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Banned math book
The applied math classic Courant & Hilbert was banned in Nazi Germany. The US seized the copyright and published an English edition.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
1052
Faster remainders when the divisor is a constant: beating compilers & libdivide
Not all instructions on modern processors cost the same. Additions and subtractions are cheaper than multiplications which are themselves cheaper than divisions. For this reason, compilers frequently replace division instructions by multiplications. Roughly speaking, it works in this manner. Suppose that you want to…
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Problem solving strategies in a graduate real analysis course (2010)
This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a…
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A new rare high-rank elliptic curve, and an orchard of Diophantine equations
I got an email the other day from mathematician Bogdan Grechuk, whose book Polynomial Diophantine Equations: A Systematic Approach ( was recently released. This is to my mind a rather remarkable bo…
1056
Making the Monty Hall problem weirder but obvious
It’s this simple: Do you want what’s behind one door or the other nine?
1057
Gödel and the unreality of time
In 1949, in a festschrift devoted to Einstein , Kurt Gödel published a very short but profound paper titled “A Remark About the Relati...
1058
Sub-pixel distance transform
High quality font rendering for WebGPU
1059
Wounded QR Codes
How do QR codes work? How much is it possible to distort one and still have it readable?
1060
The art of solving problems with Monte Carlo simulations
Using the power of randomness to answer scientific questions.
1061
Beyond automatic differentiation
Posted by Matthew Streeter, Software Engineer, Google Research Derivatives play a central role in optimization and machine learning. By locally app...
1062
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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There's more to mathematics than rigour and proofs (2007)
The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Wh…
1064
A trick to eliminate 2π (sometimes)
As a physicist, I’ve learned that the presence of 2 π 2\pi 2 π [▼] [ Or rather τ \tau τ , as it should actually be called . ] in a formula usually spells trouble. It’s kind of annoying to write by hand, easy to forget, and it’s dimensionless, so you can’t easily check if you forgot to divide or multiply by it…
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Can a Rubik's Cube be brute-forced?
a personal blog
1067
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…
1068
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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The Stack Monoid
(Updated 2020-09-06 with pointers to related work and a bit more explanation)
1071
I analyzed the chords to 1300 songs for patterns. Part 3 – Interactive Discovery
Last year, we discussed the first results of a long term effort to study the patterns found in the chords of popular songs. The reception that we got was incredibly positive, and we received a ton of great feedback. The two most common questions we’ve gotten from people have been: Our answer: Hooktheory Trends How...
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Two algorithms for randomly generating aperiodic tilings
[Part of a series: Penrose and hats | Spectres | finite-state transducers | more transducers | refining tilings ]
1074
How Far Can You Get From McDonald's?
This summer, cruising down the I-5 through California’s Central Valley to the Los Angeles Basin, I unwittingly stumbled upon a most exasperating development: the country strip mall . First, let me state that I don’t hate. I’ve got nothing against Petco, Starbucks, OfficeMax, et al. When overcome by the desire for a…
1075
What's the difference between 0/0 and 1/0?
From the highly eclectic blog of Mark Dominus
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How Fair Is My D20? (2015)
An automatic system for rolling a polyhedral die and taking photos of the rolls; extracting the image of just the die from those images; clustering the images of the die by which face is shown; and analyzing the results.
1080
Why are roller coaster loops not circular?
Why are the loops on roller coasters never circular?