Mathematics
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The Golden Ratio… nature’s obsession with 1.618
The number that shouldn’t exist There’s a number that appears so frequently in nature that Renaissance artists became convinced God had hidden a divine code in creation. It’s approximately 1.618. It has no ending. It never repeats. It’s irrational, which is to say, it cannot be expressed as a simple fraction, no matter how hard…
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The mathematics that runs your life
In 1936, a young British mathematician named Alan Turing wrote a paper that most people ignored. It wasn’t about building computers; those didn’t exist yet. It was about something stranger: whether certain mathematical questions could ever be answered by following a set of mechanical steps. The paper was theoretical, abstract, obscure. But buried in it…
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The mathematics of everything you can touch
Here’s a question that sounds simple but isn’t: What’s the difference between water and coins? Water flows. You can pour it, divide it infinitely, and measure it in fractions. There’s no “smallest unit” of water that matters; you can always split it further. Half a cup, a quarter cup, a molecule, an atom. Coins don’t…
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Suma summarum of linear algebra
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Linear algebra and maths of quantum mechanics
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Linear algebra for ML
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How linear algebra powers AI, physics, and cryptography
When most people hear the term linear algebra, they imagine rows of numbers in matrices or tedious exercises with vectors. Yet, far from being an isolated branch of mathematics, linear algebra is the hidden architecture of modern science and technology. It is the language that allows people to describe relationships, transformations, and patterns in systems…
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Orthogonal and Orthonormal vectors
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How to calculate eigenvectors?
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Understanding eigenvectors and eigenvalues
At first glance, words like eigenvector and eigenvalue look like they belong in some obscure math museum. But behind the heavy names are surprisingly simple ideas. They’re not about memorising formulas. They’re about uncovering the hidden rules that shape change: in geometry, in data, and even across the internet. Impact-Site-Verification: bc51445e-155a-462e-ac33-1e505feb70af Rubber sheets and secret…