How did mathematicians create drawings of complex geometric shapes in the past, without 3d graphics in computers? Here is one example of what I’m talking about, drawn in the 16th century:
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5I don't know what answer you're looking for, except "some people can draw well". – MathematicsStudent1122 May 22 '20 at 22:07
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The History of Science and Mathematics StackExchange might have some insights. – Blue May 22 '20 at 22:14
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Uh... they drew them by hand. The mathematics involved is not hard and would have been know and calculated in the 16 century. And almost certainly the artist would have made a model (although it wouldn't have been impossible to do without a model). – fleablood May 22 '20 at 22:14
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To learn how to draw this sort of picture, a good ref is George K. Francis's A topological picture book – achille hui May 22 '20 at 23:18
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1This is a fairly straightforward shape. More impressive is something like this. – Jair Taylor May 22 '20 at 23:34
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Quite a bit of calculation! And very precise measurements. When I was a kid, in place of internet and all that, a person could do the calculations to draw 2D projections (or, alternatively, in-perspective versions) of aesthetically pleasing objects, such as polyhedra. Some challenging trigonometry, yes.
In those days, there was a standard part of many curricula in the U.S., around 7th and 8th grade, "drafting", which required drawing orthographic projections of sometimes-complicated 3D objects... by measuring, and so on. Yes, being able to visualize things is a great help in doing these things!
Then having the precedent of that in mind, branching out to objects that are more complicated than cubes and spheres was an interesting thing...
(So, I'm thinking that if a kid in 1962 with no computers could draw such stuff...)
paul garrett
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