ABSTRACT
Both parabola and catenary may be modeled as differentiable curves. However, the author and his students find that spreadsheets iterating simple arithmetic have their advantages. Incremental construction of spreadsheets enables robust, stepwise learning. The completed calculators display a rich array of properties that support detailed design. They also highlight similarities and differences between geometries. Design variation may be introduced parametrically, or at discrete points. Finally, rigorous minds appreciate that real masonry structures and tension arrays are composed of discrete elements, so the incremental model is often more accurate than a differentiable approximation. Students working with these spreadsheets develop the confidence and ability to tackle more complex problems, such as the funicular of a dome. This curve is not a Hookean catenary but reflects the non-uniform and non-trivial weighting of a Polenian lune. Simple tools needn’t limit us to simple subjects, they enable comprehension and design of sophisticated structures.
