# Definitions

Describes the abbreviations

## Definitions

This article is meant to be an introduction to the

**Geometry**,**Analytic Geometry**and**other**types of geometries like Hilbert's geometry.## Geometry

Geometry is one of the oldest branches of mathematics .

The word geometry comes from an ancient greek word which can be translated as "Earth-measuring". In conclusion

The word geometry comes from an ancient greek word which can be translated as "Earth-measuring". In conclusion

**geometry**is a**mathematical**branch concerned with questions of**size**(areas, volumes etc),**shape**(triangle,square,cube etc) and**positions**of points(middle, the first point, center of gravity etc) or figures in an Euclidean space.The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia.

### Point

- In geometry aThus, a point is a 0-dimensional object. A point could also be defined as a sphere which has a diameter of zero (or a circle with a 0 diameter).
**point**is a**primitive**notion upon which other concepts may be defined. In geometry, points have**neither****volume**,**area**,**length**, nor any other higher dimensional analogue.

### Line

- The notion of
**line**or straight line was introduced by the ancient mathematicians (Euclidean geometry) to represent straight objects with negligible width and depth. Euclid (ancient greek mathematician) described a line as**"breadthless length"**.In the image bellow you can see a straight line.**Note**

The line has the equation

The**length**of a straight line is**infinity**.

### Triangle

- AIn Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space).
**triangle**a shape formed with**three****corners**or**vertices**and three sides or edges which are line segments.

A**triangle**with vertices , , and is denoted .**Triangles**can be classified according to the relative**lengths**of their sides in :

**equilateral**triangle, if

.**isosceles**triangle if two sides are equal in length.

**scalene**triangle if all sides are unequal.

**Triangles**can also be classified according to their internal**angles**in :

**right triangle**, if has one of its interior angles measuring 90 degrees.

**acute triangle**, if all of its angles are less then 90 degrees.

**obtuse triangle**, if has one of its angles greater then 90 degrees.

### Circle

- A
**circle**is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point, called the centre .

A circle's**diameter**is the length of a line segment whose endpoints lie on the circle and which passes through the centre.

The**radius**is half the diameter of the circle.

### Square

- A
**square**is a regular quadrilateral.

This means that it has four equal sides and four equal angles (90 degree angles, or right angles).

A square with vertices ABCD would be denoted .The**area**of a square is where is the side of the square.

The**perimeter**of a square is where is the side of the square.

## Analytic Geometry

In mathematics,

This contrasts with the synthetic approach of Euclidean geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on axioms and theorems to derive truth. **analytic geometry**, also known as**coordinate**geometry, or**Cartesian**geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.**Analytic geometry**is widely used in

**physics**and

**engineering**, and is the foundation of most modern fields of

**geometry**, including algebraic,

**differential**,

**discrete**, and computational geometry.

### Coordinate Geometry

- AFor example in a two dimensional space a point can be uniquely determined by a pair .
**coordinate system**or a**Carthesian system**is a system which uses one or more**numbers**, or**coordinates**, to**uniquely**determine the**position**of a point or other geometric element.

## Non-euclidean Geometries

A

For example : **non-Euclidean**geometry is the study of shapes and constructions that do not map directly to any n-dimensional Euclidean system**hyperbolic****geometry**or Lobachevskian geometry

**elliptic**geometry

Last Modified: 22 Feb 13 @ 15:37 Page Rendered: 2022-03-14 15:52:39