The Problem:

Historically, it has always fascinated mathematicians to find ways to draw lines of lengths that they knew were impossible to actually measure exactly…

 For example, the diagonal of a ‘unit’ square was known to have exact length , even though it was impossible to actually check this, by measuring exactly or using fractions (or, more recently, decimals). 

As an example of the method, here are two easy ways to construct  exactly, using only ruler and compasses:


Both of these constructions depend on Pythagoras’ Theorem.

Can you work out how to construct   in two different ways?

 What’s the first square root you think you can construct in three different ways?!


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Last modified: June 18, 2007