It is important to know properties of these shapes as questions will often involve knowing angle and length properties. For example, remember that each angle in an equilateral triangle is 60°. When a ...

It is important to know properties of these shapes as questions will often involve knowing angle and length properties. For example, remember that each angle in an equilateral triangle is 60°. When a ...

Google updated its search engine and Lens tool with new features to help you visualize and solve problems in more difficult subjects like geometry, physics, trigonometry and calculus. The update ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry. In the mid-1980s, the mathematician Jean ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...

Computers are working to solve an age-old geometry problem. Humans can’t “square the circle” by hand, which was proven in the 1800s. Computer solutions involve infinity, complexity, and some ...

The computer scientist Erik Demaine and his artist and computer scientist father, Martin Demaine, have been pushing the limits of paper folding for years. Their intricate origami sculptures are part ...

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A research team led by Maxim Kontsevich, a professor at the French Institute of Advanced Scientific Studies (IHES) and a 1998 Fields Medalist, has released a proof claiming to solve a long-standing pr ...