Parametric Form
A right spherical hypercone can be described by the function
with vertex at the origin and expansion speed s.
An oblique spherical hypercone could then be described by the function
where is the 3-velocity of the center of the expanding sphere. An example of such a cone would be an expanding sound wave as seen from the point of view of a moving reference frame: e.g. the sound wave of a jet aircraft as seen from the jet's own reference frame.
Note that the 3D-surfaces above enclose 4D-hypervolumes, which are the 4-cones proper.
Read more about this topic: Spherical Cone
Famous quotes containing the word form:
“Who among us has not, in moments of ambition, dreamt of the miracle of a form of poetic prose, musical but without rhythm and rhyme, both supple and staccato enough to adapt itself to the lyrical movements of our souls, the undulating movements of our reveries, and the convulsive movements of our consciences? This obsessive ideal springs above all from frequent contact with enormous cities, from the junction of their innumerable connections.”
—Charles Baudelaire (1821–1867)