# OpenMath Content Dictionary: plangeo2

Canonical URL:
http://www.openmath.org/cd/plangeo2.ocd
CD Base:
http://www.openmath.org/cd
CD File:
plangeo2.ocd
CD as XML Encoded OpenMath:
plangeo2.omcd
Defines:
corner, endpoint, endpoints, halfline, segment
Date:
2004-06-01
Version:
0 (Revision 2)
Review Date:
2006-06-01
Status:
experimental

This CD defines symbols for planar Euclidean geometry.

## segment

Description:

The segment of a line between two points of the line. The segment is contained in the affine part of the line. The symbol takes as arguments the two points.

Example:
The segment AB:
$\mathrm{segment}\left(A,B\right)$
Signatures:
sts

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## halfline

Description:

The halfline starting at A and going through B. The symbol takes as arguments the points A and B.

Example:
$\mathrm{halfline}\left(A,B\right)$
Signatures:
sts

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## corner

Description:

The corner between two halflines L and M, both starting at the same point. Given three points A, B and C, the corner A, B, C is the corner of the two halflines BA and BC. Corresponding to the two cases, the symbol can have as arguments two halflines or three points.

Example:
$\mathrm{corner}\left(L,M\right)$
or
$\mathrm{corner}\left(A,B,C\right)$
Signatures:
sts

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## endpoint

Description:

The endpoint of a halfline.

Example:
The endpoint of a halfline H is given by
$\mathrm{endpoint}\left(H\right)$
Signatures:
sts

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## endpoints

Description:

The two endpoints of a segment.

Example:
The set of the two endpoints of a segment S is given by
$\mathrm{endpoints}\left(S\right)$
Signatures:
sts

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