Abstract: Accurate measurement of contact geometry is essential for robotic perception and manipulation, enabling object recognition, pose estimation, and precise in-hand control. Photometric ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

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Left, a 3-flower. Right, a 5-flower. Credit: Journal of Geometry and Physics, 10.1016/j.geomphys.2025.105458 Monash University researchers have extended Descartes’ Circle Theorem by finding a general ...

Mathematicians from New York University and the University of British Columbia have resolved a decades-old geometric problem, the Kakeya conjecture in 3D, which studies the shape left behind by a ...

Google's second generation of its AI mathematics system combines a language model with a symbolic engine to solve complex geometry problems better than International Mathematical Olympiad (IMO) gold ...

Abstract: In this paper, a new geometric snake model is proposed, based upon techniques of curve evolution and the utilization of gradient information and region information simultaneously. This model ...