Classic problems
To trisect the angle CAB
Archimedes method
This method is usually attributed to Archimedes (born: 287 BC
in Syracuse, Sicily, died: 212 BC in Syracuse, Sicily) and uses
the principal of Archimedes' spiral.
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The conchoid of Nicomedes
This second method is usually attributed to Pappus (born: 8
Feb 411 in Constantinople (now Istanbul), Byzantium (now Turkey),
died: 17 April 485 in Athens, Greece) and is based on a curve
known as the conchoid of Nicomedes (born: about 280 BC in Greece,
died: about 210 BC). Pappus wrote: Nicomedes trisected any
rectilinear angle by means of the conchoidal curves, the construction,
order and properties of which he handed down, being himself
the discoverer of their peculiar character.
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Note
Neither of these methods construct the required trisection in the
way that other constructions do. In both cases, the identification
of the final position for the trisecting line depends on measurement,
in other words on using a ruler as opposed to a straight edge. This
breaks the basic rule for constructability. |
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