/explore

Click through on any links that interest you or select the planets on the right to continue exploring the Outer Web.
You are here

 sriku.org
On the Pythagorean "theorem" | Codaholic
| | thenumb.at
Functions are Vectors
3.0 parsecs away

Travel
| | [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...
| | www.scientificamerican.com
2 High School Students Prove Pythagorean Theorem. Here's What That Means | Scientific American
2.0 parsecs away

Travel
| | At an American Mathematical Society meeting, high school students presented a proof of the Pythagorean theorem that used trigonometry-an approach that some once considered impossible
| | mathscholar.org
Simple proofs: The fundamental theorem of calculus « Math Scholar
2.1 parsecs away

Travel
| | [AI summary] The text presents a detailed, self-contained proof of the Fundamental Theorem of Calculus (FTC) using basic principles of calculus and real analysis. It breaks the proof into two parts: Part 1 establishes that the integral of a continuous function defines a differentiable function whose derivative is the original function, and Part 2 shows that the definite integral of a continuous function can be computed as the difference of an antiderivative evaluated at the endpoints. The proof relies on lemmas about continuity, differentiability, and the properties of integrals, avoiding advanced techniques. The text is structured to provide a clear, step-by-step derivation of the FTC for readers familiar with calculus fundamentals.
| | vxlabs.com
Variational Autoencoder in PyTorch, commented and annotated. - vxlabs
17.3 parsecs away

Travel
| I have recently become fascinated with (Variational) Autoencoders and with PyTorch. Kevin Frans has a beautiful blog post online explaining variational autoencoders, with examples in TensorFlow and, importantly, with cat pictures. Jaan Altosaar's blog post takes an even deeper look at VAEs from both the deep learning perspective and the perspective of graphical models. Both of these posts, as well as Diederik Kingma's original 2014 paper Auto-Encoding Variational Bayes, are more than worth your time.