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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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July 19, 2026
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July 13, 2026 Scientists at Nanyang Technological University in Singapore have discovered a surprisingly simple way to create exotic light structures called optical skyrmions using a 200-year-old optical effect known as the Poisson spot. Instead of relying on ...
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July 11, 2026 Researchers have achieved a major milestone by creating a long-sought two-dimensional quantum material and confirming its unusual conducting edge states. The ability to control these states through ...
July 11, 2026 Ultra-fine bubbles may offer a cleaner way to perfect inkjet printing for next-generation electronics. By simply changing the number of bubbles in each droplet, researchers were able to dramatically reshape the final printed pattern without leaving ...
July 8, 2026 Scientists have created a silicon chip that can write dozens of DNA sequences simultaneously using electricity and water-based enzymes, offering a cleaner alternative to conventional DNA manufacturing. The breakthrough could eventually support ...
July 8, 2026 Water’s odd behavior becomes even more dramatic when it is supercooled, but scientists have struggled to compare the many different ways of describing its microscopic structure. Researchers at the University of Osaka used an AI model trained on ...
July 8, 2026 Researchers have created an AI-based simulation that makes it much faster to model how neutron star mergers produce many of the universe's heaviest elements. The new tool could improve predictions of these powerful explosions while helping ...
July 7, 2026 A newly developed material can control and "program" heat, allowing it to direct thermal radiation, switch modes, and remember its settings without continuous power. The innovation could lead to smarter infrared sensors, better energy technologies, ...
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July 13, 2026 Physicists from Heinrich Heine University Düsseldorf (HHU) have examined a fundamental property of quantum mechanics in collaboration with the German Aerospace Center (DLR). In the scientific ...
July 7, 2026 Scientists have combined machine learning with quantum physics to discover two new superconductors and create a much faster way to search for many more. The technique could bring researchers ...
July 5, 2026 Quantum mechanics has journeyed from a strange and controversial idea to the foundation of some of humanity’s most advanced technologies. Now researchers are pushing its boundaries even further, ...
July 2, 2026 A major breakthrough in quantum technology has turned magnons, tiny magnetic waves once considered too short-lived for practical use, into promising carriers of quantum information. Researchers ...
July 1, 2026 A new quantum device can generate precisely controlled bursts of sound-like particles, or phonons, by forcing electrons through an ultra-thin crystal at extremely low temperatures. The surprising ...
June 30, 2026 A strange gamma-ray glow at the center of the Milky Way has long sparked debate over whether it comes from hidden neutron stars or elusive dark matter. By applying machine learning to more than a ...
June 29, 2026 A new AI-powered framework could transform how astronomers measure the expansion of the Universe. By analyzing images of Type Ia supernovae and modeling their environments in unprecedented detail, ...
June 20, 2026 Researchers found that twisting layered sheets of hexagonal boron nitride can dramatically change the light produced by quantum emitters embedded within the material. The technique offers an ...
June 19, 2026 Researchers developed a Wordle-solving strategy that succeeds 99% of the time by focusing on information gain rather than likely answers. The method uses Shannon entropy to identify guesses that ...
June 18, 2026 The race to build data centers in space is gaining momentum as AI drives unprecedented demand for computing power. Orbital facilities could tap into abundant solar energy and avoid many of the ...