A proof (visual or otherwise) shows "how" some statement is true, as in how it is built by the preceding truths. But I always wanted to know "why" something is true. For example, a biological cell grows and division happens. I could find tons of literature which talks about "how" this happens, but not "why" this happens. What's the motivation or goal? And why that goal is pursued? What is the force behind seeking of that goal?
This error can be made for calculating the length of any curve. If you add the deltas in only one dimension, then you end up with a bounding box length measurement that doesn't follow the contours of the curve. It's a misuse of calculus, that can be done with or without the visualization.
On of the first things my geometry teacher emphasized in 9th grade was that a drawing (even a very carefully measured one) didn't prove anything. Proof had to be derived from axioms and other proven facts.
These are neat! I guess you have to be comfortable with geometric proofs for them to really pop as obvious visual proofs, and certainly Archimedes was. I would have just started summing until it got close to 1/3, which is brutish by comparison to these beauties.
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[ 3.1 ms ] story [ 26.9 ms ] threadThey’re great and cool for things you already know to be true, but they can be tricky.
https://evanberkowitz.com/images/2014-03-15-quarters/Triangl...
https://evanberkowitz.com/images/2014-03-16-eighths/EighthsA... https://evanberkowitz.com/images/2014-03-17-ninths/NinthsAni...