Portfolios-Artwork > 2012-2018 Trigonometries

Higher-Dimensional Euclidean Geometry
Higher-Dimensional Euclidean Geometry
oil and pencil on acrylic on canvas
48 x 60"

A triangle, a basic geometric shape, is a polygon with three edges and three vertices. In euclidean geometry any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane, or a two-dimensional, flat, "euclidean space". In other words there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the euclidean plane, there is only one plane and all triangles are contained in it. However, in higher-dimensional euclidean spaces, which is the underlying concept of this painting, this is no longer true.