coordinates system
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This document discusses the five main types of coordinate systems: Cartesian, polar, cylindrical, spherical, and curvilinear. It provides details on the definition and key aspects of each system. The Cartesian system is attributed to René Descartes and uses perpendicular x and y axes. The polar system specifies points using an angle and distance from a central point. Cylindrical coordinates use distance from an axis, angle from a reference direction, and distance from a plane. Spherical coordinates rely on radial distance and two angular measurements. Curvilinear coordinates involve curved coordinate lines rather than straight ones.
coordinates system
- 1. 11/9/2018 1 Course Title: Analytical and Vector Geometry Course Code: MAT 103 Coordinate system
- 2. 11/9/2018 2
- 4. How many types of Coordinate system in Analytics and Vector Geometry ? 11/9/2018 4 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 11/9/2018 5 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 11/9/2018 6 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.
- 7. 11/9/2018 7 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:
- 8. 11/9/2018 8 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 11/9/2018 9 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.
- 10. 11/9/2018 10 3D Figure for clear concept of Cylindrical co-ordinate system
- 11. 11/9/2018 11 Relation Between Polar and Cartesian Co-ordinate system: x=rcos0 Y=r sin tan0=y/x or, 0=tan^-1(y/x)
- 12. 11/9/2018 12 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.
- 13. 11/9/2018 13 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)
- 14. 11/9/2018 14 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.
- 15. 11/9/2018 15 3D clear concept of curvilinear coordinates
- 16. 11/9/2018 16 DO YOU HAVE ANY QUESTIONS ?
- 17. 11/9/2018 17