The figure shows a square ABCD
inscribed in a circle O. S is the area of the right triangle
AOB, S1 is the area of the lune of Hippocrates bounded by the semi-circle of
diameter AB and the arc AB. A radius OE extended cuts
semi-circle AB at F. S2 is the area of the
kite EHFG (H
on OA extended, G on OB extended). S3 and S4 are the areas of
the triangles EFH and EFG, respectively. S5 and S6 are the areas
of the curved triangles AFE and BFE.
Prove that (1) S3 = S5; (2)
S4 = S6; (3) S = S1 = S2; (4) AB2 = 4.AH.BG.
This entry contributed by
Markus Heisss, Wurzburg, Bavaria. Published in: "Die Wurzel - Zeitschrift fur Mathematik, Heft 11/2015",
Art of Geometry Problem 1335 using Mobile Apps. Circle Patterns.
Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.
A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.
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Last updated: May 7, 2017