Gombocs

[SaxonViolence]

I just learned of these Fascinating Gadgets yesterday.

 

They are the result of a relatively recent Discovery in Geometry.

 

They're really neat.

 

Over $200 worth of neat?

 

Not for me--I'm poor.

 

Can someone tell me, precisely which branch of modern mathematics this falls under?

 

Anyway, check it out. If you're intrigued, there are numerous links on the web.

 

I thought the "Wikipedia" was pretty thorough.

 

http://www.scientificsonline.com/gomboc.html

 

Saxon Violence

[Turtle]

I just learned of these Fascinating Gadgets yesterday.

 

They are the result of a relatively recent Discovery in Geometry.

 

They're really neat.

 

Over $200 worth of neat?

 

Not for me--I'm poor.

 

Can someone tell me, precisely which branch of modern mathematics this falls under?

 

Anyway, check it out. If you're intrigued, there are numerous links on the web.

 

I thought the "Wikipedia" was pretty thorough.

 

http://www.scientificsonline.com/gomboc.html

 

Saxon Violence

 

what a rip off! :omg: (i'm poor too. :D) anyway, it reminds me of the toy called a "rattleback". here's a link to the wiki article and a quote from it on the physics involved. (the turtles in the photo are a happy coinkydink. )

 

rattleback

Physics

The spin-reversal motion follows from the growth of instabilities on the other rotation axes, that are rolling (on the main axis) and pitching (on the crosswise axis).

 

Rolling and pitching motions

When there is an asymmetry in the mass distribution with respect to the plane formed by the pitching and the vertical axes, a coupling of these two instabilities arises; one can imagine how the asymmetry in mass will deviate the rattleback when pitching, which will create some rolling.

 

The amplified mode will differ depending on the spin direction, which explains the rattleback's asymmetrical behavior. Depending on whether it is rather a pitching or rolling instability that dominates, the growth rate will be very high or quite low.

 

This explains why, due to friction, most rattlebacks appear to exhibit spin-reversal motion only when spun in the pitching-unstable direction, also known as the strong reversal direction. When the rattleback is spun in the "stable direction", also known as the weak reversal direction, friction and damping often slow the rattleback to a stop before the rolling instability has time to fully build. Some rattlebacks, however, exhibit "unstable behavior" when spun in either direction, and incur several successive spin reversals per spin.[2] ...

[CraigD]

I just learned of these Fascinating Gadgets yesterday.

Me too – thanks! :thumbs_up

 

Can someone tell me, precisely which branch of modern mathematics this falls under?

Math subject boundaries aren’t precise, but I’d put this under the “applied”, “mechanical”, and “solid classical geometric” categories.

 

Dokomos’s department at Budapest U of Technology & Economics is “Mechanics, Materials and Structures”, while Varkonyi’s post-doc program when he and Dokomos published their proof of the existence of “mono-monostatic” bodies in 2006 was “Applied and Computational Math” – if this is helpful.

 

what a rip off! :omg: (i'm poor too. :D)

They are pricey! :( You can beat the US$ 275 Edmund’s price for the 1 kg “standard” Gomboc with a €149 ($195) 0.450 kg “mini” from gomboc-shop.com.

 

From what I’ve read, they’re not so much as a rip-off as an example of esoteric supply and demand. Since they must have a very constant density and be molded or carved to within 1 part in 10000, they can’t be readily mass-produced or easily hand-crafted. As best I can tell, they’re all currently made with computer-controlled 3-D milling machines or 3-D printers – pretty pricey pieces of hardware themselves.

 

You’ve either got to precisely machine a small one, or less precisely make a big one. Slightly exceeding the allowed tolerance results in the body having many stable equilibria rather than 1 – that is, one that comes to rest in many positions.

 

Rather an “ultimate challenge” for a knife and sandpaper craftsperson, I’d say. I bet if you managed to make one by hand, you could get some fame and a spot in goomboc.eu’s gallery.

 

Another challenge would be to see how small you could make one – though I imagine you’d need access to a pretty expensive machine shop to get into this one.

 

For us on the cheap, with nothing but our little supercomputers, Dokomos and Varkonyi are offering $10,000/n for an n-faced polyhedron that will come to rest on the same face every time – though how much the prize might actually be, nobody can yet say. As a starting place, we’ve known since 1991 that it could be done in 2 dimensions with a 19-edged polyhedron (see here), so it can be done trivially with a pyramid-tipped prism 57-face polyhedron ($175.43 winnings).

 

Sounds like some fun and educational programming. :)

[maddog]

Can someone tell me, precisely which branch of modern mathematics this falls under?

I'm not so sure it really fits in a mathematics branch per se. What you are describing is some solid object that has a bi-stable moment of inertia. So this is really physics. It is not some regular polyhedral geometrical object. It is made of Aluminum weighs very precisely 1 Kg, so maybe it is more of an Engineering marvel. That is my opinion.

 

maddog

Edited April 20, 2012 by maddog

[Turtle]

I'm not so sure it really fits in a mathematics branch per se. What you are describing is some solid object that has a bi-stable moment of inertia. So this is really physics. It is not some regular polyhedral geometrical object. It is made of Aluminum weighs very precisely 1 Kg, so maybe it is more of an Engineering marvel. That is my opinion.

 

maddog

 

according to craig's post, "...Varkonyi’s post-doc program when he and Dokomos published their proof of the existence of “mono-monostatic” bodies in 2006 was “Applied and Computational Math” ". since these 2 fellas invented & made the gomboc, what is the reason for you doubting them?