The common fallacy that geometry pertains specifically to idealizations—that it applies to the world but is not about the world—begins with Euclid saying, “A point is that which has no part. A line is a breadthless length.” That fallacy persists to this day.

That geometry is useful is not in dispute. But its objects are held to inhabit a separate geometrical universe, reminiscent of Plato’s world of forms. Euclid’s propositions and, most significantly, his arguments are considered valid only in this separate universe.

A proper perspective must challenge all three of these misconceptions. Drawing on key Objectivist insights, Dr. Knapp will maintain that straight lines, circles, and triangles are shapes that exist on earth. That Euclid’s propositions pertain to shapes and relationships that exist in the world. Most critically, that Euclid’s arguments are valid: Every step in Euclid’s arguments pertains to this world.