Conoid
Encyclopedia
In geometry
, a conoid is a Catalan surface
all of whose rulings intersect a fixed line
, called the axis of the conoid. If all its rulings are perpendicular to its axis, then the conoid is called a right conoid
.http://books.google.com/books?id=K31Nzi_xhoQC&pg=PA277&dq=conoid+maple&lr=&ei=B9hvSs_qKYzSkASR8c3XDg
For example, the hyperbolic paraboloid z = xy is a conoid (in fact, a right conoid) with x-axis and y-axis as its two axes.
A conoid can be represented by parametric equations
where {ℓ, m, n} is a vector parallel to the axis of the conoid and ƒ(u) is some function.
If ℓ = m = 0 and n = 1, then the conoid is a right conoid
.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a conoid is a Catalan surface
Catalan surface
In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose rulings are parallel to a fixed plane. The vector equation of a Catalan surface is given by...
all of whose rulings intersect a fixed line
Line (geometry)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
, called the axis of the conoid. If all its rulings are perpendicular to its axis, then the conoid is called a right conoid
Right conoid
In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly a fixed straight line, called the axis of the right conoid....
.http://books.google.com/books?id=K31Nzi_xhoQC&pg=PA277&dq=conoid+maple&lr=&ei=B9hvSs_qKYzSkASR8c3XDg
For example, the hyperbolic paraboloid z = xy is a conoid (in fact, a right conoid) with x-axis and y-axis as its two axes.
A conoid can be represented by parametric equations
where {ℓ, m, n} is a vector parallel to the axis of the conoid and ƒ(u) is some function.
If ℓ = m = 0 and n = 1, then the conoid is a right conoid
Right conoid
In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly a fixed straight line, called the axis of the right conoid....
.