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:

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
    <OMS cd="plangeo2" name="segment"/>
      <OMV name="A"/>
      <OMV name="B"/>
    </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="plangeo2">segment</csymbol><ci>A</ci><ci>B</ci></apply></math>

Prefix

segment ( A, B)

Popcorn

plangeo2.segment($A, $B)

Rendered Presentation MathML

$$\mathrm{segment}(A,B)$$

Signatures:

sts

halfline

Description:

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

Example:

OpenMath XML (source)

 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
    <OMS cd="plangeo2" name="halfline"/>
      <OMV name="A"/>
      <OMV name="B"/>
    </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="plangeo2">halfline</csymbol><ci>A</ci><ci>B</ci></apply></math>

Prefix

halfline ( A, B)

Popcorn

plangeo2.halfline($A, $B)

Rendered Presentation MathML

$$\mathrm{halfline}(A,B)$$

Signatures:

sts

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:

OpenMath XML (source)

 
 
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
    <OMS cd="plangeo2" name="corner"/>
      <OMV name="L"/>
      <OMV name="M"/>
    </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="plangeo2">corner</csymbol><ci>L</ci><ci>M</ci></apply></math>

Prefix

corner ( L, M)

Popcorn

plangeo2.corner($L, $M)

Rendered Presentation MathML

$$\mathrm{corner}(L,M)$$

or

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
    <OMS cd="plangeo2" name="corner"/>
      <OMV name="A"/>
      <OMV name="B"/>
      <OMV name="C"/>
    </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="plangeo2">corner</csymbol><ci>A</ci><ci>B</ci><ci>C</ci></apply>
</math>

Prefix

corner ( A, B, C)

Popcorn

plangeo2.corner($A, $B, $C)

Rendered Presentation MathML

$$\mathrm{corner}(A,B,C)$$

Signatures:

sts

endpoint

Description:

The endpoint of a halfline.

Example:

The endpoint of a halfline H is given by

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
  <OMS cd="plangeo2" name="endpoint"/>
    <OMV name="H"/>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="plangeo2">endpoint</csymbol><ci>H</ci></apply></math>

Prefix

endpoint ( H)

Popcorn

plangeo2.endpoint($H)

Rendered Presentation MathML

$$\mathrm{endpoint}\left(H\right)$$

Signatures:

sts

endpoints

Description:

The two endpoints of a segment.

Example:

The set of the two endpoints of a segment S is given by

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
<OMA>
  <OMS cd="plangeo2" name="endpoints"/>
    <OMV name="S"/>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol cd="plangeo2">endpoints</csymbol><ci>S</ci></apply></math>

Prefix

endpoints ( S)

Popcorn

plangeo2.endpoints($S)

Rendered Presentation MathML

$$\mathrm{endpoints}\left(S\right)$$

Signatures:

sts