A 3d duocylinder

[Keiji]

I was messing about in Valve Hammer Editor ages ago and came up with this shape:

http://www.gamezcentre.co.uk/users/bobx ... linder.png

Now, I went to look at it. Surely this would roll, in a straight line, and if rotated 90 degrees in any direction it would continue to roll in a straight line. How can this be, if it is a 3d object? According to your Rotatopes, it must be composed of two digits, both greater than 1. Yet, this is impossible with a 3d object as they will add up to more than 3.

[alkaline]

I have actually thought of that shape before, and i named it a "crind". Me and polyhedron dude have discussed it at least a little bit before. When i was trying to figure out the duocylinder at first i thought that it was a type of crind. The difference between this shape and the rotatopes is that the angle between the round sides isn't 90 degrees at every point, like it is with the cylinder, cubinder, duocylinder, and spherinder.

[alkaline]

oh and something interesting to note, this shape is the intersection of two cylinders perpendicular to each other.

[Keiji]

Well, that IS how I made the shape...

[alkaline]

apparently the official name of this shape is the "Steinmetz Solid". Here is the article about it on Mathworld:

http://mathworld.wolfram.com/SteinmetzSolid.html

A "bicylinder" is two equal cylinders intersecting at right angles; the Steinmetz Solid is the intersection of these cylinders.

If the two cylinders are oriented on the z and x axes, their surfaces are

x[sup]2[/sup] + y[sup]2[/sup] = r[sup]2[/sup]
y[sup]2[/sup] + z[sup]2[/sup] = r[sup]2[/sup]

solving for x and y, you get these parametric equations:

x = +/-z
y = +/- root(r[sup]2[/sup] - z[sup]2[/sup])

[Yoshi]

alkaline, are u smart, or does everybody who passes calculas like you?

[Aale de Winkel]

Alkaline, homo universalis esse , I tried to do that myself but unfortunately that problems squares when knowledge lineairily expans. .

I still havn't the faintest idea how to calculate the laplacian in glomar coördinates, although I'm a beta-it-scientist. Alkaline seems to understand this high level of calculus, while as far as I know he is an alpha-it-scientist.

It has just been to long ago (20+ years) since I did this real work, so I'm a bit rusty. It's time to refuel my marbles, much study to be done :wink: .

[alkaline]

well i'm in advanced calculus now, where i'm basically proving the concepts I already learned in calculus... Anyone can appear smart to someone else if they know more than that person :-)

[Geosphere]

Anyone can appear smart to someone else if they know more than that person

Reminds me of the concept that any sufficiently advanced technology appears to be magic to those who cannot comprehend it.

[arsenic]

The 3d duo cylinder has two surface to cover it (those two surface look like two empthy sphere ) and there is no surface to cover it on it's side

Some 2d object cannot be viewed in 2d such as sphere's skin is a 2d object that cannot be viewed in 2d but it can be viewed in 3d

a 2d objects that can be viewed in 2d must have line to cover all of their
aera the 2d object that has no line to cover it's aera such as sphere surface or 2d object that has some aera which does not has line to
cover their aera such as cylinder's surface cannot be viewed in 2d

3d duo cylinder is a 3d object that cannot be viewed in 3d but it can be viewed in 4d

3d object that has part of it's volume (which is does not has surface to cover it's volume) cannot be viewed in 3d

[Keiji]

What? Taht object is perfectly manufacturable. Take a cylinder and push it through a cylindrical cutter the same size in a perpendicular direction. Voila, a "3d duocylinder" or crind.

[Geosphere]

Arsenic, I think you're confusing viewable volume with dimesion. Just because you cannot see whether or not the inside of a box is divided until you open it, does not render that box only viewable in the fourth dimension.