# 25++ 4d torus info

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**4d Torus**. Been sliced by a series of hyperplanes. It seems as though the answer may be obvious but then seemingly simple math questions can have surprising. For example the volume of a rectangular box is found by measuring and multiplying its. Every point on this hypersurface is at the same distance from the origin.

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Im thinking the circle cross-section of the pinched torus would similarly pop out into the 4th dimension and somehow rotate in 4D space avoiding pinch points. For a few years Ive theorized. Does there exist a 4D torus with a spherical cross-section analogous to a circle for the 3D case. 1 begingroup I dont mean to be a bother. Of the two alternatives the perspective projection looks much more appealing. A four-dimensional torus has a skin which is a circle times a circle times a circle.

### Im thinking the circle cross-section of the pinched torus would similarly pop out into the 4th dimension and somehow rotate in 4D space avoiding pinch points.

You cant build a model of a 4D torus in 3D space any more than you can build a 3D shape inside a thin plane. This video shows the answer as the slicing hyperplane gradually moves through the 4D torus. Active 4 years 11 months ago. Gerard Balmens November 2012. Torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N 2 3 or more dimensions with processors connected to their nearest neighbors and corresponding processors on opposite edges of the array connected. Howeve the evidence from CMB observations does not support a spherical topology rather the lar.

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Basically its the 4D version of this. A four-dimensional torus has a skin which is a circle times a circle times a circle. This movie shows what the cross-sections look like. Theres even more potential here. There is a general preference for a spherical topology for closed Universes because the maths is fairly simple and we see lots of ball-shapes anyway.

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Introduction to 5D 4D and 6D torus thinking on FZJs JUQUEEN supercomputer Workshop Introduction to Blue GeneQ Jülich Supercomputing Centre 2012-05-10 Michael Hennecke Client Technical Architect High Performance Computing. Howeve the evidence from CMB observations does not support a spherical topology rather the lar. Unlike in 3D where there is just one torus there are four distinct four-dimensional torii. Every point on this hypersurface is at the same distance from the origin. A four-dimensional space 4D is a mathematical extension of the concept of three-dimensional or 3D spaceThree-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers called dimensions to describe the sizes or locations of objects in the everyday world.

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Every point on this hypersurface is at the same distance from the origin. Been sliced by a series of hyperplanes. A four-dimensional space 4D is a mathematical extension of the concept of three-dimensional or 3D spaceThree-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers called dimensions to describe the sizes or locations of objects in the everyday world. The Clifford torus is a torus lies on the surface of the hypersphere in 4d. Unlike in 3D where there is just one torus there are four distinct four-dimensional torii.

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Ask Question Asked 6 years 3 months ago. Im thinking the circle cross-section of the pinched torus would similarly pop out into the 4th dimension and somehow rotate in 4D space avoiding pinch points. What do you get if you slice through a four dimensional torus. Torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N 2 3 or more dimensions with processors connected to their nearest neighbors and corresponding processors on opposite edges of the array connected. Does there exist a 4D torus with a spherical cross-section analogous to a circle for the 3D case.

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We can generalize the rule from the figures above. Does there exist a 4D torus with a spherical cross-section analogous to a circle for the 3D case. 1 begingroup I dont mean to be a bother. If you slice a 5 or 6D torus in 4D then project in 3D you can morph a product of tigers into 3-tori by rotation. For example the volume of a rectangular box is found by measuring and multiplying its.

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Active 4 years 11 months ago. A four-dimensional torus has a skin which is a circle times a circle times a circle. Und wieder mal Spaß mit dem Colorizer Hoffe es gefällt Euch And again Fun with the Colorizer Hope you like it Inspiration herehttpswwwbehanc. Howeve the evidence from CMB observations does not support a spherical topology rather the lar. The program projects the 4d torus to 3d using either a perspective or an orthographic projection.

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You cant build a model of a 4D torus in 3D space any more than you can build a 3D shape inside a thin plane. Fullscreen The Demonstration rotates the stereographic projection of a 4D Clifford torus or square torus defined by the points. A four-dimensional torus has a skin which is a circle times a circle times a circle. The program projects the 4d torus to 3d using either a perspective or an orthographic projection. Unlike in 3D where there is just one torus there are four distinct four-dimensional torii.

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Basically its the 4D version of this. Viewed 1k times 6. Gerard Balmens November 2012. Und wieder mal Spaß mit dem Colorizer Hoffe es gefällt Euch And again Fun with the Colorizer Hope you like it Inspiration herehttpswwwbehanc. Of the two alternatives the perspective projection looks much more appealing.

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A four-dimensional torus has a skin which is a circle times a circle times a circle. Und wieder mal Spaß mit dem Colorizer Hoffe es gefällt Euch And again Fun with the Colorizer Hope you like it Inspiration herehttpswwwbehanc. A 4d torus has here. Howeve the evidence from CMB observations does not support a spherical topology rather the lar. 1 begingroup I dont mean to be a bother.

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Howeve the evidence from CMB observations does not support a spherical topology rather the lar. Howeve the evidence from CMB observations does not support a spherical topology rather the lar. Using a parametric equation with 4 or 5 time variables one can make animations of 4D rotation morphs projected in 3D. This video shows the answer as the slicing hyperplane gradually moves through the 4D torus. We can generalize the rule from the figures above.

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Fullscreen The Demonstration rotates the stereographic projection of a 4D Clifford torus or square torus defined by the points. These together with the glome make up the full set of closed4D toratopes. This movie shows what the cross-sections look like. What do you get if you slice through a four dimensional torus. But Id like to have help in understanding this intuitively - or if theres an image or animation that helps visualize it.

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Theres even more potential here. Fullscreen The Demonstration rotates the stereographic projection of a 4D Clifford torus or square torus defined by the points. Does there exist a 4D torus with a spherical cross-section analogous to a circle for the 3D case. This page attempts to help the reader understand where these four different figures come from and what they look like. Im thinking the circle cross-section of the pinched torus would similarly pop out into the 4th dimension and somehow rotate in 4D space avoiding pinch points.

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We can generalize the rule from the figures above. But Id like to have help in understanding this intuitively - or if theres an image or animation that helps visualize it. Unlike in 3D where there is just one torus there are four distinct four-dimensional torii. But if you slice the 4D shape you get a 3D slice. Active 4 years 11 months ago.

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Unlike in 3D where there is just one torus there are four distinct four-dimensional torii. Introduction to 5D 4D and 6D torus thinking on FZJs JUQUEEN supercomputer Workshop Introduction to Blue GeneQ Jülich Supercomputing Centre 2012-05-10 Michael Hennecke Client Technical Architect High Performance Computing. If you slice a 5 or 6D torus in 4D then project in 3D you can morph a product of tigers into 3-tori by rotation. Theres even more potential here. Viewed 1k times 6.

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Unlike in 3D where there is just one torus there are four distinct four-dimensional torii. This movie shows what the cross-sections look like. But if you slice the 4D shape you get a 3D slice. For example the volume of a rectangular box is found by measuring and multiplying its. Gerard Balmens November 2012.

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A 4d torus has here. Animate it treat animation as 4th dimention - so we kinda have a 4d cylinder now where each 3d slice is one frame of animation now bend this 4d cylinder into a 4d torus randomly rotate this torus and slice it. Theres even more potential here. A 4d torus has here. To get the pictures on this page I took lots of slices of a 4D torus.

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A 4d torus has here. Theres even more potential here. If you slice a 5 or 6D torus in 4D then project in 3D you can morph a product of tigers into 3-tori by rotation. The program projects the 4d torus to 3d using either a perspective or an orthographic projection. Torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N 2 3 or more dimensions with processors connected to their nearest neighbors and corresponding processors on opposite edges of the array connected.

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Animate it treat animation as 4th dimention - so we kinda have a 4d cylinder now where each 3d slice is one frame of animation now bend this 4d cylinder into a 4d torus randomly rotate this torus and slice it. This page attempts to help the reader understand where these four different figures come from and what they look like. What do you get if you slice through a four dimensional torus. You cant build a model of a 4D torus in 3D space any more than you can build a 3D shape inside a thin plane. Howeve the evidence from CMB observations does not support a spherical topology rather the lar.

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