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www.reedbeta.com | ||
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jaydaigle.net
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| | | | | We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating. | |
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www.johndcook.com
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| | | | | Analogs of Euler's formula exp(ix) = cos(x) + i sin(x) in other number systems, namely dual numbers and double numbers. | |
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thenumb.at
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| | | | | [AI summary] The text discusses the representation of functions as vectors and their applications in various domains such as signal processing, geometry, and physics. It explains how functions can be treated as vectors in a vector space, leading to the concept of eigenfunctions and eigenvalues, which are crucial for understanding and manipulating signals and geometries. The text also covers different types of Laplacians, including the standard Laplacian, higher-dimensional Laplacians, and the Laplace-Beltrami operator, and their applications in fields like image compression, computer graphics, and quantum mechanics. The discussion includes spherical harmonics, which are used in representing functions on spheres, and their applications in game engines and glo... | |
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vitalik.eth.limo
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| | | [AI summary] An accessible technical introduction explaining how zk-SNARKs use polynomials, finite fields, and polynomial commitments to create succinct and private zero-knowledge proofs. | ||
