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Ancient Circle Problem Solved After 1,800 Years

9/27/2025

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Summary

Story summary

In the third century BCE, Apollonius of Perga posed a problem about circles tangent to three given circles at one point.
It took 1,800 years to prove the answer is eight.
Ancient Greeks favored such questions, shaping the field of enumerative geometry.
Recent work delivers solutions to the original problems and variations in exotic number systems, attracting new talent.

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Story summary

In the third century BCE, Apollonius of Perga posed a problem about circles tangent to three given circles at one point.
It took 1,800 years to prove the answer is eight.
Ancient Greeks favored such questions, shaping the field of enumerative geometry.
Recent work delivers solutions to the original problems and variations in exotic number systems, attracting new talent.