Download reports on bending of long rectangular plates to a cylindrical surface

After reading through this information about bending of long rectangular plates to a cylindrical surface you will now be better informed about bending of long rectangular plates to a cylindrical surface.

How many letters can be made by cutting 1/6 out of a donut?
This is not just silly but challenging, how many of the 26 letters uppercase and lowercase can you make, by cutting 1/6 out of a donut? I found six so far…- You can cut out any pieces of any shape(s) from any part of the donut, as long as they amount to 1/6 of the volume.You may then discard or reassemble the cutout piece(s) any way you like, and you may then rotate or view the donut cutout any way you like.- For convention, let’s say you start with donut (torus) in the x-y plane, and you’re viewing it from vertically above ( z-axis).- Then you make cuts of your choice (straight, curved, Peano, whatever). Then you discard or reassemble the cutout piece(s). Unless otherwise stated, it/they are assumed bending of long rectangular plates to a cylindrical surface to be discarded.- Finally you can optionally move your viewing-point (unless otherwise stated, it remains on z-axis)- I guess to make letters like A and Z, we would have to allow you to make further cuts without discarding them – state your assumptions, in particular how many cuts total you need for each letter.So here are the 6 (upper-case) letters I figured out how to make… there are only 20 upper-case and 26 lower-case remaining…:C: cut out a 60-degree sector vertically (parallel to z-axis), and discard itO: make a cut on the underneath of the donut, (parallel to xy-plane), this can’t be seen from on top, and discard itI: make any straight cut on the underneath or side of the donut which cannot then be seen when you rotate your viewpoint to the x-axis. Now you just see the torus from sideways, i.e. a rectangle.T: make a straight vertical (segment) cut, now rotate the viewpoint to x-axis (so the remaining donut looks like an I), also rotate the cutout piece so it looks rectangular in side view, and place it on top to form the crossbar of the ‘T’.L: similar to the ‘T’, put the rectangular-looking cutout at bottom of the donut.Q: figure how to make a cut which is rectangular in side-view, and reassemble it so it looks like the stroke of the Q.P and B: …are tricky? I guess we have to allow bending the donut.lower-case i: cut out spheres or hemispheres totalling 1/6 of volume.These form the dot of the ‘i’ (if there are several of them, we can hide them behind each other). Rotate viewpoint to x-axis.
Powered by Yahoo! Answers