# Teresa Downard

Mathematics Instructor

Mathematics Department, Western Washington University

Bellingham, Washington, USA

Symbolism, abstraction, and symmetry are my favorite ideas common to math and art. Lately, I've been interested in using mathematical ideas as design tools. To do that, you need to be able to understand the visualization of the mathematical ideas fluently so they can be used intuitively when drawing or painting to avoid interrupting the creative process.

Perspective from a line

28 x 36 cm

Oil on panel

2019

A visualization of triangles that are perspective from a line. The triangles in green are in perspective from the bold line below (or above) them. The two families are arranged to shape a symbolic eye. To test that two triangles are in perspective from the line: trace the orange lines that extend from respective edges of the triangles, they intersect at a point and all three points of lie on the line.

In perspective from a point, three lines go through a point and the respective vertices of each triangle lie on the lines. From duality in projective geometry, exchange the idea of point and the idea of line to get perspective from a line: Three points are on a line and the respective edges of each triangle meet at the points.

In perspective from a point, three lines go through a point and the respective vertices of each triangle lie on the lines. From duality in projective geometry, exchange the idea of point and the idea of line to get perspective from a line: Three points are on a line and the respective edges of each triangle meet at the points.