OpenMath Content Dictionary: ThreeDgeo1

Canonical URL:
http://nash.sip.ucm.es/LAD-3D/3DgeoCDs/ThreeDgeo1.ocd
CD File:
ThreeDgeo1.ocd
CD as XML Encoded OpenMath:
ThreeDgeo1.omcd
Defines:
circle, endpoints, line, midpoint, plane, point, segment, sphere
Date:
2008-01-21
Version:
0 (Revision 3)
Review Date:
2017-12-31
Status:
experimental


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  Author: Jesús Escribano

This CD defines symbols for 3-dimensional Euclidean geometry


point

Description:

The symbol is used to indicate a point of 3-dimensional Euclidean geometry by a variable. The point may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.

Example:
Given two lines l and m, a point A on l and m is defined by:
point ( A , incident ( A , l ) , incident ( A , m ) )
Signatures:
sts


[Next: line] [Last: sphere] [Top]

line

Description:

The symbol is used to indicate a line of 3-dimensional Euclidean geometry by a variable. The line may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.

Example:
Given points A and B in 3-dimensional space, a line l through A and B is defined by:
line ( l , incident ( A , l ) , incident ( B , l ) )
Signatures:
sts


[Next: segment] [Previous: point] [Top]

segment

Description:

The symbol is used to indicate a segment of a line in 3-dimensional Euclidean geometry by a variable. The segment is contained in the affine part of the line. The symbol takes the variable as the first argument and the endpoints as second and third arguments.

Example:
The segment s with endpoints A and B is given by
segment ( s , A , B )
Signatures:
sts


[Next: endpoints] [Previous: line] [Top]

endpoints

Description:

The symbol is used to indicate the set of the two endpoints of a segment in 3-dimensional Euclidean geometry by a variable. The symbol takes the variable as the first argument and the segment as second argument.

Example:
The set E of the two endpoints of a segment s is given by:
endpoints ( E , s )
Signatures:
sts


[Next: midpoint] [Previous: segment] [Top]

midpoint

Description:

The symbol is used to indicate the midpoint of a segment in 3-dimensional Euclidean geometry by a variable. The symbol takes the variable as the first argument and the segment as second argument.

Example:
The midpoint M of the segment s is given by
midpoint ( M , s )
Signatures:
sts


[Next: plane] [Previous: endpoints] [Top]

plane

Description:

The symbol is used to indicate a plane in 3-dimensional Euclidean geometry by a variable. The plane may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.

Example:
Given points A, B and C in 3-dimensional space, a plane p through A, B and C is defined by:
plane ( p , incident ( A , p ) , incident ( B , p ) , incident ( C , p ) )
Signatures:
sts


[Next: circle] [Previous: midpoint] [Top]

circle

Description:

The symbol is used to indicate a circle in 3-dimensional Euclidean geometry by a variable. The circle may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.

Example:
The circle c with center at A and passing through the point B is given by:
circle ( c , circle_center ( c , A ) , incident ( B , c ) )
Signatures:
sts


[Next: sphere] [Previous: plane] [Top]

sphere

Description:

The symbol is used to indicate a sphere in 3-dimensional Euclidean geometry by a variable. The sphere may (but need not) be subject to constraints. The symbol takes the variable as the first argument and the constraints as further arguments.

Example:
The sphere s with center at A and passing through the point B is given by:
sphere ( s , sphere_center ( s , A ) , incident ( B , s ) )
Signatures:
sts


[First: point] [Previous: circle] [Top]