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How to lie using visual proofs
Since the channel centers so heavily on visual intuition and visual proofs, it seems only right to give a few examples of where visual proofs can lead you astray.
Here we explore three examples of visual “proofs” that give incorrect results, one showing how the surface area of a sphere is π^2 * R^2, another showing how the circumference of a circle is 8, and a third demonstrating that all triangles are equilateral.
Aside from acting as cautionary tales, each one has a similar look and feel to various other famous visual proofs out there, so analyzing exactly why they’re wrong tells us something about what’s needed ot make all the other poofs out there rigorous.
On another note, we just added a “quotebook notebook” to the 3b1b store.
Each page includes some quote about mathematics, with the thought that as each of you works on your own math and sketch out whatever notes you like to take, the various musings of mathematicians at the top of each page act as a mixture of inspiration and delight.
We went for a bit of a nicer quality on the cover, and filled it with lightly gridded A5 pages.