Enhancing Plane Euclidean Geometry with Three-Dimensional Analogs

Abstract

Human beings are born with an ability to sense, perceive, and then remember, and as we grow and develop this ability matures through exercise and practice. Most of us can recall learning to see how circles and lines are tangent to one another, how midpoints and perpendiculars partition triangles, and how one might prove conjectures about these. Learning how to see literally, how to make images of the world, and how to perceive the world more completely and accurately is part of that educational process.