Geometry
Articles tagged with Geometry
Lessons from Finland: FAU researcher reveals gaps in special education math instruction
A study of Finnish special needs and special class teachers found that data processing, statistics, and probability are under-taught areas, mirroring trends in the US. The researchers emphasize the need for stronger teacher preparation, ongoing professional development, and support to ensure effective strategies are used consistently.
From teeth to thorns: Coincidences shape the universal form of nature’s pointed tips
Research finds that the rounded shape of natural tips is due to random mechanical wear, not just evolutionary optimization. The experiment with pencils demonstrates how collisions can lead to a universal parabolic shape across different structures.
Geometry shapes life
Researchers at ISTA have found that the zebrafish embryo's geometry is essential for its development, guiding cell division and gene activation. The study's findings could improve IVF embryo assessments by understanding how the embryo interprets its geometry.
How viruses build perfectly symmetrical protective shells
Research by University of California, Riverside physicist Roya Zandi reveals how viruses form highly symmetrical icosahedral structures around their genomes through a process of self-correction, driven by protein elasticity. This study could lead to designing synthetic nanocontainers for medical and biotech uses.
Mathematics: Manuel Krannich receives ERC starting grant
Researcher Manuel Krannich has been awarded a five-year ERC starting grant to investigate the connections between symmetries of high-dimensional manifolds and laws of algebra. His project, 'Manifolds and Functor Calculus' (MaFC), combines manifold theory with higher-level algebra.
Mathematical proof provides new perspectives on the effects of blending
Researchers from OIST and universities provided a new proof for the BBL inequality using heat and diffusion equations, taking an unconventional approach. The study offers fresh insights on the concept, which has vast applications across many fields, including computer science, medical imaging, and resource distribution.
Peeking inside AI brains: Machines learn like us
A new study in Nature Communications found that AI models exhibit a geometric property called convexity, which helps humans form and share concepts. Convexity is also linked to the performance of AI models on specific tasks.
Integrating hard silicon for high-performance soft electronics via geometry engineering
Researchers review how geometry engineering improves c-Si's mechanical properties, allowing for high-performance soft electronics. Silicon nanowires with enhanced flexibility, superior mechanical properties, and excellent electrical performance are poised to transform the landscape of flexible electronics.
Discovery of novel octupole topological insulator in brillouin three-dimensional real projective space
Researchers unveiled a new class of topological insulator with an octupole phase protected by a three-dimensional momentum-space nonsymmorphic symmetry group. The discovery broadens the understanding of higher-order topological phases and provides new insights into band theory in the Brillouin real projective space.
Scientists create optical device that mimics black holes
Researchers have designed an optical device that functions as an optical black hole or white hole, behaving like a cosmic object that either swallows or repels light. This device relies on coherent perfect absorption of light waves and offers new possibilities for manipulating light-matter interactions.
Frustration incorporated: Revealing a natural strategy for making 'superior' materials
The study reveals that frustrated assemblies can lead to materials with desirable properties like strength and toughness. By understanding the relationship between structure and property, researchers aim to design advanced materials for medical devices and sustainable construction.
BESSY II: Magnetic ‘microflowers’ enhance local magnetic fields
Researchers have developed a nickel-iron alloy metamaterial that can concentrate and locally enhance magnetic fields. By controlling the geometry and number of 'petals', the effect can be increased, making it suitable for improving the sensitivity of magnetic sensors.
From order to chaos: Understanding the principles behind collective motion in bacteria
Researchers discovered how bacterial swarms transition from organized movement to chaotic flow as confinement radius increases. The study reveals intermediate states between order and turbulence through large-scale experiments, computer modeling, and mathematical analysis. These findings provide insights into the universal properties o...
Researchers successfully prove the solution to Dudeney’s 120-year-old dissection puzzle
A team of researchers from Japan Advanced Institute of Science and Technology proved that Dudeney's original solution to the famous dissection problem is the optimal solution. They used a novel approach, including matching diagrams, to show that no dissection between an equilateral triangle and a square can be achieved with three or fe...
Efficient exploration unleashed: The BIG framework for autonomous navigation
The BIG framework reduces computational demands by at least 20% while boosting efficiency in long-range exploration and navigation tasks. It optimizes exploration with geometric parameters, guides agents to target locations, and creates experience maps through spatio-temporal clustering.
Eddy-mean flow energy exchange depends on three variables
Researchers found that the eddy-mean kinetic energy exchange term is separated into three parts: one associated with cross-stream variation, one with along-stream variation, and one with mean flow direction. This new framework describes eddy-mean energy exchange without accounting for forces or physical properties.
The molecular einstein
Researchers at Swiss Federal Laboratories for Materials Science and Technology (EMPA) solve the molecular einstein problem, revealing a unique arrangement of chiral molecules on silver surfaces. The discovery sheds light on the properties of these molecules and their potential applications in physics.
When art imitates life's mathematics: Fractals and how we perceive trees
Using fractal math, researchers found that artists' preservation of a tree's branch diameter scaling exponent enables viewers to easily recognize trees, even without other distinguishing features. This universal factor applies across styles and cultures, linking artistic beauty with mathematical complexity.
The hidden mechanics of earthquake ignition
Researchers unveil groundbreaking insights into earthquake nucleation, showing that slow, aseismic motion is necessary and triggers seismic rupture. The study's findings also emphasize the critical role of geometric transitions in controlling nucleation dynamics.
First evidence in the Levant (and among the first in the world) of communal worship in caves and the development of religious rituals
A 35,000-year-old ritual complex in the Manot Cave offers insight into the spiritual practices of Paleolithic hunter-gatherer groups. The discovery reveals evidence of human-made engravings, ash remains from fire, and acoustic tests that suggest a unique auditory experience for communal activities.
Variability in when and how cells divide promotes healthy development in embryos
Researchers have found that variability in when and how cells divide during embryo development leads to more optimal arrangements of cells, promoting robust tissue formation. This study challenges traditional views on the role of cell division variability in embryonic development.
Big algebras: A dictionary of abstract math
Researchers have developed big algebras, a new mathematical tool that connects abstract algebra and geometry, enabling unprecedented insights into symmetry groups. This breakthrough has the potential to strengthen the connection between quantum physics and number theory.
Breakthrough design strategy revolutionizes discovery of metal-organic frameworks
Researchers developed a novel strategy for designing MOFs, merging bottom-up and top-down approaches to explore structures based on metal clusters. The Up-Down Approach enables the creation of novel materials with tailored properties, including high chemical stability and diverse chemical properties.
Radiative cooling technology with adaptive temperature management for enhanced energy efficiency
Researchers developed a new type of temperature-adaptive radiative cooling device with improved performance, reducing solar absorptance by 7.54% and increasing emissivity by 13.3%. This advancement holds promise for optimizing energy use and advancing sustainable thermal management solutions.
Breaking ground: Could geometry offer a new explanation for why earthquakes happen?
Researchers at Brown University discovered that the alignment of faults in rock formations plays a crucial role in determining where and when earthquakes occur. The study found that complex geometry beneath the surface contributes to stronger ground motions and more frequent earthquakes.
Researchers developed a new metamaterial that can detect the order of external operations
A novel mechanical metamaterial, 'Chaco,' exhibits history-dependent behavior, allowing it to remember the sequence of actions performed on it. This property enables potential applications in memory storage and robotics.
Ice-ray patterns: A rediscovery of past design for the future
A study discovers that traditional Chinese ice-ray lattice designs can provide unique stiffness and strength under asymmetric loads, offering an alternative to conventional gridshells. The research also explores the potential of integrating complex geometry into facade design and micro-scale material design.
Synthetic dimension dynamics to manipulate light
Scientists have developed a new method to manipulate light using synthetic dimension dynamics, enabling precise control over light propagation and confinement. This breakthrough has significant implications for applications such as mode lasing, quantum optics, and data transmission.
Opening design using bayesian optimization
This work proposes a method to design openings as natural light sources, utilizing photorealistic rendering, designer preferences, and Bayesian optimization. The approach aims to maximize natural light usage and minimize artificial lighting requirements during the day.
Innovative design marks groundbreaking progress in terahertz technology
Researchers developed a carbon-based tunable metasurface absorber with an ultrawide, tunable bandwidth in the THz range. The absorber boasts high absorption efficiency and insensitivity to polarization angles, paving the way for advanced technological applications.
A new mathematical language for biological networks
Researchers developed a new mathematical framework to analyze genetic interactions and identified key regulators in entire biological networks. The approach, which combines geometry and statistics, reveals how individual genes and species influence network dynamics.
New insights into broken symmetries
The study reveals a way to extend the Lorentz reciprocal theorem to systems with broken symmetries, enabling analytical calculations for fluids and self-propelled microorganisms. This generalization opens up new avenues for exploring systems with odd viscosities.
Machine learning used to probe the building blocks of shapes
Researchers from Imperial College London and the University of Nottingham used machine learning to identify 'atomic shapes' that form basic pieces of geometry in higher dimensions. The findings reveal unexpected patterns in these shapes and demonstrate the potential for machine learning to accelerate mathematical discoveries.
Clever lapwings use cover to hide in plain sight
Research shows that lapwings can hide their eggs by using small variations in the terrain, making them invisible to ground predators. The study found that habitat geometry rather than visual acuity limits the visibility of a ground-nesting bird's clutch to terrestrial predators.
Contours that kill: Geometry influences prey capture in carnivorous pitcher plants
Researchers at the University of Oxford's Botanic Garden and Mathematical Institute have found that the shape, size, and geometry of pitcher plants determines the type of prey they trap. The study showed that large, flared rims are suited to capturing walking insects such as ants.
Study observes sudden acceleration of flow, generates new boundary layer
Aerodynamic researchers at University of Illinois create wind tunnel experiment to study internal boundary layers and their impact on flow behavior. They identify a new internal boundary layer that changes the flow's behavior, providing insights into aerodynamics physics and improving turbulence models for complex designs.
Aston University researcher turns one of the basic rules of construction upside down
An Aston University researcher has overturned a fundamental principle in construction by showing that a hanging chain and an arch are incompatible mechanical systems. This finding highlights the limitations of traditional analogies used to design and assess curved structures.
New study reveals design clues for silver-based superatomic molecules
Researchers from Japan have synthesized two di-superatomic molecules composed of Ag and evaluated the factors involved in their formation. The study found that a twist between the two icosahedral structures stabilizes the nanocluster by shortening the distance between them. Additionally, the presence of Pd and Pt central atoms was foun...
Creating a blueprint for optimized ear tubes and other implantable fluid-transporting devices
Researchers have developed a new ear tube design that combines liquid-infused materials with optimized geometry to improve treatment outcomes for patients with ear infections. The design enables better performance and reduces complications such as impaired hearing and scarring of the eardrum.
Discovery of crucial clue to accelerate development of carbon-neutral porous materials
Researchers at Ulsan National Institute of Science and Technology (UNIST) have identified seven types of zirconium metal clusters found in MOFs and fourteen potential new metal building blocks. This discovery provides a crucial clue to accelerate the development of carbon-neutral porous materials.
Brandon Levin wins NSF CAREER Award
Brandon Levin, an assistant professor of mathematics at Rice University, has won a prestigious National Science Foundation CAREER Award to pursue his research on major unsolved problems in number theory. He aims to build theoretical bridges between arithmetic world and representation theory.
Metasurface enters laser fiber cavity for spatiotemporal mode control
Direct incorporation of a metasurface in a laser cavity enables spatiotemporally modulated laser pulses. Giant nonlinear saturable absorption allows pulsed laser generation via Q-switching process.
The geometry of conflict
Conflicts between divergent goals can continue indefinitely through evolutionary time, causing devastating damage to complex organisms and social structures. Modular design is a crucial enabler of complex adaptation and transformative changes in social organisation.
OCTOPUS, an optimized device for growing mini-organs in a dish
Engineers create OCTOPUS device to grow organs-in-a-dish, achieving higher levels of maturity than traditional methods. The device allows for more mature organs with complex cell relationships, providing valuable tools for studying human organ development.
Need a hand? This robotic hand can help you pick your food items and plate your dish
Researchers from Singapore University of Technology and Design developed a new reconfigurable workspace soft robotic gripper that can pick and place a wide range of consumer items. The RWS gripper's adaptive capabilities make it particularly useful in logistics and food industries where robotic automation is crucial.
The brain’s ability to perceive space expands like the universe
Researchers found that neurons in the hippocampus represent space in a nonlinear hyperbolic geometry that grows outward exponentially with time spent exploring an environment. This discovery provides valuable methods for analyzing data on neurocognitive disorders involving learning and memory.
Think before you design your brand's logo: How marketers can capitalize on the power of perception to influence beliefs about brand performance
A new study found that structured visual design properties, such as symmetry and balance, reinforce claims about a brand's utilitarian benefits. In contrast, unstructured designs are associated with hedonic benefits. The research suggests marketers can use perception to influence beliefs about brand performance and consumer choice.
Playing all the angles: A high-contrast grating structure for direction-tunable lasing
Researchers developed a one-dimensional suspended high-contrast grating structure to enable directional lasing with high energy efficiency. The device can adjust the emission angle over a wide range, from -40° to +40°, making it suitable for solid-state LiDAR applications.
New findings on neuronal activities in the sensorimotor cortex
The study found conserved structures of neuronal activity in the sensorimotor cortex of freely moving rats, revealing a clear gradient for contralateral bias. This breakthrough helps understand brain control of movements under natural conditions and enables further development of neuroprosthetic devices.
A closer look at the dynamics of the p-Laplacian Allen–Cahn equation
A team of researchers from Korea investigated the dynamics of the p-Laplacian AC equation, finding that solutions maintain three criteria: phase separation, boundedness, and energy decay properties. They also identified an advantage of p-AC equation over classical Laplacian in adjusting interface sharpness.
High-throughput computational microscopy imaging
Researchers develop hybrid brightfield-darkfield transport of intensity approach, expanding accessible sample spatial frequencies and achieving 5-fold resolution increase. This method enables precise detection and quantitative analysis of subcellular features in large-scale cell studies.
These engineers drew inspiration from geometrical frustration
Engineers have created a new type of surface that can change its physical properties across different directions. By combining cells with adjustable shapes, the researchers can alter compressibility, flexibility and density. This technique has potential applications in medical devices, architecture and aerospace.
New potential from ‘one-pot-and-one-step’ polymer synthesis
Researchers at Hokkaido University have developed a one-pot-and-one-step synthesis procedure to create long and geometrically interlinked polymer molecules. This process can produce a wide range of advanced materials with applications in drug delivery, data storage, microelectronics, and nanolithography.
Inflammation adversely affects bone health, dietary intervention with prunes may counteract
A study found that higher levels of inflammatory markers are associated with lower trabecular bone scores, indicating poorer bone health. Dietary intervention with prunes may counteract inflammation's negative effects on bone health, preserving cortical bone density and strength in postmenopausal women.
3D printing drones work like bees to build and repair structures while flying
Researchers have developed a technology using flying robots that mimic the collective building methods of bees and wasps to construct and repair large structures. The Aerial Additive Manufacturing system consists of drones that work autonomously but are monitored by human controllers, adapting their techniques as needed.
Growing the perfect diamond: Simulations reveal interesting geometric patterns
Scientists have simulated the growth of ultra-thin polycrystalline diamond films with promising results. The two-dimensional simulations revealed interesting geometric structures and shed light on how to create robust materials. The research has implications for biomedical science, quantum devices, and other applications.
Australian mathematician reveals world’s oldest example of applied geometry
A 3700-year-old clay tablet, discovered in central Iraq, is the oldest known example of applied geometry. The UNSW scientist's analysis reveals a human story of land surveying and geometric understanding, with Pythagorean triples used to make accurate right angles.
Ventura fault could cause stronger shaking, new research finds
A recent study suggests the Ventura-Pitas Point fault in southern California has a 'ramp-flat geometry' with a flat section between two tilting sections, similar to a staircase. This structure would result in stronger shaking and more damage during an earthquake.
Three magnetic states for each hole
Researchers at Helmholtz-Zentrum Dresden-Rossendorf have developed cobalt grids that can be reliably programmed at room temperature. Three distinct magnetic states, denoted as G, C, and Q, were found around each hole in the grid. This discovery could lead to more efficient computing using spin-waves instead of electric current.