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Comparing City Street Orientations
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
1202
Better Geometry Through Graph Theory (2018)
A few months ago, I decided to implement set operations on curved regions. I had the the canonical textbook on computational geometry , which described approaches for polygons comprised of straight lines, and it seemed like other projects had extended these techniques to parametric curves . I figured it would take a…
1203
Erdős Problem #1026
Problem 1026 on the Erdős problem web site recently got solved through an interesting combination of existing literature, online collaboration, and AI tools. The purpose of this blog post is to try…
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The Fibonacci Matrix
When you think about the Fibonacci sequence, you probably imagine a swirling vortex of oscillating points stretching outwards to infinity: Okay, no, obviously you don’t. Yet.
1206
Learning the Integral of a Diffusion Model
A deep dive on flow maps.
1207
Paxos derived
Lamport's fault-intolerant state machine replication algorithm In 1978, Lamport published his classic "Time, Clocks, and the Ordering of E...
1208
A primer on Bezier curves
A detailed explanation of Bézier curves, and how to do the many things that we commonly want to do with them.
1209
A homework question in someone’s 11th grade statistics class
My son is in 11th grade. Below you’ll find a HW question which was given in my son’s statistics class. How would you answer?
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The most common errors in undergraduate mathematics
This page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies.
1212
Diving into the world of hash tables
Diving into the world of Hash Tables and understanding the underlying mechanics is extremely interesting, and very rewarding. So let's get into it and get started from the beginning. They are used commonly in algorithm design.
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Planes in 3D Space
Visual and interactive introduction to 2D planes in 3D space.
1215
My favourite small hash table
I'm the kind of person who thinks about the design and implementation of hash tables. One design which I find particularly cute, and I think deserves a bit more publicity, is Robin Hood open-addressing with linear probing and power-of-two table size. If you're not familiar with hash table terminology, that might look…
1216
AI for math resources, and erdosproblems.com
This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistan…
1217
Evaluating a class of infinite sums in closed form
A family of infinite sums that evaluate to rational numbers, sometimes integers, and and effective algorithm for finding the sum.
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Zero-knowledge proofs, encoding Sudoku and Mario speedruns without semantic leak
We published our video on zero-knowledge proofs! Surprisingly, making this video took a lot of work. Zero-knowledge proofs for coloring are one of those algorithms that, in hindsight, seem beautifu…
1220
Lovelace's Leap
There's a great deal said about Ada, Countess of Lovelace that I find misguided. And, worse, the real intellectual triumph of Lovelace is ...
1221
A (Long) Peek into Reinforcement Learning
[Updated on 2020-09-03: Updated the algorithm of SARSA and Q-learning so that the difference is more pronounced. [Updated on 2021-09-19: Thanks to 爱吃猫的鱼, we have this post in Chinese].
1222
CRDT: Text Buffer
Collaboratively editing strings of text is a common desire in peer-to-peer applications. For example, a note-taking app might represent each document as a single collaboratively-edited string of text.
1223
How did Einstein Think?
John D. Norton Department of History and Philosophy of Science and Center for Philosophy of Science University of Pittsburgh http://www.pitt.edu/~jdnorton This page at http://www.pitt.edu/~jdnorton/Goodies Prepared to accompany cityLIVE! "everything einstein" November 15, 2007, 6:30 pm The New Hazlett Theater…
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A riddle wrapped in a curve
If you’re looking for a nice dose of crypto conspiracy theorizing and want to read a paper by some very knowledgeable cryptographers, I have just the paper for you. Titled “A Riddle Wrapped in an E…
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Demystifying the regular expression that checks if a number is prime (2016)
Ever wondered how the ^.?$|^(..+?)\1+$ regular expression can tell you if a number is not prime? In this blog post you'll learn how and why it works. Code examples in Java, JavaScript, Python and Perl are provided.
1227
The Mathematics of 2048: Counting States with Combinatorics
How many board configurations are there in the game of 2048? Let's estimate using combinatorics.
1228
Simple Pathtracing (2012)
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
1229
After Math
[This is a guest post by Silvia De Toffoli and Eamon Duede. This blog post was initially written in a different file format and converted using AI. — T.] Silvia De Toffoli (University School …
1230
A “perfect” voting system
A voting system that sidesteps Arrow's theorem entirely. The scare quotes around