I might venture to say that as engineers our education in the field of geometry is much the same as any other students' - starting with elementary shapes and ending with trigonometry. Should we be attributing more of our systems and structures understanding to geometry? How do we formally expand its study prior and within practice?
In preschool we learn the 2D shapes, elementary school we might add some volume, by middle school we are learning about angles, and in high school mastering trigonometry. By college we mix things up by learning the inverses of sin, cos, tan! I was fortunate to have a 5th grade teacher introduce the golden ratio... while interesting.... what was it's application or derivation in nature? Perhaps that is a great starting point for all advanced geometric studies.
In high school AutoCAD class, we started with mechanical drafting. Draw this bushing... I had no idea what a bushing was, but I drew them! Our teacher had 3D models of components that we would measure with vernier calipers, which we would then draft in AutoCAD. But this was an elective and probably my only academic exposure to 3D physical modeling.
Study of geometry teaches us how to visualize in 3D. It introduces the basic principles of stability and scale. What are some other benefits of studying geometry?
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Chad Morrison P.E., F.ASCE
Professional Engineer
Greenville RI
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