Tag

Geometry

All articles tagged with #geometry

technology11 days ago•6 min saved

ChatGPT-5.2 Demonstrates Original Geometry Proof via 'Vibe-Proving'

A study from VUB reports that ChatGPT-5.2 can autonomously generate an original mathematical proof, solving a 2024 geometry conjecture. The proof emerged through seven chat sessions and four evolving argument drafts, with human researchers verifying final steps. The work introduces the term vibe-proving as a new AI reasoning approach and suggests AI can accelerate theoretical discovery while maintaining essential human oversight.

via scitechdaily.com|

#ai #chatgpt #geometry

archaeology18 days ago•5 min saved

Ancient ostrich eggshell engravings hint at humanity's first geometric grammar

Analysis of 112 engraved ostrich eggshell fragments from Diepkloof, Klipdrift, Apollo 11 and Namibia shows that over 80% display coherent spatial organization—grids, parallel lines and right angles—indicating intentional, systematic thought and suggesting an embryonic visual grammar marking early geometric and abstract thinking about 60,000 years ago.

via The Jerusalem Post|

#abstract-thought #africa #archaeology

science20 days ago•4 min saved

60,000-Year-Old Ostrich Eggshell Art Reveals Early Human Geometry

A study of 112 engraved ostrich eggshell fragments from southern Africa, dating about 60,000 years ago, shows coherent geometric patterns—grids, right angles, and repeating lines—indicating early Homo sapiens used abstract, visuo-spatial planning and developed a geometric grammar that underpins later symbolic thought.

via ScienceAlert|

#africa #archaeology #cognition

science1 month ago•6 min saved

Chimpanzee Crystal Craze Hints at Ancient Geometry

Researchers at a Spanish chimpanzee sanctuary handed quartz crystals to two groups of rescued chimps; the apes showed strong interest—dragging, examining, and even trading bananas or yogurt to recover the largest crystal—while others sorted crystals by type. García-Ruiz suggests chimps’ attraction to crystals may stem from their Euclidean geometry, hinting at ancient cognitive roots shared with humans.

via Boing Boing|

#animal-cognition #chimpanzees #crystals

science1 month ago•3 min saved

Ancient Ostrich Egg Engravings Point to Early Geometric Thinking

A PLOS One study of 112 ostrich eggshell fragments from three southern African sites dating over 60,000 years finds engravings with coherent geometric organization—parallel lines, grids, rotations and repetitions—suggesting ancient humans may have had abstract geometric thinking, though the meaning of the markings remains uncertain.

via Gizmodo|

#cognitive-archaeology #geometry #ostrich-eggshells

science1 month ago•6 min saved

Geometric fix completes Schrödinger’s color theory after a century

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.

via ScienceDaily|

#color-perception #geometry #neutral-axis

science2 months ago•1 min saved

Infinite Pancake Scrutiny: Extending the Lazy Caterer’s Puzzle with an Endless Knife

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.

via The New York Times|

#combinatorics #geometry #infinity

science3 months ago•8 min saved

The Manifold: Revolutionizing Mathematical Space Concepts

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.

via WIRED|

#geometry #manifolds #mathematics

reviews3 months ago•7 min saved

Yeti LTe Review: A Magical Experience

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.

via Pinkbike|

#emtb #geometry #performance

science5 months ago•2 min saved

Is the Higgs boson essential for mass creation?

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.

via Phys.org|

#extra-dimensions #geometry #higgs-boson

science5 months ago•4 min saved

Centuries-Old Royal Bet Geometry Problem Finally Solved

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.

via Good News Network|

#geometry #mathematics #noperthedron

science5 months ago•7 min saved

Shark Data Reveals Animals Grow Geometrically

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.

via Quanta Magazine|

#biological-constraints #evolution #geometry

science5 months ago•5 min saved

Mathematician Solves 50-Year-Old Mobius Strip Puzzle

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.

via ZME Science|

#geometry #mathematics #mobius-strip

science6 months ago•8 min saved

Origami Techniques Unravel Key Physics Mystery

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.

via Quanta Magazine|

#amplituhedron #geometry #mathematics

sports6 months ago•8 min saved

Mike Kazimer's Specialized Chisel FS Staff Ride

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.

via Pinkbike|

#geometry #lightweight #specialized-chisel-fs