Tie a trefoil knot in a piece of string, seal the ends together, and try to wiggle it free without cutting. In three-dimensional space, the knot holds firm. Add a fourth spatial dimension, however, ...

Scientists have solved a long-standing geometry problem by discovering the first compact Bonnet torus pair after over a ...

For over 150 years, a rule of thumb dating back to the French mathematician Pierre Ossian Bonnet has been accepted in surface ...

Researchers at the University of Illinois have discovered a surprising mathematical connection between two areas of condensed-matter physics that were long considered separate. The electronic and ...

The conceptual architecture of black holes has undergone a radical transformation between 2024 and 2026, transitioning from the classical bottomless pits of general relativity to the intricate ...

Atomically thin semiconductors such as tungsten disulfide (WS2) are promising materials for future photonic technologies.

Abstract: High-security intelligent perception systems increasingly rely on heterogeneous sensor fusion, where complementary data from cameras, radars, and LiDARs can significantly enhance multimodal ...

Changing light's polarization can reverse the structure of a patterned light field, opening a new way to control geometry and information in optics. (Nanowerk Spotlight) Light can be bent, focused, or ...

Learn the simple science behind projecting 3D spheres onto 2D surfaces and how geometry makes this transformation possible. Mother gorilla proudly presents her newborn at zoo Analysis: Russia’s ...

Physicists recently mapped the hidden shape that underlies the quantum behaviors of a crystal, using a new method that’s expected to become ubiquitous. Famously, at the quantum scale, particles can be ...

Abstract: In this article, we present two fast and interpretable decomposition methods for 2D homography, which are named Similarity-Kernel-Similarity (SKS) and Affine-Core-Affine (ACA) ...