Geometry: Difference between revisions
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The most common type of geometry used in pre-[[college|collegiate]] [[mathematics competitions]] is Euclidean geometry. This type of geometry was first formally outlined by the Greek [[mathematician]] [[Euclid]] in his book ''[[The Elements]]''. | The most common type of geometry used in pre-[[college|collegiate]] [[mathematics competitions]] is Euclidean geometry. This type of geometry was first formally outlined by the Greek [[mathematician]] [[Euclid]] in his book ''[[The Elements]]''. | ||
=== | ===Parallel Postulate=== | ||
{{main| | {{main|Parallel Postulate}} | ||
The | The seventh [[postulate]] stated in the book, | ||
:''“Through any line and a point not on the line, there is exactly one line passing through that point parallel to the line”'' | :''“Through any line and a point not on the line, there is exactly one line passing through that point parallel to the line”'' | ||
was the subject of a controversy for many centuries. This postulate is the basis of Euclidean geometry. | was the subject of a controversy for many centuries, with many attempted proofs. It is much less simple than the other postulates, and more wordy. This postulate is the basis of Euclidean geometry. | ||
== Non-Euclidean Geometry == | == Non-Euclidean Geometry == | ||
Revision as of 13:12, 22 December 2007
Geometry is the field of mathematics dealing with figures in a given space.
Euclidean Geometry
- Main article: Euclidean geometry
The most common type of geometry used in pre-collegiate mathematics competitions is Euclidean geometry. This type of geometry was first formally outlined by the Greek mathematician Euclid in his book The Elements.
Parallel Postulate
- Main article: Parallel Postulate
The seventh postulate stated in the book,
- “Through any line and a point not on the line, there is exactly one line passing through that point parallel to the line”
was the subject of a controversy for many centuries, with many attempted proofs. It is much less simple than the other postulates, and more wordy. This postulate is the basis of Euclidean geometry.
Non-Euclidean Geometry
Non-Euclidean geometry are geometries in which the eleventh postulate is altered. Types of non-Euclidean geometry include:
Student Guides to Geometry
Other Topics of Interest
- The notion of dimensions
