Duocylinder (EntityTopic, 14)

From Hi.gher. Space

Revision as of 10:55, 16 June 2007 by Keiji (Talk | contribs)

Template:Shape

Geometry

A duocylinder is the Cartesian product of two circles.

Equations

  • Variables:
a ⇒ radius of the circle in the xy plane
b ⇒ radius of the circle in the zw plane
  • All points (x, y, z, w) that lie on the 2D margin of a duocylinder will satisfy the following equations:
x2 + y2 = a2
z2 + w2 = b2
  • A duocylinder has two bounding surfaces (3D volumes) which meet at the 2D margin. These are given respectively by the systems of equations:
  1. x2 + y2 = a2; z2 + w2b2
  2. x2 + y2a2; z2 + w2 = b2
Each of these bounding volumes are topologically equivalent to the inside of a 3D torus. The set of points (w,x,y,z) that satisfy either the first or the second set of equations constitute the surface of the duocylinder.
total surface area = 4π2ab
surcell volume = 2π2ab(a + b)
bulk = π2a2b2
  • The orthogonal projections of a duocylinder are cylinders. The perspective projections of a duocylinder are intertwined toroidal and hourglass-like shapes.

Template:Polychora Template:Rotopes


Online Casino - Choosing the best casinos. online casino online casino games play casino games game play casino games Casino rules. casinos strategy Online casino - Poker in casino roulette tips online casino gamble