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Euclidean geometry
Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been one of the most influential books in history, as much for its method as for its mathematical content. The method consists of assuming a small set of intuitively appealing axioms, and then proving many other propositions (theorems) from those axioms. Although many of Euclid's results had been stated by earlier Greek mathematicians, Euclid was the first to show how these propositions could be fitted together into a comprehensive deductive and logical system.
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Computers & Math News
September 20, 2026
Sep. 19, 2026 A single-celled organism can shrink to one-quarter of its length in milliseconds using a remarkable calcium-powered protein “fishnet.” Scientists hope its unusual machinery could inspire artificial muscles capable of moving far faster than ...
Sep. 19, 2026 Complex systems may work better when their parts are not perfectly alike. Northwestern physicists found that carefully balanced variation, or “disorder,” can make networks such as power grids, ecosystems, neurons, and materials more stable. Even ...
Sep. 18, 2026 A new Caltech device can redirect a beam of light in just 74 femtoseconds using another beam and a nanoscale silicon metasurface. The breakthrough could pave the way for dramatically faster photonic communications, computing, and sensing ...
Sep. 17, 2026 A pocket-sized, roughly $100 detector can reveal the invisible stream of cosmic particles constantly passing through Earth and even through our bodies. What began as a student physics project is now being used in major experiments, balloon missions, ...
Sep. 15, 2026 A mathematical shape famous for covering a surface without ever repeating has revealed an unexpected ability to twist light into unusual chiral patterns. The discovery could lead to new ways of controlling light, polarization, and advanced optical ...
Sep. 13, 2026 Scientists are combining an electron microscope with a quantum computer to squeeze far more information from each electron. The approach could reveal faint details with fewer electrons, helping protect fragile samples that conventional microscopy ...
Sep. 13, 2026 Researchers have experimentally demonstrated the optical Magnus effect for the first time, revealing that a tightly focused laser interacts most strongly with an atom slightly away from the beam’s center. The unexpected shift is similar to the ...
Sep. 13, 2026 AI analysis of 400,000 Reddit posts found that users of drugs such as Ozempic, Wegovy, Mounjaro, and Zepbound reported unexpected symptoms including menstrual changes, chills, hot flashes, and fatigue. Researchers cannot say the medications caused ...
Sep. 12, 2026 Researchers at Harvard have demonstrated a way to protect quantum information using microscopic sound waves. By continuously surrounding a diamond-based qubit with mechanical vibrations, they extended its coherence time by roughly threefold. The ...
Sep. 12, 2026 Researchers at Binghamton University have developed a mathematical strategy that can solve Wordle with a 99% success rate. Instead of simply guessing words packed with common letters or choosing the most likely answer, the method uses Shannon ...
Sep. 11, 2026 Scientists have created an ultra-small nanolaser that could eventually allow microchips to transmit information with light instead of electricity, potentially making computers faster while cutting energy use roughly in half. Thousands of the lasers ...
Sep. 11, 2026 Researchers have found a way to perform certain quantum operations more than 1,000 times faster, cutting thousands of repeated control cycles down to just one. The advance could reduce errors and bring reliable, fault-tolerant quantum computers ...
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Sep. 17, 2026 New supercomputer simulations suggest JWST’s puzzling Little Red Dots are rapidly growing black holes from the early Universe. Extreme radiation ...
Sep. 7, 2026 A more realistic quantum model has revealed evidence that strange, nearly immobile quasiparticles called fractons could exist in solid materials. Their inability to move freely could make them ...
Sep. 6, 2026 Scientists have devised a new way to switch magnetic computer memory while using far less energy than today's leading technologies. By mathematically ...
Sep. 6, 2026 Princeton researchers have tested an AI system that can monitor and control fusion plasma in milliseconds, reacting far faster than a human operator. In one experiment, it predicted a damaging ...
Sep. 4, 2026 Harvard researchers have transformed ordinary knitting into a platform for creating fabrics that can snap between different shapes and perform useful functions. Using elastic yarns and industrial ...
Sep. 4, 2026 MIT researchers have created bacterial “transistors” that can be wired together into living circuits capable of performing calculations and directing chemical signals. One day, these biological ...
Sep. 3, 2026 Scientists at Carnegie Mellon University have discovered an unexpected form of the Hall effect, overturning the long-held assumption that this electrical response only appears when a magnetic field ...
Aug. 31, 2026 Scientists have uncovered hidden complexity inside two ultrathin superconductors that seemed much simpler than they really are. Niobium diselenide and tantalum disulfide appeared to have a single ...
Aug. 31, 2026 Physicists have demonstrated a new way to entangle distant quantum bits without the constant measurements and active control normally required. The team created a “quantum bath,” a shared ...
Aug. 30, 2026 Physicists have mathematically captured a bizarre “spacetime crystal” that can either dissolve or collapse into a microscopic black hole after only a tiny change in energy. Their breakthrough ...