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 .Studio files if you would like to make sliceforms of the sphere or torus 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


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

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TorusCirclesVillarceauCircleXSections
Four circles may be drawn through an arbitrary point P 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.

Here are the Silhouette .Studio files for all...the sphere. Make two copies for one sphere. Very easy to put together.  They slide together to form the sphere.  I used cardstock to make all of the models.

https://drive.google.com/file/d/0B7oGIyVDbRGYclVnMzlPaEVYUkE/edit?usp=sharing.

and the scalloped torus.  Make one copy of each file. Align the different size tabs and slide together.

https://docs.google.com/file/d/0B7oGIyVDbRGYUGRManozVFJqbkE/edit?usp=sharing
https://docs.google.com/file/d/0B7oGIyVDbRGYVzdCSXR3MXZOblU/edit?usp=sharing

and the zigzag torus.  Make one copy of each file. This model is a little harder to put together than the scallop version. 

https://docs.google.com/file/d/0B7oGIyVDbRGYUVlETEM4SHdubnM/edit?usp=sharing
https://docs.google.com/file/d/0B7oGIyVDbRGYMFF1dnFBejFma0E/edit?usp=sharing



Extra:  Here is a sliceform cube that I just made.

https://docs.google.com/file/d/0B7oGIyVDbRGYTTJXYjN6bktiYU0/edit?usp=sharing

#sliceforms #Silhouettecameo #Villarceau #torus