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 Construction**The 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. The geometry files are on http://i2geo.net/.

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. The geometry files are on http://i2geo.net/.

Linda Fahlberg-Stojanovska has published a paper on compass and straightedge construction, which includes a simpler proof and procedure for inscribing a semicircle in a square. At http://geogebrawiki.pbworks.com/ciit10

Posted by: Colin McAllister | 05/09/2010 at 03:54 PM