Abstract: A simple, fast method generates various visually appealing spiral patterns. The method is based on the concept that spiral patterns comprise a symmetry group of tilings. It employs invariant ...

(exact-integer-sqrt k) returns floor of square root and the "remainder" More documentation in docstrings.

Over 8,000 years ago, early farming communities in northern Mesopotamia were already thinking mathematically—long before numbers were written down. By closely studying Halafian pottery, researchers ...

HYDERABAD: Scientists use mathematical models to explain why mosquito populations surge after rain, how species disappear without warning or why ecosystems recover when a missing element is restored.

Abstract: This third installment of the Beautiful Math articles considers the visualization of aesthetic patterns with hyperbolic-triangle-group symmetries. A flexible form of invariant mappings ...

It began as a strange discovery buried in chaos theory — a mathematical pattern that seemed to predict real events before they happened. From climate shifts to stock market crashes, scientists now ...

Royalty-free licenses let you pay once to use copyrighted images and video clips in personal and commercial projects on an ongoing basis without requiring additional payments each time you use that ...

Summary: A new study shows how math helps explain why babies nap erratically, teens stay up late, and older adults wake earlier. Researchers expanded the classic two-process sleep model by adding the ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...