Three false proofs, and what lessons they teach.
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Here’s a nice short video on the false pi = 4 proof
Time stamps:
0:00 – Fake sphere proof
1:39 – Fake pi = 4 proof
5:16 – Fake proof that all triangles are isosceles
9:54 – Sphere “proof” explanation
15:09 – pi = 4 “proof” explanation
16:57 – Triangle “proof” explanation and conclusion
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amazing.. thank you'
The leinght of the triangle is not the same because the leingths of the small trianges’ sides are changed, meaning that the sides that are the same can be one in a side of the large triangle and the other equal side of the other triangle can be out of a side of the large triangle
its not SAA ,its AAS and SSA is actually RHS congruency rule
i hate math but somehow you make me love it in your videos… HOW
SSA can’t prove congruency it can only prove similarity
For the sphere, you can't turn the small curved triangles into flat triangle or else you will be stretching out the triangle.
I knew why the first two didn't work, but I never would have gotten that the intersection point between the angle bisector and the perpendicular bisector was outside the triangle for the third one. No gold stars for me.
The π=4 arguement actually “proves” that a circle is a square.
I understood everything you explained here but all this just makes me loss faith in derivation and proofs.
Although for the isosceles proof, I had a different explanation…kinda. when you draw a line from P to the midpoint of the other two lines there is no reason why you can assume right angles.
Isnt that enough?
7:34 – triangles are not equal. You need to have no just a side and two angles, but a side between these two angles.
No, I don't try to flex, and I've failed at realizing bad stuff with fake sphere at the beggining, and I had to google the rule for determining whether triangles are equal. But it was cool that I have immediately noticed that equality of triangles by that side they share is a trick.
Isn't the coastline paradox because of what was talked about in the second proof
Ig it can be the rule that in an isosceles triangle the bisector is the height and the median and others at the same time,it is the rule,ig
Lol no way that sphere is correctly done, you did a transformation to flat or a projection that is so incorrect to represent like that on a flat surface
Let's see hmm
1:29 when i saw this it seems like some part of "unraveling" the slices into flat shapes is an approximation for the actual curvature, and the actual difference between the 2 areas boils down to approximating 4 as pi (or vice versa) in some capacity
as a visual person who doesnt like alphabet mixed in math this seems to be incredibly easy, already at 7:32 excusing sloppy drawing is not acceptable since you make bigger inaccuracies than difference in triangle sides, which immediately pushed me to imagining triangle with tiny side where it could never create P inside triangle also never trust proofs done with ruler while not being up to scale
That viral triangle problem he did where you rearrange the shapes and seem to lose area, any reason the ratios were prime, or is that just your choice of ratios?
i feel the same way with sum positive ints = -1/12
Hum… first proof, the triangles you create each have 2 right angles, which is weird for triangles. Not saying it’s wrong in a spherical context, but you’ve taken them out of the spherical context by flattening them.
What a good video, I’m really curious when I’ll get to learn this stuff
My assumption on the third one is that the perpendicular bisector doesn’t have same lenght? same goes to the angle bisector. Let’s see if that’s the case…
"You eat my food?"
"No."
"Prove it"
"Alr let me show you"
Hmm, pi is indeed not equal to 4.
Pi = 3 = e.
The way to prove the surface area of a sphere is pie ²and r² is not working because the sum of the angles do not sum up to 180.
So they are not triangles
11:10
Beautiful! Thank you!
A bit late to the party, but on the note of the second illusion: how does one prove the limit of the square curves is the circle?
Toying with it in my head, one can imagine building a list of the points (x,y) which both the square curves and circle both contain. That list doubles in size with every iteration, so obviously it goes to infinity – but it feels ripe for some Cantor-esque argument where you build a point (x,y) that the circle must have, but isn't included in your list of points, proving the circle and the square curve are not the same set of points. That shouldn't be possible if the limit of the square curves is the circle itself.
I feel like I've missed some crucial step along the way, like maybe that list is uncountably infinite, or there's provably no way to generate these absent points, but I can't put my finger on it currently.
ur ur ur ur mom
You also need to account for edge cases and assumptions in programming. This shows that programming and algebra have a lot in common. From my experience, learning one makes you better at the other. One of the many reasons I believe that school curricula (plural of curriculum) should change so that computer science is a requirement.
The truth is there is NO limit with Pi its a dimensionless constant like Log E. Did you know that the first verse of the Bible expresses itself mathmatically as Pi? The first verse of john does the same thing but with Log E which is AMAZING seeing how they BOTH speak of creation.
The shape of all creation is Pi and Log E.
if you were to REALLY interlace them they wouldnt fit as the edges are slightly curved still.
just point P is outside triangle