About An Arbitrary Axis
Consider an infinite cylinder whose axis lies along the vector
We make use of spherical coordinates:
These variables can be used to define A and B, the orthogonal vectors that form the basis for the cylinder:
With these defined, we may use the familiar formula for a cylinder:
where R is the radius of the cylinder. These results are usually derived using rotation matrices.
Read more about this topic: Cylinder (geometry)
Famous quotes containing the words arbitrary and/or axis:
“A state that denies its citizens their basic rights becomes a danger to its neighbors as well: internal arbitrary rule will be reflected in arbitrary external relations. The suppression of public opinion, the abolition of public competition for power and its public exercise opens the way for the state power to arm itself in any way it sees fit.... A state that does not hesitate to lie to its own people will not hesitate to lie to other states.”
—Václav Havel (b. 1936)
“Our security depends on the Allied Powers winning against aggressors. The Axis Powers intend to destroy democracy, it is anathema to them. We cannot provide that aid if the public are against it; therefore, it is our responsibility to persuade the public that aid to the victims of aggression is aid to American security. I expect the members of my administration to take every opportunity to speak to this issue wherever they are invited to address public forums in the weeks ahead.”
—Franklin D. Roosevelt (1882–1945)