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Hornbein

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A 4D planet has no axis of rotation. Nothing special about planets, all freely rotating 4D bodies have two perpendicular planes of rigid rotation. (Clifford proved this in the 19th century.)

Now there is nothing stopping us from thinking of planes of rotation here in 3D Universe. It's the plane passing through the center of mass that is perpendicular to the axis of rotation. Here on 3D Earth the intersection of the plane of rotation with the surface of the Earth is called the Equator. (Instead of axis and cross product, one may choose to use geometric algebra. It uses planes of rotation and the geometric product to get exactly the same result. In 4D with no axis then geometric algebra must be used.) Note that planes of rotation are always 2D, no matter how many dimensions one may imagine. From now on when we say planes we always mean these 2D planes.

In 4D, two planes can be even more perpendicular than they are in our 3D world. Such planes may intersect only at a point. The planes of rotation of 4D Earth are like that.

4D Earth has no axis so it does not have poles. Instead the intersection of these two perpendicular circles of rotation with the surface makes for two perpendicular great circles of rotation. We will show that these two circles have more in common with our two pointlike poles than with the great circle that is our equator.

An equator partitions a planet into two equal halves. In 4D a great circle does not partition the surface of a 4D sphere, so it isn't an equator. Instead, extremes of climate may be found at the two circles, so they have that in common with our poles. Excepting seasonless planets, one circle has the coldest climate on the planet, the other the hottest. Every point on each of these circles is the same distance from every point on the other circle. Just like our poles.

OK, then how about the set of points on the surface of 4D Earth that are halfway between these two circles? Yes, that is our Equator. For a shape it has the surface of a four dimensional torus. Unlike a 3D torus, the major and minor radii of a 4D torus may be of equal value without the torus intersecting itself, or even getting anywhere close to intersecting itself. This torus surface partitions the surface of the planet into two equal parts, so it is an equator. To get from the hotter hemisphere to the colder one, you must cross the Equator.

The circles are perpendicular, so to get from one to the other one need traverse only 90 degrees worth of the Earth's surface. To go from circle to Equator, 45 degrees.

https://www.researchgate.net/publication/359213812_Elsewhere_Everyday_Life_On_A_Hypergeometric_Earth.

Now there is nothing stopping us from thinking of planes of rotation here in 3D Universe. It's the plane passing through the center of mass that is perpendicular to the axis of rotation. Here on 3D Earth the intersection of the plane of rotation with the surface of the Earth is called the Equator. (Instead of axis and cross product, one may choose to use geometric algebra. It uses planes of rotation and the geometric product to get exactly the same result. In 4D with no axis then geometric algebra must be used.) Note that planes of rotation are always 2D, no matter how many dimensions one may imagine. From now on when we say planes we always mean these 2D planes.

In 4D, two planes can be even more perpendicular than they are in our 3D world. Such planes may intersect only at a point. The planes of rotation of 4D Earth are like that.

4D Earth has no axis so it does not have poles. Instead the intersection of these two perpendicular circles of rotation with the surface makes for two perpendicular great circles of rotation. We will show that these two circles have more in common with our two pointlike poles than with the great circle that is our equator.

An equator partitions a planet into two equal halves. In 4D a great circle does not partition the surface of a 4D sphere, so it isn't an equator. Instead, extremes of climate may be found at the two circles, so they have that in common with our poles. Excepting seasonless planets, one circle has the coldest climate on the planet, the other the hottest. Every point on each of these circles is the same distance from every point on the other circle. Just like our poles.

OK, then how about the set of points on the surface of 4D Earth that are halfway between these two circles? Yes, that is our Equator. For a shape it has the surface of a four dimensional torus. Unlike a 3D torus, the major and minor radii of a 4D torus may be of equal value without the torus intersecting itself, or even getting anywhere close to intersecting itself. This torus surface partitions the surface of the planet into two equal parts, so it is an equator. To get from the hotter hemisphere to the colder one, you must cross the Equator.

The circles are perpendicular, so to get from one to the other one need traverse only 90 degrees worth of the Earth's surface. To go from circle to Equator, 45 degrees.

https://www.researchgate.net/publication/359213812_Elsewhere_Everyday_Life_On_A_Hypergeometric_Earth.

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