The starburst icosahedron with long bars

The starburst icosahedron with long bars

Postby karlhorton » Sun Dec 27, 2009 2:13 am

How did those guys at Geomag come up with the new bar length? Here's one possibility - first let's
take some careful measurements:

2009-12-26_IMG_2902_sq.JPG


So, the geometric length turns out to be: 69.94mm

Now, a double-length Geomag original bar has geometric length: 65.78mm

and the ratio between these two numbers is: 0.94 - remember that!

Look in wikipedia to get the circumradius of the icosahedron
http://en.wikipedia.org/wiki/Icosahedron
it's 1/4sqrt(10+2*sqrt(5)) = 0.95106

Coincidence? maybe.

Some calculations give away that a double-length Geomag classic rod is
just 0.74mm short of the required length to act as the radius element
for a starburst icosahedron. And 0.8mm is 1/32" which is just the size of
some little magnetic shims I happen to have handy.

2009-12-26_IMG_2911_sq.JPG


Here's a detail of 12 rods arranged around a ball with icosahedral symmetry.

2009-12-26_IMG_2918_small.JPG


Should you wish to try this at home, you can manufacture shims easily by
using a hole-punch on one of those magnetic stickers you probably have on the fridge: the
disks ejected by the hole punch are just the right size for Geomag bars.

Here's an example: http://www.flickr.com/photos/karlhorton/404972512/in/set-72157594564548492/
User avatar
karlhorton
 
Posts: 38
Joined: Sat Oct 31, 2009 4:54 pm
Location: San Francisco, CA
Real name: Karl Horton

Return to Math-related Geomag discussions

Who is online

Users browsing this forum: No registered users and 1 guest

cron