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The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
At last, the Hamiltonian circuit problem for Rubik's Cube has a solution! To be a little more mathematically precise, a Hamiltonian circuit of the quarter-turn metric Cayley graph for the Rubik's Cube group has been found.
Here’s a followup to last month’s post about Penrose Tiling in Obfuscated Python. The Mandelbrot set is a traditional favorite among authors of obfuscated code. You …
The soft maximum approximates the maximum function, and approaches it in the limit, but is easier to work with.
Graphists, animators, game programmers, font designers, and other graphics professionals and enthusiasts are often working with Bézier curves. They're popular, extensively documented, and used pretty much everywhere. That being said, I find them being explained almost exclusively in 2 or 3 dimensions, which can be a…
Personal blog about system engineering and devops
Made in Notion, the connected workspace where AI agents and teams organize docs, projects and knowledge together.
Let me tell you about a language. But if you wish to go play instead go here. It's going to get a little abstract below. There is a Canvas to Compose Upon The canvas is a square with the largest circle that has a radius of ρ. There are
Usually I write about solutions to problems I’ve worked out, but I’ve found myself increasingly becoming interesting in where solutions come from. Maybe it’s because I’ve been reading Boorstin’s excellent The Discoverers , which I’d strongly recommend.
The partition function p ( n ) counts the number of partitions of n , i.e. the number of ways n can be written as a sum of positive integers when disregarding the order of the terms. For example, 4 has the five distinct partitions 4, 3+1, 2+2, 2+1+1, 1+1+1+1, so p (4) = 5. This week, I set a new record by computing…
By Devine Lu Linvega
LaTeX Code for Cryptographic Images.
Multiple Neighborhood Cellular Automata (MNCA) produce complex and robust emergent structures not commonly seen in simpler models
Understanding gradient boosting with interactive 3d-demonstrations
Elliptic Curve Cryptography (ECC) has grown to be very popular in public-key cryptographic systems, most popularly used in Bitcoin. ECC is…
Hash tables are the most popular probabilistic data structure, by quite a margin. You compute some hash code then compute an array index from that hash code. If you’re using open addressing-c…
One of the saddest and most fascinating things about applied cryptography is how little cryptography we actually use. This is not to say that cryptography isn’t widely used in industry —…
Understanding derivatives and logarithms of transforms
Generalized linear models (GLMs) are indispensable tools in the data science toolbox. They are applicable to many real-world problems involving continuous, yes/no, count and survival data (and more). The models themselves are intuitive and can be used for inference and prediction. A few very high quality free and open…
Applying probabilistic models to data usually involves integrating a complex, multi-dimensional probability distribution. For example, calculating the expectation/mean of a model distribution invol…
On efficient algorithms, the exponential time hypothesis, and losing the plot.
Thomas Ptacek wondered on mastodon whether there were any Spelling Bee pangrams that would get you to the highest scoring level on spelling bee just by finding that word.
Computers often need random numbers. Most times, random numbers are not actually random... in the sense that they are the output of a mathematical function that is purely deterministic. And it is not even entirely clear what "really random" would mean. It is not clear that we live in a randomized universe... it seems…
Mathematics is famously concerned with numbers . However, most of the physical quantities that we encounter in everyday experience cannot be expressed as numbers alone.
A deep link between two seemingly unconnected areas of modern science - quantum physics and game theory - is described by researchers from the Universities of Bristol and Geneva in a paper published in Nature Communications.
Using graph theory and Ryanair route data to find cheap multi-city flight loops through Europe.
