Clifford Singer

Statement

"In that I produce paintings, my intent is to present a mathematical picture. Apollonius, Locus with Respect to Asymptote, 2022, is integrated with Apollonian hyperbola, tangents, points of bisection, double cone, and asymptote, respectively ordinate points of parallels meeting curves. Similar triangles are a given by nature of parallels. The hyperbola is the locus of a point from a fixed point and straight line. Lemma is used as a proven minor proposition. It is the idea to form the Locus of a sufficient affine plane curve by drawing hyperbola. Apollonius along with classical geometers did not use infinite, but as modern geometers we can introduce the infinite concept of asymptote. Collinear points are key in finding a complete picture."

Artworks

Research into Apollonius Conic Sections since 1974.