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Topics in Non-Euclidean geometry [PDF]

, 1959
Thesis (M.A.)-- University of Wichita, College of Liberal Arts and Sciences, Dept. of MathematicsIt is difficult for a high school student to fully appreciate the study of Euclidean geometry without some notion of its relation to other geometries and ...
Carter, Martin
core   +2 more sources

Did Lobachevsky Have A Model Of His imaginary Geometry ? [PDF]

, 2010
The invention of non-Euclidean geometries is often seen through the optics of Hilbertian formal axiomatic method developed later in the 19th century. However such an anachronistic approach fails to provide a sound reading of Lobachevsky's geometrical ...
Rodin, Andrei
core  

Full‐Field Damage Monitoring in Architected Lattices Using In situ Electrical Impedance Tomography

Advanced Functional Materials, EarlyView.
In situ electrical impedance tomography (EIT) turns 3D‐printed, CNT‐infused architected lattices into full‐field damage‐imaging systems. Tunable Voronoi‐based geometries act as active sensing architectures, enabling conductivity maps to detect early‐stage damage and localise sequential ligament fracture before catastrophic failure.
Akash Deep, Andrea Samore, Alistair McEwan, Andrew McBride, Shanmugam Kumar   +4 more
wiley   +1 more source

Poisson's Ratio‐Driven Control of Myogenic Differentiation and Maturation in Auxetic Metamaterials under Dynamic Mechanical Stimulation

Advanced Functional Materials, EarlyView.
This study explored how innovative “auxetic” scaffolds, which expand when stretched, influence skeletal muscle development. Researchers cultured muscle cells on different scaffold designs and applied repeated stretching over 10 days. They found that scaffold geometry affected muscle cell differentiation and fiber formation.
Maria Kalogeropoulou, Prabhdeep Kaur, Monica Boffito, Pierpaolo Fucile, Gianluca Ciardelli, Lorenzo Moroni   +5 more
wiley   +1 more source

Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures

Machine Learning: Science and Technology
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space.
Mathilde Papillon, Sophia Sanborn, Johan Mathe, Louisa Cornelis, Abby Bertics, Domas Buracas, Hansen J Lillemark, Christian Shewmake, Fatih Dinc, Xavier Pennec, Nina Miolane   +10 more
doaj   +1 more source

An Overview of Existing Problems in Teaching the Science ”Fundamentals of Geometry”

International Journal of Social Sciences & Educational Studies
This paper goes into the challenges faced in the teaching of geometry, emphasizing its foundational principles. It investigates an alternate viewpoint by relating geometric principles to verses from the Holy Quran, implying that geometric conceptions ...
Safarov Tulqin Nazarovich, Abdullah Kurudirek   +1 more
doaj   +1 more source

Geometric Reinforcement Learning for Robotic Manipulation

IEEE Access, 2023
Reinforcement learning (RL) is a popular technique that allows an agent to learn by trial and error while interacting with a dynamic environment.
Naseem Alhousani, Matteo Saveriano, Ibrahim Sevinc, Talha Abdulkuddus, Hatice Kose, Fares J. Abu-Dakka   +5 more
doaj   +1 more source

Hydrogel‐Based Method for High‐Resolution Measurements of Contact Mechanics in Rapid Biological Adhesives: A Case Study in Cuttlefish Tentacle Strikes

Advanced Functional Materials, EarlyView.
Cuttlefish and squid can catch their prey within milliseconds using specialized tentacles and suckers. The physics of how the suckers can attach so quickly has remained a mystery given the technical challenges of studying them in vivo. In this publication, we develop a hydrogel that retains imprints of the suckers in order to estimate the forces they ...
Alexander Koehnsen, Mila F Krikke, Thomas E Kodger, Florian T Muijres, Guillermo J Amador   +4 more
wiley   +1 more source

On the non-generic Tzitzeica-Johnson's Configuration

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012
Working in the context of Hilbert's axiomatic system, we prove that the Tzitzeica-Johnson configuration has sense in neutral geometry. The elements of a Tzitzeica-Johnson configuration allow us to analyse the Euclidean or the non-Euclidean character of ...
Boskoff Wladimir G., Bărcănescu Şerban, Bobe Alexandru   +2 more
doaj   +1 more source

After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics

Journal for the History of Analytical Philosophy, 2018
The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry.
Janet Folina
doaj   +1 more source