Geonum: Geometric Number Library for Unlimited Dimensions with O(1) Complexity
By
embedding-shape
Pure flour-power. Hearty enough to carry you through lunch.
Summary
The article introduces Geonum, a geometric number library that supports unlimited dimensions with O(1) complexity. It critiques traditional mathematical approaches that separate numbers from their geometric context by creating 'scalars' that discard angle information. The library aims to preserve geometric primitives and avoid the computational overhead of artificial dimension superstructures, offering a more efficient approach to scientific computing.
Key quotes
· 4 pulledremoving an explicit angle from numbers in the name of 'pure' math throws away primitive geometric information
once you amputate the angle from a number to create a 'scalar', you throw away its compass
computing angles when they deserve to be static forces math into a cave where numbers must be cast from linearly combined shadows
you start by creating a massive artificial 'scalar' superstructure of 'dimensions' to store every possible position where your scalar vector component can appear
You might also wanna read
Survey of Fast Hyperbolic Tangent Approximation Techniques for Neural Networks and Audio Processing
This article surveys various mathematical approximation techniques for the hyperbolic tangent (tanh) function, focusing on computational eff
Interval Calculator: Working with Interval Union Arithmetic
This article describes an interval calculator that operates on unions of intervals rather than just real numbers. It implements Interval Uni
victorpoughon.github.io·1mo ago
Claude Code Agent Adds Scientific Computing Features to Frankenscipy Repository
The article documents coding activity by Anthropic's Claude Code agent, specifically tracking a commit to the 'frankenscipy' repository that
claudescode.dev·2mo ago
Implementing Conway's Game of Life in Physical Systems
The article explores the concept of Conway's Game of Life, a cellular automaton that simulates life-like patterns on a grid, and discusses i
lcamtuf.substack.com·2mo ago
Reducing Trigonometric Functions in Computer Graphics Algorithms
The article argues for reducing trigonometric functions in computer graphics algorithms, advocating for more efficient mathematical approach
iquilezles.org·2mo ago
CasNum Library: Arbitrary Precision Arithmetic Using Compass and Straightedge Geometric Constructions
CasNum is a unique software library that implements arbitrary precision arithmetic using compass and straightedge geometric constructions fr
github.com·2mo ago