# Tiger (EntityTopic, 11)

### From Hi.gher. Space

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*The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | *The [[realmic]] [[cross-section]]s (''n'') of a coninder are: | ||

- | <blockquote> | + | <blockquote>For realms parallel to one of the axes, they are formed by rotating Cassini ovals around a line parallel with their major axis, and not intersecting the ovals. </blockquote> |

{{Polychora}} | {{Polychora}} | ||

{{Rotope Nav|43|44|45|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|IIIII<br>Pentacube|chora}} | {{Rotope Nav|43|44|45|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|IIIII<br>Pentacube|chora}} |

## Revision as of 07:09, 21 June 2007

## Geometry

### Equations

- Assumption: Tiger is centered at the origin.
- Variables:

a⇒ major radius of the tiger in the xy plane

b⇒ major radius of the tiger in the zw plane

r⇒ minor radius of the tiger

- All points (
*x*,*y*,*z*,*w*) that lie on the surcell of a tiger will satisfy the following equation:

(sqrt(*x*^{2}+*y*^{2}) - *a*)^{2} + (sqrt(*z*^{2}+*w*^{2}) - *b*)^{2} = *r*^{2}

- The parametric equations are:

x=acos(θ) +_{1}rcos(θ)cos(_{1}θ)_{3}

y=asin(θ) +_{1}rsin(θ)cos(_{1}θ)_{3}

z=bcos(θ) +_{2}rcos(θ)sin(_{2}θ)_{3}

w=bsin(θ) +_{2}rsin(θ)sin(_{2}θ)_{3}

- The hypervolumes of a tiger are given by:

total edge length =Unknown

total surface area =Unknown

surcell volume =Unknown

bulk =Unknown

- The realmic cross-sections (
*n*) of a coninder are:

For realms parallel to one of the axes, they are formed by rotating Cassini ovals around a line parallel with their major axis, and not intersecting the ovals.