*World of Mathematics*. ©2005-2006 Thomson Gale, a part of the Thomson Corporation. All rights reserved.

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## Euclidean Construction

The ancient Greeks felt that the line and the **circle** are the basic figures and the straightedge and compass are their physical analogues. Hence they were interested in what can be done with a straightedge and compass, i.e. what figures are Euclidean constructions. For example, given a line l and a point P on l, it is possible to construct the perpendicular to l though P using only a straightedge and compass as follows: with the compass draw a circle C0 with center P. Let A and B be the intersection points of l with C0. Next draw the circles with centers A and B which pass through B and A respectively. These two circles intersect in two points E and F say. The line segment EF is perpendicular to l.

If one is given segments AB and CD of lengths x and y respectively...

This section contains 909 words(approx. 4 pages at 300 words per page) |