Sharol Nau

Sharol's Studio
Northfield, Minnesota, USA

My artistic practice involves taking a simple mathematical idea and enhancing visual interest in the composition through technique, color, shape, line or texture. Recently I’ve enjoyed experimenting with rust printing. I do strive for control yet it’s an unruly technique which offers endless occasion for serendipity. In the art sample displayed here it’s a pleasure to offer a surprise as the design behind “How Many Triangles Do You See” was determined a priori.

How Many Triangles, Base Five
How Many Triangles, Base Five
29 x 22 cm
Rust print and collage on handmade paper

Let T(n) be the number of similar triangles formed when an isosceles triangle of base length n is subdivided into similar triangles of base length 1. For the case shown where n = 5, in addition to the original base-5 triangle there are the 25 base-1 triangles, as well as three base-4, six base-3 and 13 base-2, for a total of T(5) = 48. T(n) = ? T(n) = ?