not dealing with a method that was an option for the ancients!) I thought about Berrone’s ideas, within his context of functional equations. Some pleasant surprises fell out. Then a surprising gift of functional equations back to geometry closed the circle for me – and will close this article.
KW - Functional Equation
KW - Binary Operation
KW - Mathematical Intelligencer
KW - Euclidean Geometry
KW - Pythagorean Theorem
UR - http://www.scopus.com/inward/record.url?scp=79952243292&partnerID=8YFLogxK
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U2 - 10.1007/s00283-010-9171-6
DO - 10.1007/s00283-010-9171-6
M3 - Article
AN - SCOPUS:79952243292
SN - 0343-6993
VL - 33
SP - 92
EP - 95
JO - Mathematical Intelligencer
JF - Mathematical Intelligencer
IS - 1
ER -