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2,789,561 Views • Nov 6, 2015 • Click to toggle off description
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The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission.
For those of you who’d like to play around a bit with the stunning times table diagrams that we discuss in this video, download the .cdf file www.qedcat.com/cardioid.cdf and open it with the free cdf player which you can download from Wolfram Research (the people behind Wolfram Alpha and Mathematica). If you have access to Mathematica you can also open my .cdf file in Mathematica and play with the code.
For those of you who are looking for a bit of a challenge, ponder this:
1) Starting with the fact that the nephroid arises from parallel rays being reflected inside a cylindrical coffee cup, try to convince yourself that the 3 times table really does produce the nephroid (some really neat geometry at work here, very similar to the argument for the cardioid that I talk about at the end of the video). (Added 8 November 2015 check out the proof at www.qedcat.com/nephroid_proof.pdf )
2) Why do the diagrams for all the times tables have a horizontal mirror symmetry?
3) Try to explain the pretty patterns corresponding to the 51 and 99 times tables modulo 200 that I display in the video (around the 9:30 mark).
4) (For those of you with a very strong math background) Try to figure out why the cardioid shows up in the Mandelbrot set.
The discovery of the stunning patterns that I discuss in this video is due to the mathematician Simon Plouffe. Check out this article tinyurl.com/o2hbtsa and his website plouffe.fr/ for other stunning visualisations using modular arithmetic.
Quite a few animations have been contributed by various people and linked to in the comments: Here is one of the nicest ones by Mathias Lengler:
mathiaslengler.github.io/TimesTableWebGL/
Enjoy!
P.S.: The music we are playing at the end is called Shoulder Closure by Gunnar Olsen. It's part of the free YouTube music library. A really nice piece , isn't it?
Views : 2,789,561
Genre: Education
Date of upload: Nov 6, 2015 ^^
Rating : 4.936 (1,196/73,793 LTDR)
RYD date created : 2022-04-09T04:54:57.569239Z
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YouTube Comments - 3,418 Comments
Top Comments of this video!! :3
I’ve never had a YouTube video assign me homework
1.9K |
Considering he's really looking at a white wall, he does a very good job of looking at where the animation will be later on in post.
45 |
I’m seriously procrastinating from doing my math homework to watch a video about math 🤦♂️
493 |
I'm more impressed in how precise he is at pointing something that he's not seeing.
2.2K |
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."
-- Bertrand Russell
722 |
I was studying for a test and all of a sudden I was like "oh my god is there a cardioid inside my coffee cup" it's fascinating to see math in real life! there's something really appealing about this weird shape, for some reason I find it very aesthetically pleasing
22 |
This man has instilled a great deal of happiness back into my life.
36 |
I became hypmotized and for a moment I thought I'd solved the mysteries of the universe.
188 |
Humanity: Let's decode the universe.
Universe: Look at all the cool things you can do with butts!
1.2K |
Once i took lsd and i saw patterns like these moving in my head. I didnt See them more like felt. It was like Time, conciousness, vision, hearing and feeling were Working together to create geomatrical patterns you cant usually see With your eyes. Ive never heard of this stuff before but it seems like it plays a Major role in our World.
18 |
The flow within the patterns is a beautiful dance and I love the way that you can see it in the math and that you are teaching what's hidden from most of us, without a hint. Thank you.
2 |
Mathematics is the landscape of all possible structure.
58 |
My childhood Spirograph was a math engine of art.
147 |
I'm a simple man. I see creation expressed geometrically, I click.
20 |
I like the way he kept the scope of his presentation so precise and to the point and anyone with no maths background can enjoy- excellent work
2 |
This should be taught in every high school geometry class. We're so fixated on base 10, this is the way to address that in math ed. Everyone hated times tables, this is the gateway to showing how math is cool and past learning wasn't worthless.
177 |
For those of you who’d like to play around a bit with the stunning times table diagrams that we discuss in this video, download the .cdf file www.qedcat.com/cardioid.cdf and open it with the free cdf player which you can download from Wolfram Research (the people behind Wolfram Alpha and Mathematica). If you have access to Mathematica you can also open my .cdf file in Mathematica and play with the code.
For those of you who are looking for a bit of a challenge, ponder this:
1) Starting with the fact that the nephroid arises from parallel rays being reflected inside a cylindrical coffee cup, try to convince yourself that the 3 times table really does produce the nephroid (some really neat geometry at work here, very similar to the argument for the cardioid that I talk about at the end of the video).
2) Why do the diagrams for all the times tables have a horizontal mirror symmetry?
3) Try to explain the pretty patterns corresponding to the 51 and 99 times tables modulo 200 that I display in the video (around the 9:30 mark).
4) (For those of you with a very strong math background) Try to figure out why the cardioid shows up in the Mandelbrot set.
The discovery of the stunning patterns that I discuss in this video is due to the mathematician Simon Plouffe. Check out this article tinyurl.com/o2hbtsa and his website plouffe.fr/ for other stunning visualisations using modular arithmetic.
Enjoy!
Quite a few animations have been contributed by various people and linked to in the comments: Here is one of the nicest ones by Mathias Lengler:
mathiaslengler.github.io/TimesTableWebGL/
126 |
Finally. The mathematic formula to find permutations of multiple-cheeked butts.
141 |
Oh my goodness, as an artist this is a cool new way I can utilize precise patterns
Math always had cool ways to do art
1 |
@21CenturyBreakdownX
4 years ago
In grade school: Math is pointless! In College: Math is useful! Now: Math is flippin trippy.
1.5K |