Difference between revisions of "Geometry"

(Introductory Videos)
(Introductory Videos)
Line 2: Line 2:
  
 
==Introductory Videos==
 
==Introductory Videos==
https://youtu.be/51K3uCzntWs?t=842 \\
+
[youtube]https://youtu.be/51K3uCzntWs?t=842[/youtube] \\
https://youtu.be/j3QSD5eDpzU
+
[youtube]https://youtu.be/j3QSD5eDpzU[/youtube]
  
 
== Euclidean Geometry ==
 
== Euclidean Geometry ==

Revision as of 07:59, 25 September 2020

Geometry is the field of mathematics dealing with figures in a given space. It is one of the two oldest branches of mathematics, along with arithmetic (which eventually branched into number theory and algebra). The geometry usually studied is

Introductory Videos

[youtube]https://youtu.be/51K3uCzntWs?t=842[/youtube] \\ [youtube]https://youtu.be/j3QSD5eDpzU[/youtube]

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 fifth postulate stated in the book, equivalent to the following statement,

“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 fifth postulate is altered. Types of non-Euclidean geometry include:

Student Guides to Geometry

Main Concepts

  • The notion of dimensions is fundamental to geometry. N-space is a term related to this concept.
  • A point is a geometric structure with no area, length, width, or dimension. Its only property is space. It is said to be zero-dimensional.
  • A line is generally taken to mean a straight line, which is the locus of points on the Cartesian plane satisfying a linear function. It has length and position, but no other properties. It is one-dimensional. A line segment means a finite segment of a line, while a ray is a line infinitely extending in only one direction.
  • A plane is a line but in a Cartesian space. It as length, width, and position. It is two-dimensional. The point/line/plane sequence can be extended to spaces and higher dimensions.
  • An angle is a structure formed by the intersection two rays at their endpoints. It is measure in either degrees or radians, though the less-common metric unit gradian is also used.

See Also

Invalid username
Login to AoPS