Coordinates - Revision history

Lfox at 19:59, 28 February 2024

2024-02-28T19:59:22Z

← Older revision		Revision as of 19:59, 28 February 2024
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	A '''coordinate system''' is a system assigning a number (or [[Set\|tuple]] of numbers) to ~~every~~ [[point]] on an [[entity]]. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point.		A '''coordinate system''' is a system assigning a number (or [[Set\|tuple]] of numbers) to any [[point]] lying in a subregion of an [[entity]]. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point.

			An atlas is a set of coordinate systems, such that their corresponding subregions cover the entity.

	== Examples ==		== Examples ==
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	Using a similar procedure, if one picks a [[ray]] on a plane, one can use it to define a "polar" coordinate system on the plane.		Using a similar procedure, if one picks a [[ray]] on a plane, one can use it to define a "polar" coordinate system on the plane.

			== Entity vs. Manifold ==
			[TODO]

Lfox: /* Examples */

2024-02-14T04:25:43Z

Examples

← Older revision		Revision as of 04:25, 14 February 2024
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	Longitude and latitude are a coordinate system for the surface of the earth.		Longitude and latitude are a coordinate system for the surface of the earth.

	If one picks two lines on a [[Surface#Plane\|plane]] which meet at right angles, then one ~~has implicitly chosen~~ a ~~Cartesian~~ coordinate system for the plane.		If one picks two [[oriented]] lines on a [[Surface#Plane\|plane]] which meet at right angles, then one can use them to define a coordinate system for the plane, called "cartesian" coordinates. The cartesian coordinates of a point <math>p</math> on the plane are two numbers <math>(x_p, y_p)</math>, determined as follows. First, [[order]] the two lines using the right-hand rule: the [[cross product]] of the first line with second line should point away from you. Project <math>p</math> onto the first line, and let <math>x_p</math> denote the (signed) distance between its projection and the origin. Similarly, project <math>p</math> onto the second line, and let <math>y_p</math> denote the (signed) distance between its projection and the origin.

			Using a similar procedure, if one picks a [[ray]] on a plane, one can use it to define a "polar" coordinate system on the plane.

Lfox: Created page with "A '''coordinate system''' is a system assigning a number (or tuple of numbers) to every point on an entity. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point. == Examples == Longitude and latitude are a coordinate system for the surface of the earth. If one picks two lines on a plane which meet at right angles, then one has implicitly chosen a Cartesian coordinate..."

2024-02-14T04:12:18Z

Created page with "A '''coordinate system''' is a system assigning a number (or tuple of numbers) to every point on an entity. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point. == Examples == Longitude and latitude are a coordinate system for the surface of the earth. If one picks two lines on a plane which meet at right angles, then one has implicitly chosen a Cartesian coordinate..."

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A '''coordinate system''' is a system assigning a number (or [[Set|tuple]] of numbers) to every [[point]] on an [[entity]]. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point.

== Examples ==
Longitude and latitude are a coordinate system for the surface of the earth.

If one picks two lines on a [[Surface#Plane|plane]] which meet at right angles, then one has implicitly chosen a Cartesian coordinate system for the plane.