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Author: Jesús Escribano
This CD defines symbols for 3-dimensional Euclidean geometry
The symbol represents the logical incidence function which is a
binary function taking arguments representing geometric objects like points and lines and returning a boolean value.
It is true if and only if the first argument is incident to the second.
Example:
That a point A is incident to a line l is given by:
The statement that a circle in 3-dimensional Euclidean space has a given point as center.
Takes the circle as first argument and the point as second argument.
Example:
The circle c with center at A and passing through the point B is given by:
The statement that a sphere in 3-dimensional Euclidean space has a given point as center.
Takes the sphere as first argument and the point as second argument.
Example:
The sphere s with center at A and passing through the point B is given by:
The symbol represents a binary boolean function with input two lines or segments.
Its value is true whenever the first argument is perpendicular to the second.
Example:
This example states that the lines l and m are perpendicular.
The symbol represents a binary boolean function with input two lines or segments.
Its value is true whenever the first argument is parallel to the second.
Example:
This example states that the lines l and m are parallel.
The symbol represents a binary boolean function with a line as first argument and a plane as second argument.
Its value is true whenever the first argument is normal to the second.
Example:
This example states that the line l is normal to the plane p.
The symbol is a boolean n-ary function. Its arguments should be points.
When applied to a sequence of points in 3-dimensional Euclidean space, its evaluated to true if and only if there is a line on which all arguments lie.
Example:
This example states that the points A, B, C, and D are collinear.
The symbol is a boolean n-ary function. Its arguments should be points.
When applied to a sequence of points in 3-dimensional Euclidean space, its evaluated to true if and only if there is a plane on which all arguments lie.
Example:
This example states that the points A, B, C, and D are coplanar.
