Geometry, Theorems and Problems

Geometry Problem 1335: the Lune of Hippocrates has the same area of a Kite. Mobile Apps. Level: College, High School.

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", www.wurzel.org.
 

Geometry Problem 1335: Geometry Problem 1335: the Lune of Hippocrates has the same area of a Kite. Mobile Apps.


 

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.

Art of problem 1335 Lune of Hippocrates and Kite,  using mobile apps, iPad, iPhone

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Last updated: May 7, 2017