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How does Cave/Glade Generator Work
Watabou’s Cave Generator is one in a series of RPG-ready map generators that Watabou has created over the years. All his work oozes style, but the cave generator was always the one I found mo…
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
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Exponential Economist Meets Finite Physicist (2012)
[ An updated treatment of some of this material appears in Chapter 2 of the Energy and Human Ambitions on a Finite Planet (free) textbook, also mirrors a 2022 article in Nature Physics . . ]
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The derivative of a number (2014)
Are you kidding? Edward Barbeau is now a professor emeritus of mathematics at the University of Toronto. Over the years he has been working to increase the interest in mathematics in general, and e…
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Don’t invert that matrix (2010)
There is hardly ever a good reason to invert a matrix. What do you do if you need to solve Ax = b where A is an n x n matrix? Isn't the solution A−1 b? Yes, theoretically. But that doesn't mean you need to actually find A−1. Solving the equation Ax = b is
1595
How thick is a three-sided coin?
Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018: > How thick is a three-sided coin? Translated into mathematician-ese, this means > What aspect ratio of a flipped coin leads to the chance of landing on…
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Ssss: Shamir's Secret Sharing Scheme (2006)
Shamir's Secret Sharing Scheme
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Indices Point Between Elements
If you’re familiar with nearly any mainstream programming language, and I asked you to draw a diagram of an array, the array indices, and the array elements, odds are good you’d produce a diagram something like this: In this post, I want to persuade you to replace that image, or, at least, to augment it with an…
1598
There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman
When I first learned about Diffie-Hellman and especially elliptic curve Diffie-Hellman, I had one rather obvious question: Why elliptic curves? Why use this strange group that seems rather arbitrar…
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Implementing strict three-point perspective
Implementing strict three point perspective is ridiculous. You’ll never need it. Let’s do it anyway.
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Ramanujan Factorial Approximation (2012)
Ramanujan came up with an approximation for factorial that resembles Stirling's famous approximation but is much more accurate. As with Stirling's approximation, the relative error in Ramanujan's approximation decreases as n gets larger. Typically these approximations are not useful for small values of n. For n = 5…
1603
All you need is λ, part one: booleans
Words by Rob Rix.
1604
The Poincaré Conjecture, Explained
Poincaré began working on what is now considered to be the foundation of topology and algebraic topology in the 1890s with the work Analysis Situs (1895) and five later supplements (1899; 1900, 1902a, 1902b, 1904).
1605
Categories from scratch
Note The latest version of this document can be found online at https://dr-knz.net/categories-from-scratch.html. Alternate formats: Source, PDF. Prologue The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all “good” explanations of categories so far have…
1606
Deep Learning without Backpropagation
A machine learning craftsmanship blog.
1607
Twenty Questions Of Maddening, Delicious Geometry
The geometry puzzles that are lighting up Twitter.
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A Visual Intro to Complex Numbers
A visual and intuitive intro to complex number system providing a historical overview of how it was developed and why it is useful.
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When random numbers are too random: Low discrepancy sequences (2017)
Random numbers can be useful in graphics and game development, but they have a pesky and sometimes undesirable habit of clumping together. This is a problem in path tracing and monte carlo integrat…
1612
The seven specification ur-languages
A brief overview of the formal specification landscape
1613
The convolution empire strikes back
ConvNets Match Vision Transformers at Scale
1614
Generalized Knights
Knights in chess move in an L-shape: 2 squares in one direction and 1 square perpendicular. But what if it didn't have to be like that?
1615
Beyond Bézier Curves (2013)
There is a new feature of Pages and Keynote, not mentioned in any of Apple’s publicity nor in any press coverage I’ve seen, that is really very interesting. Perhaps it will even one day prove to ha…
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The Land Before Binary
In the early days of computing, 1 + 1 didn’t always equal 10
1618
Borges on Chaos Theory
About a weird, lovely short story
1619
Gödel, Turing and Cantor: The Math
This is mathematical section of the parent essay Gödel Incompleteness for Startups Gödel Numbering A formal system is just a collection of axioms and rules. Just like we did before we can record ax…
1620
Making MathBox: Presentation-Quality Math with Three.js and WebGL
Presentation-quality math with Three.js and WebGL.