This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work. Moreover if
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
not name a derived Content Dictionary `mathN' where N is an integer.
However you are free to name it `private_mathN' or some such. This
is because the names `mathN' may be used by the OpenMath Society
for future extensions.
c) The derived work is distributed under terms that allow the
compilation of derived works, but keep paragraphs a) and b)
intact. The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
If you have questions about this license please contact the OpenMath
society at http://www.openmath.org.
Author: Jesús Escribano
This CD defines symbols for 3-dimensional Euclidean geometry
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:
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
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:
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.
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.
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.
