Equator for 4d Planets

Discussion of shapes with curves and holes in various dimensions.

Equator for 4d Planets

Postby anderscolingustafson » Sat Mar 08, 2014 4:12 am

I know for a 4d planet there would be two great circles perpendicular to each other that don't intersect and between them there would be some kind of a Toratope. I was just wondering would the Toratope that would be between the two great circles on a 4d planet be a Duocylinder? The Duocylinder has the equation x2+y2=r12, z2+w2=r22. So the equation of the Duocylinder is basically two equations for circles. So is the Duocylinder the Toratope that would be the equator of a 4d planet?
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Re: Equator for 4d Planets

Postby wendy » Sat Mar 08, 2014 7:10 am

There is an equator, but you don't have to cross it: there are no hemispheres.

In 3d, you have the N and S hemispheres, which are six months apart (the N trails the S by six or eighteen months). In 4d, you have year-zones like day-zones. So just like you have GMT-10 (ie 2 am when it's 12 noon GMT), you have also 'year-zones', which means that when it's Mid-Winter in Greenwich, it can be early autumn or late spring or something somewhere else.

In a temeperate zone, you have eg 'summer sports' and 'winter sports'. These move from hemisphere to hemisphere to follow the seasons. You have in 4d, they can follow the seasons, so you move the distance from say london to new york, so that 'late summer' becomes 'early summer'. You hang around there to late summer and move onto the next venue. So, for example, test cricket could come mid summer, but this would follow the sun, so to speak.

The sun never crosses the equator. Instead, it is restricted to the tropics, and the zenith is over something like 'tropic of leo' or 'tropic of aquarius', meaning that the sun is overhead in leo or aquarius.
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