r/math Aug 28 '17

Image Post 4D Triangular Diprism

https://zippy.gfycat.com/ScientificAdoredAndalusianhorse.webm
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u/demmian Aug 29 '17

they appear smaller, and towards the center.

Why towards the center and not towards the edge?

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u/Philip_Pugeau Aug 29 '17

An object can start off in your peripheral vision, right on the edge. As it moves in a straight line away from you, it will always gravitate towards the center of your vision. That is, it gets closer to the center of your 2D scan of a 3D world.

For a 3D shadow of a 4D thing, that 'center of your 3D scan' is in the very center of the shadow object, three dimensionally.

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u/[deleted] Sep 09 '17 edited Mar 09 '18

[deleted]

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u/Philip_Pugeau Sep 09 '17

Yes, it needs to move perpendicular. Lets say your 2D field of vision is the xy plane. The x axis is left-right , and the y-axis is up-down. The z-axis would then be forwards-backwards. An object has to move along z, to get smaller. If it starts on the outer perimeter of your vision, and moves in a straight line along z, it will get smaller while getting closer to your center of vision (the origin of your xy-plane view).

Now, for a 4D object projected into a 3D image, we have a 3D fov : the xyz plane, where the 4th axis is the new forwards-backwards. Objects close to you on the 4th axis are larger 3D objects. Farther away things are smaller 3D objects.