Riff on an integration bee integral
I saw an integral posted online that came from this year’s MIT Integration Bee. My thoughts on seeing this were, in order: It looks like a beta function. The answer is a small number. You can evaluate the integral using the substitution u = 1 − x2025. I imagine most
Read moreThe Basics of Node.js Streams
Explore the fundamentals of Node.js streams for efficient I/O operations. Learn how readable, writable, and transform streams work with practical examples of data handling, piping, and backpressure management in this comprehensive guide. Continue reading The Basics of Node.js Streams on SitePoint.
Read moreWhether AI is a bubble or revolution, how does software survive?
Money is pouring into the AI industry. Will software survive the disruption it causes?
Read moreAnother little chess puzzle
Here’s another little chess puzzle by Martin Gardner, taken from the same paper as earlier. The task is to place two rooks, two bishops, and two knights on a 4 by 4 chessboard so that no piece attacks any other. As before, there are two basic solutions, here and here,
Read moreMultiplying by quaternions on the left and right
The map that takes a quaternion x to the quaternion qx is linear, so it can be represented as multiplication by a matrix. The same is true of the map that takes x to xq, but the two matrices are not the same because quaternion multiplication does not commute. Let q = a + bi
Read moreEmbeddings, Projections, and Inverses
I just revised a post from a week ago about rotations. The revision makes explicit the process of embedding a 3D vector into the quaternions, then pulling it back out. The 3D vector is embedded in the quaternions by making it the vector part of a quaternion with zero real
Read moreWhy Your Automation Needs AI Decision-Making (And How Wordware Delivers)
Discover why traditional automation tools fall short for complex workflows and how Wordware's AI decision-making capabilities transform business processes through intelligent context understanding, adaptive learning, and natural language programming. Continue reading Why Your Automation Needs AI Decision-Making (And How Wordware Delivers) on SitePoint.
Read moreAlternative exp and log notation
The other day I stumbled on an article [1] that advocated writing ab as a↑b and loga(b) as a↓b. This is a special case of Knuth’s up arrow and down arrow notation. Knuth introduces his arrows with the intention of repeating them to represent hyperexponentiation and iterated logarithms. But the emphasis in
Read moreDecimal Separator and Internationalization
This morning I ran across the following tip from Joost Helberg on Mastodon: TIL don’t report numbers with three digits after the decimal point. People may interpret the decimal point as a thousands separator. Using 2 or 4 digits, although wrong, avoids off by a factor thousand errors. I usually
Read moreA crowded little chess puzzle
Here’s a puzzle by Martin Garnder [1]. Can a queen, king, rook, bishop, and knight be placed on a 4² board so no piece attacks another? There are two solutions, plus symmetries. Note that in all non-attacking chess puzzles, the colors of the pieces are irrelevant. In the solutions I
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