The Tonias Algorithm

Abstract

This paper casts light upon the significance both practical and theoretical of a paper entitled “Spiral Problems for an Electronic Computer,” by Elias C. Tonias, which has acquired wide circulation among computer programmers while remaining unknown to the majority of highway engineers and surveyors. It is the intent of this paper to demonstrate that Tonias's 1965 paper brought into focus the true computational basis of the transition spiral, and to demonstrate the practical usefulness of this vision to the surveyor who, in 1995, often carries a programmable handheld calculator that is perfectly adequate for implementing the Tonias algorithm.