Sketchup Sliceform – About the Torus

A torus is a shape like a ring doughnut (or donut in US English). It can be constructed geometrically by taking a circle and rotating about an axis.

You can find out more about a torus on Wikipedia or on Wolfram MathWorld

There are a number of ways to slice a torus to end up with circles. The first is to cut a perpendicular to the axis of rotation. The second is to cut with a plane through the axis; this yields the circles that are being rotated to generate the torus. I am going to slice the torus to show Villarceau circles details of which are on Wikipedia.

I will slice in the direction of a tangent plane.

(Image By Kieff  via Wikimedia Commons)

This video shows the slicing at the tangent I am going to use.

Villarceau’s original paper was published in 1848:

Théorème sur le tore de M. Villarceau (Yvon). Nouvelles annales de mathématiques, journal des candidats aux écoles polytechnique et normale, Sér. 1, 7 (1848), p. 345-347

You can get this original paper by going here and searching for Villarceau.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s