Geometry is a very big topic. You can spend a lifetime learning it and still master only a fraction of the literature. It can be expressed using a variety of mathematical concepts and formalisms, each of which takes time and effort to learn before you can begin to master the geometric ideas that use such concepts. Yet most of the objects made with parametric modeling systems are geometric. How can a designer ever learn enough?

History shows us that designers have always "learned enough" about geometry in ways important to them. The medieval master masons used Euclid's compass and straight edge constructions to lay out Gothic cathedrals and their details. With a compass and straightedge, a designer can reliably make many geometric figures, including straight lines and angles, division of lines and angles into two equal parts, isoceles triangles, and sequences of lengths in ratio to each other. Between then and now, many architectural thinkers and movements have used aspects of geometry to inform design. In the late 20th Century, computer-aided design systems introduced a wide variety of construction operations.

Geometry is at the core of all of these tools, and designers using them certainly became expert, if implicit, geometers within their domain. Using the "toolbox" available at the time, designers have always developed a suite of "tricks of the trade" by which they could reliably create their intended forms. Of course, the medium massaged the design. Traces of the compass and straightedge show in the pointed arches, lancet windows and quatrefoil bosses throughout Gothic architecture. Many historians argue that the ability to create perspective changed the focus of Renaissance architecture from objects to expressing movement and views through space.

If you watch a designer using a contemporary CAD system, you are likely to see a combination of all of these techniques (explicit construction, perspective, descriptive geometry, snapping and intersection) and others at play. Designers do indeed use geometric tools in their work.
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