56 HomeYamamoto and the Secret Admirers
Neal Stephenson 


Euclid (330-260 BC)
Euclid was a Greek mathematician and is considered to be one of the founding fathers of mathematics. Whilst living at Alexandria he wrote Elements, 13 books, nine of which deal with plane and solid geometry. For 2000 years, Euclid's system was thought to be the only possible foundation of geometry, but in the 19th century it was proposed that replacing two of Euclid's postulates it was possible to produce equally valid geometries that were non-Euclidean.

The postulates of Euclidean geometry are.

 1.  Exactly one straight line can be drawn between any two points.
 2.  A straight line can be continued indefinitely.
 3.  With any point as center, a circle with any radius may be described.
 4.  All right angles are equal.
 5.  Through a given point outside a given straight line, there passes only one line  parallel to the given line; that is, such a line does not intersect the given line.

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