Buckminster Fuller Versus The Irrational : A Double Entendre (Dedicated to the Memory of R. Buckminster Fuller in the Centenary of his Birth)

R. Buckminster Fuller strongly believed in the discreteness of structure, and distrusted irrational numbers. The concept of limited resolution is introduced to relate a discrete structural model to mathematical abstractions such as straight lines and circles. Fuller also made rational approximations to irrational expressions. It is shown that such approximations are unnecessary, and in point of fact at odds with Fuller's spatial rather than linear thinking. Some fundamental principles underlying an experimental Design Science are presented. It is shown that three-dimensional structural relations in forms which are identical in at least three non-planar directions are exactly expressible in terms of small rational numbers. There are four significant angles having rational trigonometric functions, in the range between 60° and 72°, which occur commonly in such structures. It is suggested that the system presented here can be the basis of a curriculum in Visual Mathematics.