Call the table above A, and notice that each row, column and diagonal add up to 34, and each number appears exactly once. A table that satisfies this property is called a magic square. The sum of each row (or column, or diagonal) is called the magic constant of the magic square. There is a nice way of constructing a magic square whith arbitrary magic constant c. This constant has to be bigger than 34, since we are not allowing repetition of numbers in the square and we have used the smaller numbers (from 1 to 16) to fill the square in the example above. Suppose someone asks you to produce a magic square with magic constant c > 34. We can do that using the latin square above. Here is how:
Times Tables — Learn, Play and Print the Multiplication Tables
Practise every times table from 1 to 12 with free games, speed tests, printable charts and worksheets. Works on phones, tablets and computers. No sign-up.
A mystery with memory leaks and a magic number
This Most Simple Sudoku Rule = Fog Magic
Mystical
I wanted to make a programming language that resembled magical circles. This is more like a way to write PostScript that looks like a magical circle, but I will refer to it as Mystical in this document.
19.09.12 Attrell/Porreca (eds.), Picatrix: A Medieval Treatise on Astral Magic
Attrell, Dan, and David Porreca, trans. Picatrix: A Medieval Treatise on Astral Magic, Magic in History. University Park, PA: Pennsylvania State University Press, 2019. pp. xii, 372. $39.95 (hardback). ISBN: 978-0-271-08212-7 (hardback).
Reverse-Engineering the Wetware: Spiking Networks, TD Errors, and the End of Matrix Math
An engineer-friendly deep dive into how the human brain truly processes information, learns without backpropagation, and uses spiking neural networks, predictive coding, and dopamine-driven TD errors—challenging our notions of AI and matrix math.
Mathematicians still don’t know the fastest way to multiply numbers
A 23-year-old student overturned an ancient conjecture about one of math’s simplest operations
An invitation into Droste's Lair
A swords-and-sorcery programming environment for building and counting mathematical structures
Why A4? – The Mathematical Beauty of Paper Size
Unless you have skipped a lot of school, or work, or both – or you live in the USA – you have probably used an A4 sheet of paper before now. Have you ever wondered …
Narcissistic number
In number theory, a narcissistic number[1][2] (also known as a pluperfect digital invariant (PPDI),[3] an Armstrong number[4] (after Michael F. Armstrong)[5] or a plus perfect number)[6] in a given number base b {\displaystyle b} is a number that is the sum of its own digits each raised to the power of the number of digits.
Uri Bram 🔍 on Twitter / X
So I got memed into trying MathAcademy and it was one of the weirdest product experiences of my life. In short: I think they have an amazing product, but they're very opinionated about how you use it, and as a result I can't use it at all.Basically: they've figured out some…— Uri Bram 🔍 (@UriBram) January 16, 2025
Issue 084: Spreadsheets
Welcome to the 84th issue of De Programmatica Ipsum, about Spreadsheets. In this edition, we declare spreadsheets the most popular software programming environment of all time; in the Library section, we learn how to use Lotus 1-2-3 for science reading "Spreadsheet Physics" by Charles Misner and Patrick Cooney; and in our Vidéothèque section, we discover that Excel is a Turing-complete, functional programming language through the eyes of Dr. Felienne Hermans.
The Winning Variant
A/B testing, algorithmic optimization, and the small act of ignoring both — and what it means to make something by hand when a number can tell you what would have worked better.
Fidget
Fidget is a library for representing, compiling, and evaluating large-scale math expressions, i.e. hundreds or thousands of arithmetic clauses. It's mainly designed as a backend for implicit surfaces, but the library is flexible enough for many different uses!