
A most unexpected answer to a counting puzzle [video] - espeed
https://www.youtube.com/watch?v=HEfHFsfGXjs
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kylnew
I understand maybe 30% of 3blue1brown’s videos, mostly due to his excellent
visualizations, but he really gets me excited for math in a way I’ve not
experienced before. How does he make such awesome visualizations? Does anyone
know what tools are being used?

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chrisdsaldivar
He built a python library for his visualizations called manim available on his
github [1].

[1] [https://github.com/3b1b/manim](https://github.com/3b1b/manim)

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edh649
The explanation video:
[https://www.youtube.com/watch?v=jsYwFizhncE](https://www.youtube.com/watch?v=jsYwFizhncE)

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earthicus
An interesting response to the explanation video from u/functor7 on reddit:

[https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_coll...](https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_colliding_blocks_compute_pi/eekeglk/)

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PuffinBlue
This is kind of a plea for help - how can I learn maths 'via' geometry?

I just can't get my head around 'numbers'. I can't seem to really visualise
them or understand what they are. I know this sounds weird. With language or
abstract things like 'problems' I can almost see them in my head. I can
analyse a problem and all it's flows of cause and effect in a visual way.
That's literally what happens in my head.

But with numbers I can't understand them at a basic level. Like - what are
they? How do I visualise them?

When it comes to geometry it's almost like it's the 'language' of my brain,
how I think, in terms of shape and form and translation and dimension.

I'll give you an example. I learnt Pythagoras theorem aged about 13 or
something. But didn't truly understand it until I was about 20 something when
I saw a diagram showing graphically the squares of the sides like this[0].

I really need to start at the absolute beginning, like build of a whole
foundation of what maths is based on geometry. Does that even exist?

This might not be possible, but if I can even get started it would be great.

[0]
[https://mysteriesexplored.files.wordpress.com/2011/08/pythag...](https://mysteriesexplored.files.wordpress.com/2011/08/pythagoreantheorem.png)

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earthicus
If you managed to survive high school algebra, you might be able to 'redo'
your basic math education with a geometric bent from Stillwell's book 'Numbers
and Geometry', which teaches the classical link between the two subjects that
has been eliminated from elementary education to some extent. However, the
kind of intuition he presents is still semi-abstract - it's not a super duper
picture heavy book - but I think it's about as close to what you're asking for
as you are likely to find.

[https://www.amazon.com/Numbers-Geometry-Undergraduate-
Texts-...](https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-
Mathematics/dp/0387982892)

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jhrmnn
Geometric proofs of problems that do not seem to be geometric are the most
satisfying in my experience.

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ColinWright
I wrote about this nearly four years ago:

[https://aperiodical.com/2015/03/%cf%80-phase-space-and-
bounc...](https://aperiodical.com/2015/03/%cf%80-phase-space-and-bouncing-
billiard-balls/)

It doesn't have nifty visualisations, but the (mythical) interested reader
might find this a useful complement to the video and explanation provided
there.

 _Edit: Thought so - I did submit my write-up at the time:_

[https://news.ycombinator.com/item?id=9202913](https://news.ycombinator.com/item?id=9202913)

~~~
jsweojtj
Your links to the original paper are broken in that writeup.

~~~
ColinWright
Bother.

Thanks for the catch, I'll get onto the hosts and get them to fix them.

Cheers.

~~~
ColinWright
And for completeness - now fixed. Thanks again.

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qualsiasi
I wrote a small Java program to verify the collision count, just because I was
bored and laying on the sofa:

> [https://github.com/Qualsiasi85/collision-
> pi](https://github.com/Qualsiasi85/collision-pi)

warning: code is a mess - and may have all sorts of nasty bugs, but after all
this has been done for fun and doesn't need to be "enterprisey" :)

I do like this kind of videos, they tickle my fantasy and keep alive my
passion in programming (that is slowly dying because of work! :) )

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Outermeasure_A
There was an ACM problem a few years ago where it was asked to count the
collisions. We implemented the simulation and noticed the digits of PI but we
didn't actually proven the fact. Got AC.

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Aardwolf
Nice, but I miss the more fundamental series of 3Blue1Brown like "the essence
of linear algebra" series, the "essence of calculus" series, and the
unfinished "deep learning" series from more than a year ago

Shame that this awesome visualization method he uses isn't used more for more
fundamental concepts to learn from the ground up rather than specific puzzles
like lately, I learned a lot from the "essence" series!

~~~
thanatropism
The essence of linear algebra is vector spaces and linear transformations.
It's not entirely impossible (although probably way more difficult) to learn
it without reference to Euclidean spaces and geometric reasoning.

Should be called "The intuition for linear algebra". But heck, the whole
reason we have and teach the mathematical method is that intuition either
breaks down in interesting cases (e.g. stochastic integrais versus "an area
under a curve" integrals) or limits you (linear algebra in function spaces,
etc).

It's a nitpick. I love 3b1b.

