Problem 654: Salinon
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #14 (high school level) and lift up your geometry skills.
Click the figure below to see the complete problem 654
Continue reading at:
gogeometry.com/ArchBooLem14.htm
Tuesday, December 16, 2008
Archimedes' Book of Lemmas, Proposition #14
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Let AC = BD = 2p, CD = 2q
ReplyDeleteSo EF = OE + OF = OA + q = 2p + q + q = 2p +2q
Let(XY)denote area of semicircle on XY as diameter
Salmon area
=(AB)-(AC)-(DB)+(CD)]
=[Pi/2][(2p+q)^2 - p^2 - p^2 + q^2]
=[Pi/2][2p^2 + 4pq +2q^2]
=Pi(p + q)^2
=Area of circle on EF as diameter