Curious circumstances trigger trains of thought. Glancing across a library table recently, I saw this title appearing in The Arithmetic Teacher: “Geometry for the Primary Grades.” The student reading the article was evidently intrigued by the title, for he seemed to return to the title page on a number of occasions. This caused me to wonder what such notables as Euclid, Poincare, Euler, Gauss, Moebius, Bolyai, Lobachevski, Riemann, and all of the other great minds, both past and present, would have written under the same title. I began to wonder what would emerge if these immortals were to coauthor this topic with another group that included Piaget, Montessori, Bruner, Suppes, Hawley and others. What unified, harmonious medley of understanding would emerge? This surely had all the overtones of a setting of individuals bent on a course that might bring together the necessary components for a panacean program of geometry in the primary grades—a program that would be organized on a logical and psychological basis that takes into consideration the age of the child. This is the context in which present-day geometry for primary-grade children is being explored— the child, the topic, and the environmental influence of both.