How to lie using visual proofs
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when a question involves the fake sphere-flattening proof, or the pi = 4 limit-of-curve-lengths paradox, since the video shows exactly where such arguments fail.
Recommended by 1 people across 1 different months, 2022 to 2024.
What it is
3Blue1Brown walks through three false visual proofs: a flattened-sphere argument for surface area, the staircase proof that pi equals 4, and the proof that all triangles are isosceles. Each is followed by an explanation of where the argument breaks and what lesson it teaches about trusting pictures. It is an animated explainer narrated by Grant Sanderson.
What people said
Recommends J.G. · 2023-04 · Mathematics Stack Exchange · on “Integrating infinitesimal discs to find the volume of a sphere”
Hint: the thickness is parallel to the $\theta=0$ radius, so is actually $R|\cos\theta|d\theta$. Compare this [this video] .
Cites OverLordGoldDragon · 2022-07 · Mathematics Stack Exchange · on “Limit of length of curves vs length of limit of curves”
3Blue1Brown clip [this video] shows a false proof on $\pi=4$ , as we fold a square onto a circle, with the frame What exactly is the distinction between $lim(len(c))$ and $len(lim(c))$ ? I heard vaguely about continuity and Euclidean vs Taxicab distance but these don't explain it to me. Following the integral definition of arc length and it involving the curve's derivative, I do see the argument on the velocity vector, but can't make a connection to this. I'd expect $lim$ and $len$ to commute. What would be the exact mathematical expression for each? (Or for a close enough alternative example, showing lack of commutativity with full mathematical expressions )
Cites Thomas Lesgourgues · 2023-05 · Mathematics Stack Exchange · on “Validity of visual proof for surface area of sphere”
You should have a look at this video by 3B1B : [this video] It includes a "false proof" that the surface area of the surface is $\pi^2 R^2$, flattening the sphere in a similar way.
Cites Tristan Liu · 2023-05 · Mathematics Stack Exchange · on “Validity of visual proof for surface area of sphere”
I watched the video and the proof in the gif seems to be more akin to the "correct" area preserving wedges that grow according to a sine curve ( [this video] ) that yield the true answer. Wouldn't this lend credence to the visual proof then?
Cites Aditya Agarwal · 2024-07 · Mathematics Stack Exchange · on “Shape of a flattened wedge from the surface of a sphere (3Blue1Brown video)”
[LINK] In this video of 3B1B, he shows flattening of "triangular" wedges from the sphere. Lets take one wedge, and label the top pole as A, lower left corner as B, low right corner as C and the mid point of B and C (which is on the equator), as O. Now consider their positions relative to each other after flattening. By thickness logic (as he mentions in his video), we can definitely say that the left and right edges would be as shown (bulging outwards). But what about the lower edge? If we conside the distances AB, AC and AO, they all should be equal. So this shows that the lower edge should also be bulging outwards. So according to me, the final flattened wedge should be like a triangle wit