How to lie using visual proofs

My Calc II prof would always do this. He'd start going through a proof like it was critical to the course and we'd all be furiously copying it off the board. Then he'd get to the 1=2 conclusion at the end and laugh at how none of us saw it coming. Then we'd spend time trying to see where the error was (usually a very well hidden "divide by 0" mistake) I'll always remember him. He made calculus actually fun and interesting. The world needs more educators like him

You know you’re a good math communicator when you can lie with proofs.

The pi=4 "method" can also be used to "prove " √ 2 = 2 by approximating a diagonal with finer and finer scale taxicab paths

when he drew the triangle and split the base in "two" i was like "wait that's not even close to the middle"

As a non-math person who does a lot of CGI work, I’m rather proud of myself for getting the first one right. That sort of warping is something we have to watch out for all the time in UV Unwrapping. Yay!

I got the third one. I'm usually not smart enough to figure out anything that this channel says is "tricky" by myself so I was really satisfied with that

I am a seamstress, an knew from my experience taking 2D shapes to make 3D objects that the "triangles" of the sphere should have a curve. It was very exciting learning the maths behind my empirical knowledge, thank you so much!

This was the last video I watched before leaving my aunt's house. This was around 3 months ago, the last conversation I had with her was about my college classes and this math video I watched on YouTube (being you). She passed away roughly a month later and every time I watch this video I get reminded of her. I know you'll never read this comment, but your channel does mean a lot to me and you've helped me learn and nurture my curiosity about mathematics. I don't have any sort of deep statement, I just love these videos and they remind me a lot about days gone by. Thanks for making these, keep up the good work.

This is the video mathematicians want to make after being told convergence proofs are "unnecessary details, it's obvious" for the 1000th time. Great work!

One of my favorite ways to determine if a statement is plausible is to draw an extreme example. For the triangle proof, I drew a scalene triangle with one very short side. As soon as I tried to connect P, it was obvious it wasn't going to work because the intersection points existed outside of the original triangle. TL;DR I got three gold stars from Grant and I'm very proud of myself.

The fact that any circle drawn on a TV will have the same edge length as a square or rectangle which perfectly houses that pixel-based circle is honestly mind boggling. It makes perfect mathematical sense, but at the same time I just can’t wrap my head around it! Thank you for this enlightening piece of information - I’ll be sure to spread it to random people next time I’m drunk!

I've never been great at math. I barely passed geometry and algebra, and I've never even touched a calculus textbook. But something about your math videos make me feel like I understand it all, it brings back a sort of childlike curiosity where I don't have to feel bad about making mistakes or being wrong, I just get to sit here and learn things. It's oddly soothing for me and I love your videos :)

I had a SAT prep book way back in the 80s that said whenever the test says "Not drawn to scale", you should immediately redraw it to scale. That rule of thumb has served me well my entire life. Unfortunately, most people will throw out everything they know in the face of a confident deception.

The fun thing about the second "proof", you don't even need to do it with curves. Apply it to a diagonal of a square, and you can "prove" that the square root of 2 equals 2.

Found the flaw. Obviously it was because he assumed that it was a triangle. It was actually just a shape with three angles and three sides.

There’s something so frustrating about knowing you’re right, but not being able to prove it… good job, magic numbers man, that last example really got me.

A note on the sphere proof explanation: We can also prove that those "triangles" don't have flat sides by looking at their angles. The dividing lines on the sphere are all perpendicular to the "equator" of the sphere, so each of those triangles would have two right angles.

It's interesting how the Pi listeners in the animation react when something is noteworthy or thought provoking. I noticed myself understanding better when I saw the pi people understanding together. Very kewl

I actually got that last one, but even then it took me 2 minutes or so, despite me spending essentially all of my life until the age of 19 at math competitions. What I'm saying is: If you construct a false proof cleverly enough, you can fool anyone. Including yourself, sometimes. And not just in mathematics.

That’s funny. I knew the sphere example was wrong, I know you can’t flatten sections of a sphere without the pieces looking deformed. But you flattened it out and I said “huh, I must be wrong”. Blind trust I guess.