Classic problems
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There are three classical problems in Greek geometry
that have fascinated mathematicans for centuries:
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- One: squaring the circle
You can square the polygon but can you square the circle?
(See also sacred geometry).
- Two: doubling the cube
The problem of constructing a cube whose volume is twice
that of a given cube is known as the Delian problem. In
430 BC the oracle at Delos told the Athenians that to stave
off a plague they must double in size the altar of Apollo.
- Three: trisecting an angle
Some angles can be trisected, for example 180° and 90°
- since 60° and 30° can be constructed. However,
there is no method, using only an unmarked straight edge
and compass, to trisect an arbitary angle.
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