A Visual Dictionary of Famous Plane Curves

January 19, 2008 5:58 PM

A Visual Dictionary of Famous Plane Curves is an outstanding resource for curves found in nature, man-made objects, and mathematics. Other websites that list exotically named curves also animate how they are created. One of the most unusually named curves, the “Witch of Agnesi”, has an unusual etymology. A number of these curves will be familiar to anyone who has used a Spirograph. Previously.
posted by Tube (13 comments total)

FYI, a Real (resp. Complex) curve is a 1-dimensional Real (resp. Complex) object. Complex curves look like (real) surfaces. For example, a complex curve could look like a donut, or several donuts welded together.

A plane (complex) curve is a complex curve together with an embedding into the complex projective plane.

The genus of a (complex) curve is how many holes the multi-donut shaped surface has.

The degree of a plane curve is how many times it intersects a generic line in the plane.

An example of a plane curve of genus 3 and degree 4 is Klein's curve.
posted by proj08 at 6:20 PM on January 19, 2008

I know Xah Lee as a bit of a troll on comp.lang.python a few years ago. It's good to be reminded that just because you were a troll in one place and one time, you might not be a troll at all places and at all times. In fact, those curves are pretty neat.
posted by jepler at 6:24 PM on January 19, 2008

... turn a sphere inside out
posted by hortense at 6:26 PM on January 19, 2008 [5 favorites]

The most famous plane curve of all
posted by bicyclefish at 7:41 PM on January 19, 2008

Thanks for leading me to the coolest looking vegetable ever!!
posted by not_on_display at 8:07 PM on January 19, 2008

Wow, hortense, that was really cool! Then I realized that I went to high school with one of the animators/ writers, did some poking around, and found his extensive CV. Now I don't know what to think.

I have wasted my life.
posted by exlotuseater at 9:29 PM on January 19, 2008

also, some nice "curlicues" here (scroll down, please) oh, my!
posted by exlotuseater at 9:32 PM on January 19, 2008 [1 favorite]

er..Outside In Last modified: Jun 14 1996 oh,my
posted by hortense at 11:05 PM on January 19, 2008

Neat; was just at that site a couple of days ago reading about the Trammel of Archimedes. You might know this as a do-nothing, or Hillbilly Entertainment Center.
posted by scruss at 7:52 AM on January 20, 2008

These make me think of the arbelos.
posted by marble at 9:28 AM on January 20, 2008

Thanks, Tube! I spent more hours than I care to remember forced by a sadistic art professor to create those weird curves with a compass and a ruler. Perhaps he had a point: they are really quite beautiful curves, now that I do not have to remember how to construct them to pass a stupid quiz.
posted by francesca too at 12:26 PM on January 20, 2008

exlotuseater: yes. yes, indeed.
posted by CitizenD at 1:38 PM on January 20, 2008

... turn a sphere inside out

So, although I found that cool I really didn't appreciate the meaning of it (I assume that the properties of their abstract material provides mathematicians useful ways of handling... well, something..) My toddler however ever has insisted that we watch this video repeatedly over the last few days. She must be a genius. Or like purple and gold. It could go either way... :)
posted by adamt at 4:26 AM on January 22, 2008