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 #math #calculus #online #book

The Crossed Ladders Problem janmr.com/posts/crossed-ladders-pr… #math #geometry #algebra #problem #nerdsniping

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 #python #programming

Fast Evaluation of Fibonacci Numbers janmr.com/posts/evaluation-of-fibo… #math #fibonacci #numbers #algorithm

Donald Knuth Annual Christmas Lectures www.youtube.com/playlist?list=PLoR… #math #computerscience #programming #online #lecture

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… #evolution #simulation #physics #engine

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… #astronomy #december #solstice

Evaluation of Powers janmr.com/posts/evaluation-of-powe… #programming #algorithm #cpp #exponentiation #optimality

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

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… #programming #compiler #assembler

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

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

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

Computing the Integer Binary Logarithm janmr.com/posts/computing-the-inte… #programming #algorithm #integer #binary #logarithm #numbers #cpp

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

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…) #math #computerscience #programming #online #lecture

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

Bitwise Operators and Negative Numbers janmr.com/posts/bitwise-operators-… #programming #binary #numbers

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

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…

#sorting #algorithm #rust

Visualizing the Pythagorean Theorem janmr.com/posts/visualizing-the-py… #math #visualization #proof

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

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

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

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

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

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 #math #combinatorics

Continued Fractions and Continuants janmr.com/posts/continued-fraction… #math #computerscience #algoritms #continuedfractions

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

Online book: Mining of Massive Datasets www.mmds.org #online #book #computerscience #bigdata

Computing the Greatest Common Divisor janmr.com/posts/computing-the-grea… #math #programming #number-theory #algorithm

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

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-… #floor #ceil #functions #math #programming

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

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

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

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… #multiple-precision #arithmetic #algorithms #online #book

Nice Proof of a Geometric Progression Sum janmr.com/posts/nice-geometric-pro… #math #visualization #visual-proof

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…

An ongoing multi-author open source project to formalise a proof of Fermat's Last Theorem in the Lean theorem prover imperialcollegelondon.github.io/FL… #lean

Fast and maintainable patterns for fetching from a database by @sophiebits.com sophiebits.com/2020/01/01/fast-mai…

Celebrate 50 years of Microsoft with the company’s original source code by Bill Gates www.gatesnotes.com/home/home-page-…

Free math texts by Jim Hefferon (Linear Algebra, Theory of Computation, Introduction to Proofs) hefferon.net

@acm.org ACM has named Andrew G. Barto and Richard S. Sutton as the recipients of the 2024 ACM A.M. Turing Award for developing the conceptual and algorithmic foundations of reinforcement learning awards.acm.org/about/2024-turing

Stanford's "The Fourier Transform and Its Applications"

Videos, problem sets & more: see.stanford.edu/course/ee261

An unexpected, and extremely inefficient, way to compute pi @3blue1brown.com www.youtube.com/watch?v=HEfHFsfGXj…

Introduction to Computer Graphics, a free, on-line textbook covering the fundamentals of computer graphics and computer graphics programming math.hws.edu/graphicsbook

Videos from Math Professor Jeffrey Chasnov. Some of the playlists are videos from his Coursera courses on Mathematics for Engineers. #math #lectures #mooc www.youtube.com/@Jeff-math/playlis… www.math.hkust.edu.hk/~machas/?men…

Computer Science lectures by @timroughgarden.bsky.social www.youtube.com/channel/UCcH4Ga14Y…

Online conversion from TeX/MathML to HTML/SVG (powered by MathJax) #math #tex #mathml #svg mathjax.github.io/MathJax-demos-we…

Temml is a LaTeX-to-MathML JavaScript conversion utility. Useful online converter on homepage. temml.org #math #tex #mathml

KaTeX: A math typesetting library for the web katex.org

👻 Ghostty is a fast, feature-rich, and cross-platform terminal emulator that uses platform-native UI and GPU acceleration. ghostty.org

#AdventOfCode 2024 complete!