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polymathprojects.org | ||
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terrytao.wordpress.com
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| | | | | Building on the interest expressed in the comments to this previous post, I am now formally proposing to initiate a Polymath project on the topic of obtaining new upper bounds on the | |
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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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raphlinus.github.io
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| | | | | Finding the optimal Bézier path to fit some source curve is, surprisingly, not yet a completely solved problem. Previous posts have given good solutions for specific instances: Fitting cubic Bézier curves primarily addressed Euler spirals (which are very smooth), while Parallel curves of cubic Béziers rendered parallel curves. In this post, I describe refinements of the ideas to solve the much more general problem of simplifying arbitrary paths. Along with the theoretical ideas, a reasonably solid implementation is landing in kurbo, a Rust library for 2D shapes. | |
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susam.net
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| | | [AI summary] This article explains why the product of two negative numbers is positive, using mathematical proofs and ring axioms to generalize the rule beyond basic arithmetic. | ||
