When I was at the Joint Math Meetings in January, the evocative name "Lute of Pythagoras" jumped out at me in a talk by Ann Hanson of Columbia College in Chicago. Hanson teaches a course, Math in Art and Nature, that satisfies the general math requirement for Columbia College but comes with a healthy helping of creative arts as well. Students learn about geometric constructions, tessellations, and other mathematical ways of generating patterns and designs, and then they find or create artwork using those ideas. Columbia is an arts and communications college, so the course is particularly suited for the school.

The Lute of Pythagoras is just one of the geometric constructions Hanson uses in her course. Two of Hanson's students generously shared art they created for her class using the Lute of Pythagoras.

Both superimpose the Lute on another picture, highlighting the proportions of the underlying images.

The Lute of Pythagoras is based on the "golden" isosceles triangle, a triangle with two equal sides and an apex angle of 36 degrees.

Each of the bottom angles is twice the size of the top angle, and with liberal use of sine and cosine addition formulas, you can check for yourself that the ratio a:b is indeed (1+√5)/2, the famous Golden ratio. Some compass and straightedge steps give you a cool pentagon-y, triangle-y, starry figure, the Lute of Pythagoras.