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 ...

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries. Sphere packing might seem ...

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After cracking an unsolvable mathematics problem last year, AI is back to tackle geometry. Developed by Google DeepMind, a new algorithm, AlphaGeometry, can crush problems from past International ...

Dive into one of the most wicked geometry problems and see it explained step by step in a clear, intuitive way. This lesson breaks down the hidden structure, key insights, and clever reasoning that ...