Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

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 ...

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Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars concluding that only humans possess the foundations of this understanding.

The notion of a simple equation that you can use to generate a wide variety of geometric shapes is an immensely appealing one. Johan Gielis of Antwerp, Belgium, proposes one such formula in the March ...