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Research Paper#Geometry, Number Theory🔬 ResearchAnalyzed: Jan 3, 2026 16:40

Rational Angle Bisection and Incenters in Higher Dimensions

Published:Dec 31, 2025 06:14
1 min read
ArXiv

Analysis

This paper extends the classic rational angle bisection problem to higher dimensions and explores the rationality of incenters of simplices. It provides characterizations for when angle bisectors and incenters are rational, offering insights into geometric properties over fields. The generalization of the negative Pell's equation is a notable contribution.
Reference

“The paper provides a necessary and sufficient condition for the incenter of a given n-simplex with k-rational vertices to be k-rational.”

PermalinkArXiv
Research#machine learning📝 BlogAnalyzed: Dec 28, 2025 21:58

SmolML: A Machine Learning Library from Scratch in Python (No NumPy, No Dependencies)

Published:Dec 28, 2025 14:44
1 min read
r/learnmachinelearning

Analysis

This article introduces SmolML, a machine learning library created from scratch in Python without relying on external libraries like NumPy or scikit-learn. The project's primary goal is educational, aiming to help learners understand the underlying mechanisms of popular ML frameworks. The library includes core components such as autograd engines, N-dimensional arrays, various regression models, neural networks, decision trees, SVMs, clustering algorithms, scalers, optimizers, and loss/activation functions. The creator emphasizes the simplicity and readability of the code, making it easier to follow the implementation details. While acknowledging the inefficiency of pure Python, the project prioritizes educational value and provides detailed guides and tests for comparison with established frameworks.
Reference

“My goal was to help people learning ML understand what's actually happening under the hood of frameworks like PyTorch (though simplified).”

Permalinkr/learnmachinelearning