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Bicycle
Interactive article explaining the physics of a bicycle.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
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Airfoil
Interactive article explaining the physics of an airfoil and what makes airplanes fly
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4B If Statements
I recently stumbled upon this screenshot while researching social media on the train. Of course, it was followed by a cascade of spiteful comments, criticizing this fresh programmer’s attempt to solve a classical problem in computer science. The modulus operation.
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Mathematics for the Adventurous Self-Learner
For over six years now, I've been studying mathematics on my own in my spare time - working my way through books, exercises, and online courses. In this post I'll share what books and resources I've worked through and recommend and also tips for anyone who wants to go on a similar adventure.
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What Gödel Discovered
In 1931, a 25-year-old Kurt Gödel wrote a proof that turned mathematics upside down. The implication was so astounding, and his proof so elegant that it was...kind of funny. I wanted to share his discovery with you. Fair warning though, I’m not a mathematician; I’m a programmer. This means my understanding is…
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Visualizing Attention, a Transformer's Heart [video]
Demystifying attention, the key mechanism inside transformers and LLMs.
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Going Critical
Learn how things spread with playable simulations
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Knuth's Art of Computer Programming, V 4B, has gone into print
(I'm still looking for the catchiest way to appreciate the number MMXXVI. Exercise 7.2.1.6–122 gives 1234+.5*6+789 and -1+2345*6/7+8+9 and 1+(2/3)*45*67.8-9 ; other suggestions are welcome. The most elegant that I've seen so far is a beauty that was suggested independently by Arnaud Lefebvre and by Evangelos…
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A Programmer's Introduction to Mathematics
For the last four years I’ve been working on a book for programmers who want to learn mathematics. It’s finally done, and you can buy it today. The website for the book is pimbook.org, which has purchase links—paperback and ebook—and a preview of the first pages. You can see more snippets later in the book on the…
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Conterintuitive facts in mathematics, CS, and physics
It is possible to compute over encrypted data without access to the secret key: https://en.wikipedia.org/wiki/Homomorphic_encryption
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Too much efficiency makes everything worse (2022)
This blog is intended to be a place to share ideas and results that are too weird, incomplete, or off-topic to turn into an academic paper, but that I think may be important. Let me know what you think! Contact links to the left.
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I found two identical packs of Skittles among 468 packs
This article was discussed on Hacker News, and was cited in The Mathematical Gazette. Introduction This is a follow-up to a post from earlier this year discussing the likelihood of encountering two…
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Gravity is not a force – free-fall parabolas are straight lines in spacetime
For full functionality of this site it is necessary to enable JavaScript. Here are the instructions how to enable JavaScript in your web browser .
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Ultimate Tic Tac Toe
Once at a picnic, I saw mathematicians crowding around the last game I would have expected: Tic-tac-toe.
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Deep image prior 'learns' on just one image
Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is…
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Markov Chains Explained Visually (2014)
Markov chains, named after Andrey Markov , are mathematical systems that hop from one "state" (a situation or set of values) to another. For example, if you made a Markov chain model of a baby's behavior, you might include "playing," "eating", "sleeping," and "crying" as states, which together with other behaviors…
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Music theory for nerds
Not music nerds, obviously. I don’t know anything about music. I know there are letters but sometimes the letters have squiggles; I know an octave doubles in pitch; I know you can write a pop song with only four chords. That’s about it. The rest has always seemed completely, utterly arbitrary. Why do we have twelve…
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Poisson's Equation
If you aren’t used to staring at math, Poisson’s equation looks a little intimidating:
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How Not To Sort By Average Rating
Users are rating items on your website. How do you know what the highest-rated items are?
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Square Theory
The story starts in Crosscord, the crossword Discord server. Over 5,000 users strong, the server has emerged as a central hub for the online crossword community, a buzzing, sometimes overwhelming, sometimes delightful town square where total noobs, veteran constructors, and champion solvers alike come together to talk…
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Page Dewarping
Flattening images of curled pages, as an optimization problem.
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A visual proof that a^2 – b^2 = (a + b)(a – b)
A visual proof that a2 – b2 = (a + b)(a – b). Sophie Germain wrote, “It has been said that algebra is but written geometry and geometry is but diagrammatic algebra.”
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A recent experience with ChatGPT 5.5 Pro
We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to whi…
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Palindrome Day 20200202
Sonstiges - Learn more about palindromic dates in 2020 and in the near future. 2020-02-02 (YYYMMDD) or 02.02.2020 (DDMMYYY) and others.
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