History
The postulate, as given above, appears in (Coxford 1992, pg. 801) as part of the secondary school geometry curriculum revision of the University of Chicago School Mathematics Project (UCSMP).
The axiomatic foundation of Euclidean geometry can be dated back to the books known as Euclid's Elements (circa 300 B.C.E.). These five initial axioms (called postulates by the ancient Greeks) are not sufficient to establish Euclidean geometry. Many mathematicians have produced complete sets of axioms which do establish Euclidean geometry. One of the most notable of these is due to Hilbert who created a system in the same style as Euclid. Unfortunately, Hilbert's system requires 21 axioms. Other systems have used fewer (but different) axioms. The most appealling of these, from the viewpoint of having the fewest number of axioms, is due to Garrett Birkhoff (1932) which has only four axioms. These four are: the Unique line assumption (which was called the Point-Line Postulate by Birkhoff), the Number line assumption, the Protractor postulate (to permit the measurement of angles) and an axiom that is equivalent to Playfair's axiom (or the parallel postulate).
Read more about this topic: Point-line-plane Postulate
Famous quotes containing the word history:
“English history is all about men liking their fathers, and American history is all about men hating their fathers and trying to burn down everything they ever did.”
—Malcolm Bradbury (b. 1932)
“Yet poetry, though the last and finest result, is a natural fruit. As naturally as the oak bears an acorn, and the vine a gourd, man bears a poem, either spoken or done. It is the chief and most memorable success, for history is but a prose narrative of poetic deeds.”
—Henry David Thoreau (1817–1862)
“We said that the history of mankind depicts man; in the same way one can maintain that the history of science is science itself.”
—Johann Wolfgang Von Goethe (1749–1832)