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Is Irrationality Beautiful?

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Tags: musicartnaturesunflowertritonecontinuedfractions

What connects the Parthenon to sunflowers and the Mona Lisa? How is the musical interval that splits the octave responsible for the death of a Pythagorean, and why is it known as the devil in music? These questions are all answered in this video, which asks how beauty and irrationality are linked, and explores continued fractions, a representation that lets us define "how" irrational a number is. What is the most irrational number possible? Can this number be beautiful? In this video we weave a thread through thousands of years of history, from the discovery of irrational numbers to jazz and modern art. Far from being diabolical, these numbers contain an intrinsic beauty that displays the complexity and interconnectedness of the universe we inhabit. Rethinking the real line https://www.youtube.com/watch?v=uFWJuZQLKJs&t=133s @ProofofConceptMath Myth of the tritone https://www.youtube.com/watch?v=3MhwGnq4N9o @AdamNeely

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5.37 Overall score*

100 Rank

19 Votes

9 Comments

Comments

Is that a pihedron drawing at 1:11?

4.2

It made me interested but unsatisfied by the lingering explanations

very teacher vibe, good explanation for the beauty of irrational numbers.

I really like this subject. It tells a broad story on the irrational number called the golden ratio and how nature finds this principle on its own through maximizing efficiency. The music in between the chapters was a bit loud and hectic though. And there could have been more visuals and animations to explain things further. But all in all fun video!

6.6

I like seeing connections between those different things. I believe these play a significant role in making the new information stick.

The explanation is clear, apart from trace amounts of jargon and assumptions that some basic things are already known (like what rational numbers are).

Motivation is high as well, maybe one of the examples are something interesting to the viewer and hearing there is a connection to something else, could be surprising enough for them to keep watching.

There is no novelty in each of the examples, but there is some in how they are put together to tell the story.

Memorability might be the weakest point. There are so many pieces of information in this short video that feel disconnected. So by the end of it, some of the examples may already be forgotten.

8.2

Phenomenal video! I especially loved the question, “what’s the most irrational number?”

The presentation was choppy, but I think that with some work, it would be a 9.

3.9

I would definitely like to expand the part about nature maximizing surface area and how this leads to Fibonacci. The notion that „the most irrational” number is the one with a continued fraction containing only 1s is pretty, but I’d like more mathematical justification for the claim. The mention about Hippazos was a great little factoid that could for sure get the attention of more if it appeared earlier and was not glanced over. In general I missed a more intuitive explanation of irrationality, or maybe the simplest thing of a square with sides equal to 1 having an irrational diagonal. Maybe even the proof that sqrt(2) is irrational could be included? It should be in reach of high school students.

I find this video somewhat confusing. after watching it its not clear to me how all mentioned topics are connected. it feels like a bunch of somewhat related ideas but with fragile connections

4.3

This video is not bad, but I have seen this topic before.