The figure shows a square ABCD
inscribed in a circle O. S is the area of the right triangle
AOB, S_{1} is the area of the lune of Hippocrates
bounded by the semicircle of diameter AB and the arc AB. A
radius OE extended cuts semicircle AB at F. S_{2} is
the area of the
kite EHFG (H on OA extended, G on OB extended). S_{3}
and S_{4} are the areas of the triangles EFH and EFG,
respectively. S_{5} and S_{6} are the areas of
the curved triangles AFE and BFE. Prove that (1) S_{3}
= S_{5}; (2) S_{4} = S_{6}; (3) S = S_{1}
= S_{2}; (4) AB^{2} = 4.AH.BG. This entry
contributed by Markus Heisss, Wurzburg, Bavaria. Published in:
"Die Wurzel  Zeitschrift fur Mathematik, Heft 11/2015",
www.wurzel.org.

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
