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The Irish Logarithm
From the highly eclectic blog of Mark Dominus
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The latest blog posts to take off on Hacker News. 2,391 posts.
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An easy-to-implement, arena-friendly hash map
My last article had tips for for arena allocation . This next article demonstrates a technique for building bespoke hash maps that compose nicely with arena allocation. In addition, they’re fast, simple, and automatically scale to any problem that could reasonably be solved with an in-memory hash map. To avoid…
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Lean, Coq and other proof assistants: Visualising proofs as trees
This week we (me & Anton Kovsharov) published Paperproof, a Gentzen-tree-like proof interface for Lean 4. In this post I'll review proof visualisations from o...
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Circles do not exist
Many logos, drawings and other graphical designs have the following shape in it. What is this shape? If you thought: "Ah-ha! I'm smart and r...
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A mathematical formalization of dimensional analysis (2012)
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
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Painting with math: A gentle study of raymarching
A compilation of my Raymarching and Signed Distance Field learnings and work. In it, I teach you how to leverage those techniques along with lighting models, smoothmin, soft shadows, and some math to create beautiful 3D raymarched scenes ranging from abstract shapes to infinite realistic-looking landscapes.
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What Is Dimensional Analysis?
Mathematics is famously concerned with numbers . However, most of the physical quantities that we encounter in everyday experience cannot be expressed as numbers alone.
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How large is that number in the Law of Large Numbers?
All large numbers are large, but some are larger than others
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Category Theory Illustrated – Sets
Ready, set , begin… (you don’t know how hard I tried to resist to making that pun). We begin our inquiry with the theory of sets. Set theory and category theory share many similarities. We can view category theory as a generalization of set theory. That is, it’s meant to describe the same thing as set theory…
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Towards a new SymPy
This is the first part of a series of posts on big changes for SymPy with particular focus on speed. What I am going to describe in these posts are:
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Bézier Curves and the logic behind them
The logic behind Bézier Curves used in CSS animations and visual elements.
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Types versus sets (and what about categories?) (2022)
A recent Twitter thread brought home to me that there is widespread confusion about what types actually are, even among the most prominent researchers. In particular: are types the same thing as sets ? At the risk of repeating some of my prior posts, perhaps it’s time for a little history about type theory, set theory…
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Echo Chess: The Quest for Solvability
Chess puzzles, but you are what you eat.
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How Correlated Are You?
This post is an offshoot from Chapter 1 of Probably Overthinking It, which is available for pre-order now! Suppose you measure the arm and leg lengths of 4082 people. You would expect those measurements to be correlated, and you would be right. In the ANSUR-II dataset, among male members of the armed forces, this…
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How far can you jump from a swing?
In this post I derive the physics of pumping a swing and the physics of jumping from a swing. Then, using both pieces I compute the optimal strategy of jumping from a swing to maximize the traveled distance. I propose this game as a new Olympic sport.
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Thoughts about what worked in math circles
Thoughts about what worked in math circles After about 7 months of math circles with a group of 7- turning 8-year-old boys and girls, I decided to take a...
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Domain Repetition
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
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My favorite prime number generator
Many years ago I've re-posted a Stack Overflow answer with Python code for a terse prime sieve function that generates a potentially infinite sequence of prime numbers ("potentially" because it will run out of memory eventually). Since then, I've used this code many times - mostly because it's short and clear. In this…
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Fusion Foolery
Great. The fusion hype is bad enough already. Now its resurgence is going to interrupt the series of posts I’m in the middle of publishing in order for this post to be “timely.”
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NP-hard does not mean hard (2017)
When NP-hardness pops up on the internet, say because some silly blogger wants to write about video games, it’s often tempting to conclude that the problem being proved NP-hard is actually very hard! “Scientists proved Super Mario is NP-hard? I always knew there was a reason I wasn’t very good at it!” Sorry, these two…
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Exploring the design space of binary search trees
Open-source research project that explores the design space of binary search trees to implement persistent and concurrent linear list data structures.
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Symmetry in Chaos
The following is based upon systems of equations found in "Symmetry in Chaos, A Search for Pattern in Mathematics, Art, and Nature" (the second edition) by Michael Field and Martin Golubitsky. They ask the question whether there are aperiodic chaotic attractors that generate symmetric patterns? Can there be order…
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Fastest branchless binary search
Fastest general and simple binary search C++ implementation