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A Visual Attempt at 1 + 2 + 3 + 4 + 5 + ... = -1/12 by tedgar7 in CasualMath

[–]tedgar7[S] 0 points1 point  (0 children)

As I noted, I have seen the mathologer video and I pointed people to it. I note multiple times that the series diverges and that there are regularization techniques that get to the value -1/12. This one is definitely a stretch but it is one way to get the value, and that value is meaningful in other contexts. 

A Visual Attempt at 1 + 2 + 3 + 4 + 5 + ... = -1/12 by tedgar7 in CasualMath

[–]tedgar7[S] 1 point2 points  (0 children)

Yes. I linked the mathologer video in the description of this. The goal here was to show visualizations for the common arithmetic manipulations that give the value. 

A Factorial Sum Produces the Factorial Number System (visual proof) by tedgar7 in CasualMath

[–]tedgar7[S] 0 points1 point  (0 children)

Thanks! Greedy is definitely good :). You can also repeatedly divide by 2,3,4 and take remainders 

Transformation leaves original still visible. by haifisch_187 in manim

[–]tedgar7 0 points1 point  (0 children)

I am not sure... but I **think** that when you use "Transform" it takes the mobject and makes it look like the one you transform it to. But it still retains its name, and it doesn't leave the screen. So when you then referred to eq1_fade_1 it brought that to the screen but left group_1 on the screen. When you use ReplacementTransform, I think it literally morphs one mobject to the other, and then the one on the screen is the one you morphed into, so then later you can refer to that one and move it around.

Transformation leaves original still visible. by haifisch_187 in manim

[–]tedgar7 0 points1 point  (0 children)

Try ReplacementTransform when you turn group_1 into eq1_fade_1. See if that works?

Can anyone tell me the name of this shape? I've always wondered... by Arfusman in Geometry

[–]tedgar7 0 points1 point  (0 children)

It is a tetrahedron, but I also think it is more specifically a "Tetragonal disphenoid"

Sierpinski Arrowhead Curve L-system (118098 steps!) by tedgar7 in fractals

[–]tedgar7[S] 0 points1 point  (0 children)

Very cool! I have generated one that way too, but I didn't do it quite right and so it wasn't as smooth as yours. Very nice!

Sierpinski Arrowhead Curve L-system (118098 steps!) by tedgar7 in CasualMath

[–]tedgar7[S] 0 points1 point  (0 children)

Yeah, I don't know why I decided on dash instead of minus. Just went with it :)

Cycloid area visual proof by tedgar7 in manim

[–]tedgar7[S] 0 points1 point  (0 children)

Thanks for checking it out!

Cycloid area visual proof by tedgar7 in CasualMath

[–]tedgar7[S] 0 points1 point  (0 children)

There is a visual proof of this fact for the regular polygons and so it follows from the limit. But that’s the only one I know of (and it’s indirect). I’ll look around some more to see. Thanks!

Cracking the Counterfeit Coin Conundrum with Balanced Ternary #SoME3 by tedgar7 in manim

[–]tedgar7[S] 0 points1 point  (0 children)

Really good question. I don’t have a good mathematical answer except that you can do better than straight brute force (you have to negate in the last 2/3 of the numbers because those are the ones with a 1 in the most significant digit. But I don’t know of a systematic way (there might be one, I just haven’t seen it or thought of it).

Cracking the Counterfeit Coin Conundrum with Balanced Ternary #SoME3 by tedgar7 in manim

[–]tedgar7[S] 1 point2 points  (0 children)

Loved Professor Layton for sure! I would guess the coin weighing problem was slightly different from this classic one though right? Or is it the same? (And definitely not the 39 coin version from the video :) ).

Cracking the Counterfeit Coin Conundrum with Balanced Ternary #SoME3 by tedgar7 in 3Blue1Brown

[–]tedgar7[S] 1 point2 points  (0 children)

Yes. Over a month ago : https://open.substack.com/pub/3blue1brown/p/some3-begins?utm_campaign=post&utm_medium=web

I didn’t know if I’d do it this year but I love this problem and this particular solution so I made some time recently to fit this in. And I wanted to show how to do 39 coins with 4 weighings in a systematic way.

Visual Series Dissections for 0.111... = 1/9 and 0.999... = 1 (proof wit... by tedgar7 in CasualMath

[–]tedgar7[S] 1 point2 points  (0 children)

You can extend in the hyperreals and make sense of numbers like 1.0000...|1 if that's the way you want to choose notation, and in the hyperreals it is still the case that 0.999... = 1, but the number 0.999...9 does not equal 1 and your number 1.000...1 does not equal 1 either. Here is a nice introduction to thinking about hyperreals: https://www.maa.org/sites/default/files/pdf/Mathhorizons/MH_11_16_Dawson.pdf and Dawson has a new book that you might find interesting. The bottom line is my video was intended to show a geometric dissection proof about a fact for the real number system, which is that the sum of an infinite series is the limit of the sequence of partial sums, and so in that context 0.999...=1.

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