## Monday, July 8, 2013

### Sliceforms are my new obsession

I love sliceforms.  What are they you say?  Well, they are exactly what the term says...slices of a form.  For example, I decided to make a sliceform of a sphere.  I used my designing software with the Cameo Silhouette and created this sphere. I have included the PDF and .Studio files if you would like to make sliceforms at the end of this post. They would look great as a decoration for a party or as an ornament. The shapes took me hours to make so please pass them along and appreciate what math can do!
Marley loves it too! Amazing that it lies flat when put together.

Sliceform Sphere
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I saw a sliceform of a torus on the internet.  I made it and then decided it was not pretty enough so I created my own version. The pink torus is the scalloped version and the blue torus is the zigzag version. This time the toruses makes me think of flowers instead of food (a donut).  I love the way the variations of color are created by the shadows of the slices and the spiral in the center.  There is so much going on mathematically as well as artistically.  It makes me so happy!

For the mathematical people there are villarceau circles which create this shape.  Here is an explanation from Wolfram Alpha.

# Villarceau Circles

Four circles may be drawn through an arbitrary point  on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The third and fourth circles (which are inclined with respect to the torus) are much more unexpected and are known as the Villarceau circles.

The cube sliceform makes me think of the dividers in a box for glassware so that the glasses do not touch one another.  They have practical applications. Sliceforms are amazing!

Sliceform Cube

Here is the PDF of the sliceforms.

Here is the .Studio file.  I used cardstock to create my models.
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#sliceforms #Silhouettecameo #Villarceau #torus