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·9 min read
EML: One Operator Is All You Need
How a single binary operator — eml(x,y) = exp(x) − ln(y) — can generate every elementary function a scientific calculator knows, from addition to trigonometry.
Tag
#math
6 posts tagged with this.
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·6 min read
The Bertrand Paradox: When Randomness Needs a Definition
A deceptively simple question — what is the probability that a random chord of a circle is longer than the side of its inscribed equilateral triangle? — has three different correct answers depending on what 'random' means.
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·17 min read
Automatic Differentiation
A deep-dive into automatic differentiation: symbolic vs. numerical vs. AD, AST transformation, dual numbers, tapes, hybrid methods, and a generic C++ implementation that computes gradients and solves optimisation problems.
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·9 min read
Why Tuning a Piano is Mathematically Impossible
Perfect harmony is a mathematical impossibility. Here's the beautiful, maddening reason why — and how piano tuners have learned to live with it.
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·9 min read
The Abelian Sandpile: A Group Hiding in a Pile of Sand
The Bak–Tang–Wiesenfeld sandpile model (ASM) is a deceptively simple cellular automaton that conceals a rich algebraic structure — an abelian group whose identity element is a non-trivial fractal-like configuration.
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·3 min read
The Fourier Transform: From Sines to Signals
A visual and mathematical journey through one of the most beautiful ideas in all of mathematics — decomposing any signal into its frequency components.
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