OpenMath Content Dictionary: ThreeDgeo3

Canonical URL:
http://nash.sip.ucm.es/LAD-3D/3DgeoCDs/ThreeDgeo3.ocd
CD File:
ThreeDgeo3.ocd
CD as XML Encoded OpenMath:
ThreeDgeo3.omcd
Defines:
assertion, configuration, discovery, distance, locus, set_affine_coordinates
Date:
2008-01-21
Version:
0 (Revision 3)
Review Date:
2017-12-31
Status:
experimental


     This document is distributed in the hope that it will be useful, 
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     provided that the following conditions are met.
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          work to the original source.
       b) The fact that the derived work is not the original OpenMath 
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          both this document and the derived work are Content Dictionaries
          then the derived work must include a different CDName element,
          chosen so that it cannot be confused with any works adopted by
          the OpenMath Society.  In particular, if there is a Content 
          Dictionary Group whose name is, for example, `math' containing
          Content Dictionaries named `math1', `math2' etc., then you should 
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          However you are free to name it `private_mathN' or some such.  This
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       c) The derived work is distributed under terms that allow the
          compilation of derived works, but keep paragraphs a) and b)
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  Author: Jesús Escribano

This CD defines symbols for 3-dimensional Euclidean geometry


set_affine_coordinates

Description:

Defines the affine coordinates of an a point in 3-dimensional Euclidean space. Takes the point as first argument and the vector with the coordinates as second argument.

Example:
The description of the point A with affine coordinates (4.8,0.6,10.2) is given by:
point ( A , set_affine_coordinates ( A , ( 4.8 , 0.6 , 10.2 ) ) )
Signatures:
sts


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distance

Description:

The distance between two affine points in 3-dimensional Euclidean space is the Euclidean distance. The distance between two geometric objects O and O' in 3-dimensional Euclidean space is the infimum of the distances between two affine points, one on O and one on O'.

Example:
The distance between two points A and B is given by
distance ( A , B )
Signatures:
sts


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configuration

Description:

The symbol represents a configuration in Euclidean 3-dimensional geometry consisting of a sequence of geometric objects like points, lines, etc, but also of other configurations.

Example:
The configuration of a point A and a line l incident to A is defined by:
configuration ( point ( A ) , line ( l , incident ( A , l ) ) )
Example:
The following is the description of the configuration consisting on two different points A and B and the line l determined by them:
configuration ( point ( A ) , point ( B , ¬ ( A = B ) ) , line ( l , incident ( A , l ) , incident ( B , l ) ) )
Signatures:
sts


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assertion

Description:

The symbol is a constructor with two arguments. Its first argument is a 3-dimensional Euclidean geometry configuration, its second argument a statement about the configuration, called thesis. When applied to a configuration C and a thesis T, the OpenMath object assertion(C,T) expresses the assertion that T holds in C.

Example:
The assertion that two distinct intersecting lines meet in only one point can be expressed as follows using the assertion symbol.
assertion ( configuration ( point ( A ) , point ( B ) , line ( l , incident ( A , l ) , incident ( B , l ) ) , line ( m , incident ( A , m ) , incident ( B , m ) , ¬ ( l = m ) ) ) , A = B )
Signatures:
sts


[Next: locus] [Previous: configuration] [Top]

locus

Description:

The symbol is used to indicate by a variable the locus set traced by a point T in a 3-dimensional Euclidean geometry configuration C. That is, the set of all points satisfying the conditions imposed on T in the configuration C. The locus may (but need not) be defined by constraints on the point T additional to those in the configuration. The symbol takes the variable as the first argument, the tracer point T as second argument and the additional constraints as further arguments.

Example:
The following example describes a configuration with the locus set L of all points C equidistant to two given points A and B.
configuration ( point ( A ) , point ( B ) , point ( C ) , locus ( L , C , distance ( A , C ) = distance ( B , C ) ) )
Signatures:
sts


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discovery

Description:

The symbol is used to describe the task of finding necessary conditions for some properties to hold in a geometric configuration in 3-dimensional Euclidean geometry. The symbol takes a configuration as the first argument and the properties for which necessary conditions are to be sought as further arguments.

Example:
The following example encodes the task of finding necessary conditions for a point C to be equidistant to the points A and B.
discovery ( configuration ( point ( A ) , point ( B ) , point ( C ) ) , distance ( A , C ) = distance ( B , C ) )
Signatures:
sts


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