# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Author Message
extropalopakettle
No offense, but....

 Posted: Sun Jul 29, 2012 8:09 pm    Post subject: 1 First, I got to thinking about old puzzles in VSP that have disappeared over the years (at least I think they have) ... approachable, math/logic oriented puzzles, not overly "engineered". So I'm resurrecting an old one I once posted, but also adding a second part. If you happen to remember the solution to the first part, please leave it for others to try to solve. Part 1: Find the shape of a 3 dimensional solid object that can be placed on a flat inclined plane, and will roll down the plane in such a way that as it rolls, every point on its surface will contact the plane before rolling a certain fixed distance. Part 2: Find another such shape.
MNOWAX
0.999... of a Troll

 Posted: Sun Jul 29, 2012 11:01 pm    Post subject: 2 1:If i'm thinking correctly, Two cones joined at the base like this : <> as it rolls on one cone, the force of the roll will flip it and roll on the other cone. perhaps not?_________________The Man The Myth The Legend MNOWAX
Zag
Tired of his old title

 Posted: Sun Jul 29, 2012 11:04 pm    Post subject: 3 That was the best that I came up with, MNO, but I suspect that there is a better answer.
Jack_Ian
Big Endian

 Posted: Mon Jul 30, 2012 10:55 am    Post subject: 4 1. I remember this. I believe there was even a 3-D stereoscopic image posted of it. 2. [A pill capsule with a ball-bearing in it], but the certain fixed distance would be arbitrarily large.
novice
No harm. Pun intended!

 Posted: Mon Jul 30, 2012 11:31 am    Post subject: 5 1. Would a cone with a hemisphere at the base work?
Zag
Tired of his old title

 Posted: Mon Jul 30, 2012 12:26 pm    Post subject: 6 Any shape with a spherical part is clearly wrong. If you only have a single point of contact for some two-dimensional part of the surface, you'll never get complete coverage.
novice
No harm. Pun intended!

 Posted: Mon Jul 30, 2012 5:20 pm    Post subject: 7 Something that rolls in a slalom pattern? I'm having trouble visualising the object, something conish that segues from one roll direction to another?
extropalopakettle
No offense, but....

Posted: Mon Jul 30, 2012 5:48 pm    Post subject: 8

 Jack_Ian wrote: 1. I remember this. I believe there was even a 3-D stereoscopic image posted of it.

Yes, I modeled and rendered a stereoscopic looping animation of it rolling (using Caligari trueSpace, now a free MS product), and posted it as an animated gif ... but can't seem to find a copy.

Answer: [ What MNOWAX said is on the right track. Two 90 degree angle cones placed base to base, but then, slice that in two pieces with a plane that passes through the two cone tips. The resulting objects now have a square planar base ... rotate one 90 degrees and put them back together. It's been called a sphericon. ]

I only recently found via google what I believe to be a second object fairly dissimilar to the above which fits the criteria. (and constructed / described in a similar, but different manner than the above )
Suspence
Daedalian Member

 Posted: Mon Jul 30, 2012 5:56 pm    Post subject: 9 I found the other object while learning more about the sphericon on Wikipedia. OLOID_________________I hate people who try to write interesting things in their signature.
extropalopakettle
No offense, but....

Posted: Mon Jul 30, 2012 6:03 pm    Post subject: 10

 Suspence wrote: I found the other object while learning more about the sphericon on Wikipedia. OLOID

Yes, but it wasn't clear to me how different that is. The other one I found was much more clearly different (yet still similar in some sort of way).
Suspence
Daedalian Member

 Posted: Mon Jul 30, 2012 6:06 pm    Post subject: 11 Here's a pretty cool animation of the oloid. http://www.youtube.com/watch?v=GUyou2QelRo&feature=related If you trust Wikipedia (and who doesn't ) "the oloid is the only known object, other than some members of the sphericon family, that while rolling, develops its entire surface." This seems to suggest that the oloid is not in the sphericon family, and whatever you have found is. Or that you have discovered something totally new, which would be cooler._________________I hate people who try to write interesting things in their signature.
extropalopakettle
No offense, but....

 Posted: Mon Jul 30, 2012 6:12 pm    Post subject: 12 To me, one has to look rather carefully at the oloid to see the difference from the sphericon. I'm not sure how to qualify the similarities and differences between shapes, but I think one could morph a sphericon to an oloid with every step along the way having the same property. The other shape I found is here: http://www.softcom.net/users/sbmathias/related.htm , dubbed the "hexasphericon"
novice
No harm. Pun intended!

Posted: Mon Jul 30, 2012 7:16 pm    Post subject: 13

 novice wrote: I'm having trouble visualising the object, something conish that segues from one roll direction to another?

 Suspence wrote: Here's a pretty cool animation of the oloid. http://www.youtube.com/watch?v=GUyou2QelRo&feature=related

That's exactly what I had in mind.
Suspence
Daedalian Member

Posted: Mon Jul 30, 2012 7:24 pm    Post subject: 14

 extropalopakettle wrote: The other shape I found is here: http://www.softcom.net/users/sbmathias/related.htm , dubbed the "hexasphericon"

As that article mentions, you should be able to do the same with other shapes. Here's an octosphericon:

_________________
I hate people who try to write interesting things in their signature.
extropalopakettle
No offense, but....

Posted: Mon Jul 30, 2012 8:37 pm    Post subject: 15

extropalopakettle wrote:
 Jack_Ian wrote: 1. I remember this. I believe there was even a 3-D stereoscopic image posted of it.

Yes, I modeled and rendered a stereoscopic looping animation of it rolling (using Caligari trueSpace, now a free MS product), and posted it as an animated gif ... but can't seem to find a copy.

Chuck had an old copy! You need to kinda stare a bit past it to make the three images overlap to look like 4 image, then the middle two will be in 3D. Would be better in higher resolution on today's monitors ... maybe I can find.

extropalopakettle
No offense, but....

 Posted: Mon Jul 30, 2012 9:01 pm    Post subject: 16 More about construction of octosphericon here: http://www.ams.org/samplings/feature-column/fcarc-octo-cretan Yeah, now I see how it could be generalized to a sequence approaching a sphere in the limit. (hurts my brain to think about at what point it would fail to roll according to the mentioned criteria and just roll like a sphere)
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersextropalopakettleJack_IanMNOWAXnoviceSuspenceZag Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum