Recent content by Ray Fischer

Interesting! The Klein Bot does not have an edge the "Torbus Cup" is only one surface with one edge.. The Klein bottle is a closed surface with an inside and outside.

A three dimensional figure, similar to the Klein Bottle. The Torbus Cup is made with two Torbus Rings counter-rotated that are single-sided with one edge morphed, similar to the connecting ends of Mobius Strip, The Torbus Ring is made by folding a Cornu-type geometry.

Thanks for the additional logic. Does the tube edge still join to the Klein Bottle surface? To make the Mobius Cup only edges of the two Mobius counter rotated bands are connected. What difference does this make in the logic?

So, only 3d space is “real” or exists; my “Torbus Cup” exists and the Klein bottle is only imagery of what might exist in whatever 4d space is?When I laminate the “Twisted rings” (not a “Mobius Band”- which is not coplanar – it has a completely different geometry) with bands cut from “the...

If I cannot make a Klein bottle in 3d space; how can two Mobius Bands in 3d space make a Klein bottle? What would you call the geometric figure I made? Is a Klein bottle a real geometric figure or an illusion? How can an edge be attached to a surface? As you can tell I do not know much about...

So that is why I made a Mobius cup (or Torbus cup), both have edges, out of two Mobius Bands then cut it in half and found I still had two Mobius bands. Thanks? Check out Klein Bottle on Wikipedia ! Maybe I posted a video.

I show an animation (video) of forming a Klein bottle from a Torus on my Facebook page (Ray Fischer), it has an edge just like a Mobius Band. Splitting that geometry gives two Mobius Bands that are counter twisted. I can give you other data that has more information to shows why the Klein...

mobiusstrip16 If the Klein bottle has an edge then splitting it the two halves are two Mobius Strips one counter twisted from the other. That is what I got from the model I made! Is there something wrong with my animation?

Lavinia #6If the Klein bottle has an edge then splitting it the two halves are two Mobius Strips one counter twisted from the other.

Ref: #10 How would you describe (with your notations) a rectangle bounded by a circle moving around a ring; for each degree the rectangle moves around the ring the rectangle rotates .5 deg.in the circle (cw or ccw)? That is a "Torbus". If there is a minimum kerf, gap in the circle, between the...

Thanks for the suggetion.

OK! If you notice what is happening with the Torbus, a point in the torus is allowed to move outside of the torus on a restricted path, but the path it can move on depends on its position on the Torbus twisted ring in the tours. (Note the loci in post 7) The green dot is on the planar part of...

Another thought- Laminates on a Mobius ring can move radially, 1D or circumferentially, also 1D,or in both direction at the same time on the laminated Mobius strip, 2D. When the laminated ring is separated, as in making the sphere a point can move in 3D

Thanks again. I do not know how to multiply geometries, perhaps that is why I cannot do the math. I will attach an animated Torbus to my post (if I figure out how to do that.). If I could get your email address I could send you the 3D math geometry of the “Torbus twisted ring” in a Torus. The...

Thanks for the question but I do not understand what is ment by SxSxMo, or SxMo.The Torbus I cut from a solid wooden Torus is 3-D. There are two linked pieces after cutting the Torus 1) twisted ring and 2) rest of the Torus. I then cut 2) the remaining Torus, to extract 1) the twisted ring...