ASCII characters are not pixels: a deep dive into ASCII rendering alexharri.com/blog/ascii-rendering

A Simple Sudoku Solver janmr.com/posts/a-simple-sudoku-so…

One-page proof that π is irrational projecteuclid.org/journals/bulleti…

Multiple-Precision Subtraction, third post in a series of six on multiple-precision algorithms janmr.com/posts/multiple-precision…

$$\begin{aligned} w_i &\leftarrow (u_i - v_i - k_i) \;\text{mod}\; b, \\ k_{i+1} &\leftarrow [u_i < v_i + k_i] \end{aligned}$$

The Thue-Morse sequence is a binary sequence that is constructed by starting with the digit 0 and then repeatedly appending the binary complement of the sequence so far. Using two simple turtle graphics rules (0: forward one, 1: turn 60°), the sequence produces a Koch curve. https://en.wikipedia.org/wiki/Thue–Morse_sequence#Fractals_and_turtle_graphics oeis.org/A010060

Multiple-Precision Addition, second post in a series of six on multiple-precision algorithms janmr.com/posts/multiple-precision…

$$\begin{aligned} w_i &\leftarrow (u_i + v_i + k_i) \;\text{mod}\; b \\ k_{i+1} &\leftarrow \lfloor (u_i + v_i + k_i)/b \rfloor \end{aligned}$$

Structure and Interpretation of Computer Programs — JavaScript Edition. An open-source community effort to adapt SICP to JavaScript. sourceacademy.org/sicpjs

Multiple-Precision Number Representation, first post in a series of six on multiple-precision algorithms janmr.com/posts/multiple-precision…

$$u = (u_{n-1} \ldots u_1 u_0)_b = \sum_{k=0}^{n-1} u_k b^k, \quad 0 \leq u_k \leq b-1$$

The Twin Prime Conjecture states that there are infinitely many pairs of prime numbers that differ by 2. The current, provable, least bound on the gap between consecutive primes that is attained infinitely often is 246. oeis.org/A001223 michaelnielsen.org/polymath/index.…

List of datasets for machine learning research, computer vision and image processing en.wikipedia.org/wiki/List_of_data… en.wikipedia.org/wiki/List_of_data…

Print a calendar for the year 2026 with Python: python -m calendar 2026. Similar functionality with the *nix command cal. docs.python.org/3/library/calendar…

2026 is a semiprime. A semiprime is a natural number that is the product of two prime numbers. oeis.org/A001358

$$2026 = 2 \cdot 1013$$

The paper "MapReduce: Simplified Data Processing on Large Clusters" was published in December 2004. Map/reduce operations had been known for decades, but the paper was instrumental in the area of practical distributed computing and "big data". research.google.com/archive/mapred…

Bell numbers, the number of ways to partition a set of labeled elements janmr.com/posts/bell-numbers

$$\begin{aligned} &\{\{k_1,k_2,k_3\}\} \\ &\{\{k_1,k_2\}, \{k_3\}\} \\ &\{\{k_1,k_3\}, \{k_2\}\} \\ &\{\{k_2,k_3\}, \{k_1\}\} \\ &\{\{k_1\}, \{k_2\}, \{k_3\}\} \\ \end{aligned}$$

The Utah Teapot (also known as the Newell Teapot) is one of the most famous 3D models in computer graphics history. It was originally created by Martin Newell in 1975 and went through a number of modifications over the years. graphics.cs.utah.edu/teapot

Calculus Made Easy is a book on calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject calculusmadeeasy.org

The Crossed Ladders Problem janmr.com/posts/crossed-ladders-pr…

The Zen of Python. A listing of Python design principles and philosophies that are helpful in understanding and using the language. The listing can be found by typing import this at the interactive prompt. peps.python.org/pep-0020

Fast Evaluation of Fibonacci Numbers janmr.com/posts/evaluation-of-fibo…

Donald Knuth Annual Christmas Lectures www.youtube.com/playlist?list=PLoR…

Evolved Virtual Creatures by Karl Sims. A more than 30 years old project, but still very interesting. www.karlsims.com/evolved-virtual-c… www.youtube.com/watch?v=RZtZia4ZkX…

Today marks the December solstice, the shortest day in the Northern Hemisphere and the longest day in the Southern Hemisphere. At 15:03 UTC the North Pole is tilted maximally (about 23.4°) away from the Sun. janmr.com/posts/equinoxes-and-sols…

Evaluation of Powers janmr.com/posts/evaluation-of-powe…

$$\begin{aligned} x^0 &= 1 \\ x^{2k} &= (x^k)^2 \\ x^{2k+1} &= x \cdot x^{2k} \\ \end{aligned}$$

The M/o/Vfuscator compiles programs into "mov" instructions, and only "mov" instructions. Arithmetic, comparisons, jumps, function calls, and everything else a program needs are all performed through mov operations; there is no self-modifying code, no transport-triggered calculation, and no other form of non-mov cheating. 🤯 github.com/xoreaxeaxeax/movfuscato…

Prime Factors of Factorial Numbers janmr.com/posts/prime-factors-of-f…

$$d_p(n!) = \sum_{k=1}^\infty \left\lfloor \frac{n}{p^k} \right\rfloor = \sum_{k=1}^{\lfloor \log_p(n) \rfloor} \left\lfloor \frac{n}{p^k} \right\rfloor$$

Every position of Rubik's Cube can be solved in twenty moves or less www.cube20.org

Computing the Integer Binary Logarithm janmr.com/posts/computing-the-inte…

$$k = \lfloor \log_2 n \rfloor \quad \Leftrightarrow \quad 2^k \leq n < 2^{k+1}$$

Stanford Lecture: Dr. Don Knuth - Adventures with Knight's Tours (2025-12-04) www.youtube.com/watch?v=MKiRte-tnM… (playlist with many of Knuth's lectures: www.youtube.com/playlist?list=PL94…)

Bit Twiddling Hacks, a collection of fast and tested code snippets graphics.stanford.edu/~seander/bit…

Bitwise Operators and Negative Numbers janmr.com/posts/bitwise-operators-…

$$\overline{x} = -1 - x$$

Test and benchmark suite for sort implementations, github.com/Voultapher/sort-researc….

The current slice::sort_unstable implementation of the Rust standard library is based on ipnsort github.com/Voultapher/sort-researc… doc.rust-lang.org/1.92.0/std/primi…

Visualizing the Pythagorean Theorem janmr.com/posts/visualizing-the-py…

How to Draw a Straight Line (Peaucellier–Lipkin linkage) www.futilitycloset.com/2014/12/05/…

Fractions and Circles janmr.com/posts/fractions-and-circ…

Two Notes on Notation by Donald E. Knuth (Iverson's convention and Stirling numbers) arxiv.org/abs/math/9205211

$$[P] \quad \left[ { n \atop k } \right] \quad \left\{ { n \atop k } \right\}$$

The Stern-Brocot Tree of Fractions janmr.com/posts/the-stern-brocot-t…

Langford pairs: Arrange the 2n numbers {1, 1, 2, 2, ..., n, n} such that exactly k numbers occur between the two appearances of each digit k dialectrix.com/langford.html

Continued Fractions and Continuants janmr.com/posts/continued-fraction…

$$a_0 + \displaystyle\frac{1}{a_1 + \displaystyle\frac{1}{\ddots + \displaystyle\frac{1}{a_{n-1} + \displaystyle\frac{1}{a_n}}}}$$

Online book: Mining of Massive Datasets www.mmds.org

Computing the Greatest Common Divisor janmr.com/posts/computing-the-grea…

$$\text{gcd}(u,v) = \prod_{p \; \rm prime} p^{\min(u_p,v_p)}.$$

Guido on introducing the shortcut conditional expression to Python. Some usages are "intentionally ugly" and finishes by adding "It's still my language! :-)". mail.python.org/pipermail/python-d…

A if C else B

Useful Properties of the Floor and Ceil Functions janmr.com/posts/useful-properties-…

$$\begin{aligned} n=\lfloor x \rfloor \quad &\Longleftrightarrow \quad n \leq x < n+1, \\ n=\lfloor x \rfloor \quad &\Longleftrightarrow \quad x-1 < n \leq x, \\ n=\lceil x \rceil \quad &\Longleftrightarrow \quad n-1 < x \leq n, \\ n=\lceil x \rceil \quad &\Longleftrightarrow \quad x \leq n < x+1 \end{aligned}$$

Google humor: Did you mean recursion? www.google.com/search?q=recursion

Twelve Ways of Counting janmr.com/posts/twelve-ways-of-cou…

Modern Computer Arithmetic, a book about algorithms for performing arithmetic, and their implementation on modern computers maths-people.anu.edu.au/~brent/pub… members.loria.fr/PZimmermann/mca/p…

Nice Proof of a Geometric Progression Sum janmr.com/posts/nice-geometric-pro…

The first website info.cern.ch

Math.sumPrecise developer.mozilla.org/en-US/docs/W…

A leap year check in three instructions hueffner.de/falk/blog/a-leap-year-…

Full unicode emoji list unicode.org/emoji/charts/full-emoj…