Playing with Curves: Art and Mathematics - Gen Studies 197C - Autumn 2015

Dr. Matthew Conroy

email:
conroy(at)math.washington.edu

For my office hours, click the link above.

November 30, 2015

Sage examples.

September 28, 2015

This seminar will consider the fantastic variety of plane curves.

We will investigate their visual aspects, and play with many methods of generation of curves and creation of original curves. We will consider a number of contexts in which we may encounter plane curves.

There will be lots of pictures.

If you have any questions about the seminar, please don't hesitate to email me at conroy(at)math.washington.edu.

Below is an image of two orthogonal families (collections) of curves. Notice how, when a curve from one family intersects a curve from the other family, they are at right angles to each other.

Resources:

• The seminar board Go here for the weekly prompts, to ask questions, and to share your thoughts, examples, etc.
• Course Syllabus (pdf)

Software

• Sage We'll primarily be interested in Sage. It's free, extremelt powerful, developed at UW, and you can use it without installing anything.
• Planar Curve Explorer PCE can do some specialized things nicely.
• Gnuplot An old classic. Useful for lots of plotting, and open source, but not as good as Sage in most (all?) regards.

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Things to read

• On Growth and Form by D. W. Wentworth
  (particularly chapter 11 on the equiangular spiral)
• Remarkable Curves by A.I Markushevich
• An elementary treatise on curve sketching by Percival Frost
• A Handbook on Curves and their Properties by Robert C. Yates

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Specific Curves

• Wikipedia Curves Category Many, many interesting Wikipedia articles on curves of all sorts can be found by poking around here.

The links below are mostly old applets that I've written for investigating some curves.

• Conics
• Normal lines to a parabola
• Orthogonal tangent lines to a parabola
• The Bad Ellipse: Circles in Perspective a pdf on how to draw circles in perspective
• Cycloids
• cycloid01
• Falling Ladder
• falling ladder
• Fractals
• Mandelbrot01
• Mandelbrot02
• Mandelbrot03
• BurningShip01
• Hypocycloids, etc.
• Hypocycloid01
• Lissajous
• Lissajous01
• Orthogonal trajectories
• A gallery of orthogonal trajectories
• Rod and Circle
• Rod and Circle
• Roses
• Roses 1
• Spirals
• Archimedean spirals
• Equiangular spirals
• Tangent spirals
• Taylor polynomials
• Taylor polynomials of sin x
• Weierstrass Functions
• A short intro to Weierstrass functions, with a zoom-in animation

Artists

• Heinrich Heidersberger
• Sol Lewitt

Other UW resources:

Student Counseling Center