[math-fun] Trying to recall funny shape
I recently read of an odd solid shape, with I think an odd name, that has recently been defined. It may be this: Take a solid cylinder whose diameter equals its height, cut it in half along a square, rotate one half 90 degrees, and glue the halves back together again. Does this shape have a name, or is there something similar that does? Apparently it has very interesting rolling behavior. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
Dan, There something like that starting with a cone instead of cyliner. It's the spericon. Google gets several really nice hits, including some rollers. Robert Foote at Wabash College has turned spericons from wood - I'm pretty sure has some sphericons on his website. A sphericon with some animation can be seen at a Gallery of Space Curves that Peter Moses and I have at http://faculty.evansville.edu/ck6/Gallery/Introduction.html Clark Kimberling -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Wednesday, April 21, 2010 2:51 PM To: math-fun Subject: [math-fun] Trying to recall funny shape I recently read of an odd solid shape, with I think an odd name, that has recently been defined. It may be this: Take a solid cylinder whose diameter equals its height, cut it in half along a square, rotate one half 90 degrees, and glue the halves back together again. Does this shape have a name, or is there something similar that does? Apparently it has very interesting rolling behavior. --Dan ________________________________________________________________________ ________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
This page seems to have Dan's shape, and it calls it a squircle. http://www.pjroberts.com/sphericon/gallery.php On Wed, Apr 21, 2010 at 1:09 PM, Kimberling, Clark <ck6@evansville.edu> wrote:
Dan,
There something like that starting with a cone instead of cyliner. It's the spericon. Google gets several really nice hits, including some rollers. Robert Foote at Wabash College has turned spericons from wood - I'm pretty sure has some sphericons on his website.
A sphericon with some animation can be seen at a Gallery of Space Curves that Peter Moses and I have at http://faculty.evansville.edu/ck6/Gallery/Introduction.html
Clark Kimberling
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Wednesday, April 21, 2010 2:51 PM To: math-fun Subject: [math-fun] Trying to recall funny shape
I recently read of an odd solid shape, with I think an odd name, that has recently been defined.
It may be this:
Take a solid cylinder whose diameter equals its height, cut it in half along a square, rotate one half 90 degrees, and glue the halves back together again.
Does this shape have a name, or is there something similar that does? Apparently it has very interesting rolling behavior.
--Dan
________________________________________________________________________ ________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://thaneplambeck.typepad.com/
This is a very easy surface to develop, and I have a few patterns based on the different sphericons (although I haven't called them like this - so far) with spherical images printed on them: http://www.flickr.com/photos/sbprzd/2424037224/in/set-72157604502314691/ And there are other shapes as well: http://www.flickr.com/photos/sbprzd/3130892971/in/set-72157604502314691/ More in this set of pictures: http://www.flickr.com/photos/sbprzd/sets/72157604502314691/ Best, Seb On Wed, Apr 21, 2010 at 22:25, Thane Plambeck <tplambeck@gmail.com> wrote:
This page seems to have Dan's shape, and it calls it a squircle.
http://www.pjroberts.com/sphericon/gallery.php
On Wed, Apr 21, 2010 at 1:09 PM, Kimberling, Clark <ck6@evansville.edu> wrote:
Dan,
There something like that starting with a cone instead of cyliner. It's the spericon. Google gets several really nice hits, including some rollers. Robert Foote at Wabash College has turned spericons from wood - I'm pretty sure has some sphericons on his website.
A sphericon with some animation can be seen at a Gallery of Space Curves that Peter Moses and I have at http://faculty.evansville.edu/ck6/Gallery/Introduction.html
Clark Kimberling
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Wednesday, April 21, 2010 2:51 PM To: math-fun Subject: [math-fun] Trying to recall funny shape
I recently read of an odd solid shape, with I think an odd name, that has recently been defined.
It may be this:
Take a solid cylinder whose diameter equals its height, cut it in half along a square, rotate one half 90 degrees, and glue the halves back together again.
Does this shape have a name, or is there something similar that does? Apparently it has very interesting rolling behavior.
--Dan
________________________________________________________________________ ________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://thaneplambeck.typepad.com/
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Many examples in this general family are illustrated in this book: Woodturning Full Circle, by David Springett For example, spin a pentagram into a solid of revolution using a mirror line as the axis. Now slice along the original plane and rotate one half 2pi/5 or 4pi/5. Glue the halves back together at the pentagram faces. It's tricky to visualize how it rolls, but straightforward to make with a lathe. George http://momath.org http://georgehart.com On 4/21/2010 3:50 PM, Dan Asimov wrote:
I recently read of an odd solid shape, with I think an odd name, that has recently been defined...
participants (5)
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Dan Asimov -
George W. Hart -
Kimberling, Clark -
Seb Perez-D -
Thane Plambeck