The Pythagorean theorem stands as one of mathematics' most enduring and practical principles. Named after the ancient Greek mathematician Pythagoras, this fundamental concept has guided engineers, ...

Abstract: In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters.

The Pythagorean Theorem, a cornerstone of geometry, provides a fundamental relationship between the sides of a right triangle. Homework 3 often involves applying this theorem to solve various problems ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

A high school teacher didn't expect a solution when she set a 2,000-year-old Pythagorean Theorem problem in front of her students. Then Calcea Johnson and Ne'Kiya Jackson stepped up to the challenge.

Convolution is a remarkable property of the Fourier transform, often cited in the literature as the “faltung theorem”. Convolution is a remarkable property of the Fourier transform, often cited in the ...

In this work, we propose to represent chemical environments as vectorized objects which can be used as input for machine learning (ML) properties of atomistic systems. The proposed method efficiently ...

Automating mathematical reasoning has long been a goal in artificial intelligence, with formal frameworks like Lean 4, Isabelle, and Coq playing a significant role. These frameworks enable users to ...

They’re not our besties, but they’re more than just acquaintances. How much of ourselves do we owe them? Credit...Photo Illustration by Lauren Peters-Collaer Supported by By Lisa Miller Most of us ...