all type of coordinates system implementation

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 Course Title: Analytical and Vector Geometry
 Course Code: MAT 103
 Coordinate system

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Coordinate System

4. How many types of Coordinate system in
Analytics and Vector Geometry ?
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There Are majorly five types of Coordinate System:
1. Cartesian coordinate system
2. Polar coordinate system
3. Cylindrical coordinate system
4. Spherical coordinate system
5. Curvilinear coordinate system

5.  Cartesian Coordinate system
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At First we will try to introduce the
inventor of this co-ordinate system.
Inventor : René Descartes (1596-
1650)
French philosopher, mathematician,
and scientist.

6.  Concept about the Co-ordinate system
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There is are two axis-X and Y. Zero is the
origin 0 (0,0).
The abscissa of a point is the
signed measure of its projection on the
primary axis.
The ordinate of a point is the
signed measure of its projection on the
secondary axis, whose absolute value is the
distance between the projection and the
origin of the axis.

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In mathematics, the polar coordinate
system is a two-dimensional coordinate
system in which each point on a plane is
determined by a distance from a reference
point and an angle from a reference
direction.
The distance from the pole is called
the radial coordinate or radius, and the angle
is called the angular coordinate, polar angle,
or azimuth.
 Polar Co-ordinate System:

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The concepts of angle and radius were
already used by ancient peoples of the
first millennium BC. The Greek
astronomer and astrologer Hipparchus
(190–120 BC) created a table of chord
function and he was the first person
who gave concept about this system.
Inventor of Polar-co ordinate system

9.  Cylindrical co-ordinate system
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A cylindrical coordinate system is a three-
dimensional coordinate system that specifies
point positions by the distance from a chosen
reference axis, the direction from the axis
relative to a chosen reference direction, and
the distance from a chosen reference plane
perpendicular to the axis.

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3D Figure for clear concept of Cylindrical co-ordinate system

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Relation Between Polar and Cartesian Co-ordinate system:
x=rcos0
Y=r sin
tan0=y/x
or, 0=tan^-1(y/x)

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Spherical coordinate system
In mathematics, a spherical coordinate system is
a coordinate system for three-dimensional
space where the position of a point is specified by
three numbers: the radial distance of that point from
a fixed origin, its polar angle.

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Application : partial differential equations , Laplace's equation and Helmholtz equation, separation of
variables in spherical coordinates.
This co ordinate system is developed by
Sir, Isssac (January 4, 1643-
March 31, 1727)

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 curvilinear coordinates are
a coordinate system for Euclidean
space in which the coordinate
lines may be curved. Commonly
used curvilinear coordinate
systems include: rectangular,
spherical, and cylindrical
coordinate systems. These
coordinates may be derived from
a set of Cartesian coordinates by
using a transformation that
is locally invertible (a one-to-one
map) at each point.

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3D clear concept of curvilinear coordinates

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DO YOU
HAVE ANY
QUESTIONS
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