All articles tagged with #geometry
A Los Alamos team mathematically defines the neutral axis and shows hue, saturation and lightness arise from the intrinsic geometry of color, fixing gaps in Schrödinger’s century‑old theory. By using shortest-paths in a non‑Riemannian color space, they correct hue shifts caused by brightness (Bezold–Brücke effect) and strengthen color modeling for visualization and data interpretation.
Mathematicians explore maximizing the number of pieces from slicing an infinitely large pancake with a straight knife, reworking the classic Lazy Caterer’s puzzle in an infinite-plane setting.
The article explains how the concept of manifolds, introduced by Bernhard Riemann, revolutionized the understanding of space in mathematics and physics, enabling the study of complex, higher-dimensional spaces and playing a crucial role in fields like general relativity, data analysis, and dynamical systems.
The Yeti LTe eMTB impresses with its exceptional six-bar suspension system, well-rounded geometry, and versatile adjustability, making it a top performer in descending and climbing capabilities despite its weight. It features a high-end build, a powerful Bosch motor, and an 800Wh battery, offering a confident and adaptable ride for various terrains. However, it comes at a premium price and some minor maintenance considerations.
A new study proposes that particle mass and fundamental forces could originate from the geometry of hidden extra dimensions, specifically through evolving seven-dimensional shapes called G₂-manifolds, potentially eliminating the need for the Higgs boson in explaining mass.
Two mathematicians have disproved a 300-year-old shape property, known as the Rupert property, by discovering a shape called the Noperthedron that cannot pass through itself regardless of tilting or drilling, challenging long-held assumptions in geometric topology.
Research on over 50 shark species shows they follow a two-thirds scaling law in surface area and volume, suggesting fundamental constraints on evolution related to heat exchange, metabolism, or development. This finding supports the idea that biological forms may be governed by geometric principles, with potential implications for understanding evolution and practical applications in medicine and veterinary science.
Mathematician Richard Schwartz has solved a 50-year-old puzzle about the minimal size of a developable Möbius strip, establishing that its aspect ratio must be greater than √3 (about 1.73) to avoid collapsing, and opening new questions about twisted strips and their properties.
A mathematician at Cornell has discovered a surprising connection between origami patterns and the amplituhedron, a geometric shape that encodes particle interaction probabilities, leading to a proof that the shape can be decomposed into simpler parts, bridging a gap between physics and paper folding mathematics.
Mike Kazimer reviews the Specialized Chisel FS, highlighting its modern geometry, lightweight aluminum frame, and versatile suspension setup, making it a fun and capable cross-country bike suitable for both racing and longer rides.
The date 9/16/25 is a rare mathematical coincidence, representing a Pythagorean triple (3, 4, 5) with all numbers being perfect squares, and the full year 2025 also being a perfect square, celebrated for its mathematical beauty and significance.
The 2025 Knolly Warden is a highly specialized, long, low, and slack downhill bike with unique geometry and suspension designed for aggressive terrain, particularly steep and rough trails. While it excels in traction and stability on challenging descents, its handling can be awkward, especially on climbs and technical sections, requiring careful setup and cockpit adjustments. Best suited for experienced riders targeting steep, technical terrain, the Warden offers impressive grip and composure but demands a tailored setup to perform optimally.
Researchers have developed the world's first monostable tetrahedron, a shape that always lands on the same side, which could improve lunar lander designs by enabling them to self-right after falling over, addressing a long-standing mathematical and engineering challenge.
Mathematician Jineon Baek from Yonsei University has potentially solved the long-standing 'moving sofa problem,' which seeks to determine the largest two-dimensional shape that can navigate an L-shaped corner in a corridor. Baek's 100-page proof confirms that the maximum area for such a sofa is 2.2195 units, aligning with Joseph Gerver's 1992 proposal. This solution, yet to be peer-reviewed, could be the definitive answer to this geometric puzzle, aiding in better furniture design decisions.
Mathematician Jineon Baek has potentially solved the "sofa problem," a 60-year-old mathematical puzzle about the largest sofa shape that can navigate a right-angled hallway corner. Baek's solution, posted on ArXiv, confirms that the maximum area for such a sofa is 2.2195 units, aligning with Joseph Gerver's 1992 lower bound. The proof, which involves complex geometry and movement calculations, awaits peer review to confirm its optimality.