Celebrate the simple mathematical sequence that is hidden in everything from sunflower spirals to Da Vinci's paintings Discover why the sequence is considered nature's secret code, governing ...

If you buy something using links in our stories, we may earn a commission. This helps support our journalism. Learn more. While I understand the value of standardizing procedures and setting ...

The stable or robust transfer of matter, information, or energy, from one point in space to another is a crucial scientific and technological challenge. In 1983, Nobel laureate D. J. Thouless proposed ...

A variation of a puzzle called the “pick-up sticks problem” asks the following question: If I have some number of sticks with random lengths between 0 and 1, what are the chances that no three of ...

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Pushing the limits of structured light, applied physicists report a new type of optical vortex beam that not only twists as it travels but also changes in different parts at different rates to create ...

Pine cones. Stock-market quotations. Sunflowers. Classical architecture. Reproduction of bees. Roman poetry. What do they have in common? In one way or another, these and many more creations of nature ...

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Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. This work investigates the integration of Fibonacci patterns and Golden Ratio ...