# Elizabeth Whiteley

Studio Artist
Washington DC USA

As a studio artist working at the intersection of art and mathematics, I find it inspiring to occasionally return to geometry basics. I reviewed Euclid’s Elements, Book Three: Proposition 12. The proposition states “If two circles touch one another externally, the straight line joining their centers will pass through the point of contact.”

I drafted circles of varying diameters and explored their visual relationships, noting their point of contact. I intuitively selected curve segments to create an arabesque. I imagined the touching arcs as describing a surface and then drew chords to represent that surface. The figures only exist in 2-D.

Euclidean Arabesque 1
41 x 51 cm
graphite + color pencil on archival paper
2017

Using a compass and a pencil, I drew two circles of different diameters(radii ratio 1:.75) and selected curve segments(with arcs of 180 degrees and 270 degrees, respectively). The arcs touched at the point of contact described in Euclid’s Elements(Book Three: Proposition 12) and formed an arabesque. I connected the open ends of the arabesque with a chord and continued adding chords at regular intervals along the arabesque to form an imaginary surface.

In artistic terms, an imaginary drawing has no local color. The selection of color is my personal expression.

Euclidean Arabesque 2
41 x 51 cm
graphite + color pencil on archival paper
2017

Using a compass and a pencil, I drew two circles of different diameters(radii ratio 1:.85) and selected curve segments(both with arcs of 270 degrees). The arcs touched at the point of contact described in Euclid’s Elements(Book Three: Proposition 12) and formed an arabesque. I connected the open ends of the arabesque with a chord and continued adding chords at regular intervals along the arabesque to form an imaginary surface.

In artistic terms, an imaginary drawing has no local color. The selection of color is my personal expression.