How would you inscribe a semicircle into a square using geometric construction? I prepared this slide show to demonstrate the steps of
construction. It can be viewed or downloaded at Slideshare.net:
Inscribe Semicircle In Square by Geometric ConstructionThe slide show and my geometry examples are Public Domain. There are some exercises on slide 8, with suggested solutions.
Why
would you use this technique? It is not trivial to solve this problem
using algebra, as it involves factorisation of irrational numbers.
Geometric Construction is an ancient
mathematical technique that can be done without knowing algebra. The basic tools are a
pair of compasses and a straight-edge or ruler. On a personal computer, you can use free geometry software such as
Geogebra, as I did for these examples.
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