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Some fun with π in Julia
A Pi Day tour of π in Julia: how Julia represents π, computing it with inline assembly and Taylor series (Madhava and Machin), and finding guaranteed bounds with interval arithmetic.
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Rolling Shutter Simulation in C
The most recent Smarter Every Day (#172) explains a phenomenon that results from rolling shutter . You’ve likely seen this effect in some of your own digital photographs. When a CMOS digital camera captures a picture, it reads one row of the sensor at a time. If the subject of the picture is a fast-moving object…
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What Monoids teach us about software
Monoids are a pretty interesting concept in software development. Monoids are everywhere. Monoids are simple yet powerful. And Monoids have a lot to teach us about software, in particular about com…
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Making math more Lego-like
A trio of Harvard researchers has developed a new 3-D pictorial language for mathematics with potential as a tool across a wide spectrum, from pure math to physics.
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What is Hindley-Milner and why is it cool? (2008)
Anyone who has taken even a cursory glance at the vast menagerie of programming languages should have at least heard the phrase "Hindley-Milner". F#, one of the most promising languages ever to emerge from the forbidding depths of Microsoft Research, makes use of this mysterious algorithm, as do Haskell, OCaml and ML…
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Playing with Wolfram Playing Cards
A few weeks ago, I knocked my favorite mug off the counter and it shattered. RIP:
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A Detailed Elliptic Curve Cryptography Tutorial
When adding two integers i and j of bitlength b, the result will be of bitlength b + 1 in the worst case. This means they can easily be naively added. If the result is larger or equal to F p one has only to subtract p from the result, i.e.:
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The Limits of the CAP Theorem
This post explains how CAP-Consistent systems can be highly available, how the CAP theorem applies to CockroachDB, and why consistency is the better choice.
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Learning to break ciphers
Every now and then, I read a question about learning how to break ciphers, or more generally how to become a cryptographer/cryptologist. From my viewpoint, the most important part of learning this…
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The strange story of “Extended Random”
Yesterday, David Benjamin posted a pretty esoteric note on the IETF’s TLS mailing list. At a superficial level, the post describes some seizure-inducingly boring flaws in older Canon printers…
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Base-4 fractions in Telugu
From the highly eclectic blog of Mark Dominus
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Twitter, but for Math, with Toots
Hooray, it’s yet another social network for you to join! I’m skeptical about new social media, but I’ve been seeing enough posts about mathstodon.xyz that I finally caved and got an account. Mathstodon is the math(s) “instance” of mastodon , a new open-source, decentralized microblogging social network. It’s a lot…
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The Hungarian Approach and How It Fits the American Educational Landscape (2015)
By Ryota Matsuura , Assistant Professor of Mathematics at St. Olaf College and North American Director of Budapest Semesters in Mathematics Education .
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Pi and the Golden Ratio
Two of my favorite numbers are pi: $latex \pi = 3.14159… $ and the golden ratio: $latex \displaystyle{ \Phi = \frac{\sqrt{5} + 1}{2} } = 1.6180339… $ They’re related: $latex \pi =…
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A dive into spatial search algorithms
Searching through millions of points in an instant
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What are the complex numbers, really?
Where did complex numbers come from? You might think that people invented \(i\) just so that they had a solution to the quadratic equat...
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How to defeat Ed25519 and EdDSA using faults
The Latest News from Research at Kudelski Security
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Understanding deep learning requires re-thinking generalization
Understanding deep learning requires re-thinking generalization Zhang et al., ICLR’17 This paper has a wonderful combination of properties: the results are easy to understand, somewhat surpri…
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A reasonably speedy Python ray tracer
Cyrille Rossant's small ray-tracer is an nice self-contained Python program (using NumPy) that renders this 400×300 image in about 15 seconds on a fast PC:
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220,000 cores and counting: largest ever public cloud job
An MIT researcher recently broke the record for the largest ever Compute Engine cluster, with 220,000 cores on Preemptible VMs , the largest known high-performance computing cluster to ever run in the public cloud.
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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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The Mathematics of 2048: Counting States with Combinatorics
How many board configurations are there in the game of 2048? Let's estimate using combinatorics.
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Voronoi Tessellations
Mapping nearest locations.