ConstructARoot 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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