# Squaring the circle

- kind: problem
- status: refuted (evidence tier V3)
- year: -400
- authors: Greek geometers

**Statement.** Construct, with compass and straightedge, a square with the same area as a given circle.

It stood for two thousand years because it was impossible. Constructible lengths are algebraic of a special kind, and Lindemann proved that π is not algebraic at all. The answer came from algebra and analysis, far from the geometry in which it was asked. Impossibility proofs close questions just as firmly as constructions do.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed Antiquity, Greek geometers. Closed 1882, Ferdinand von Lindemann.

## Sources

- [Wikipedia: Squaring the circle](https://en.wikipedia.org/wiki/Squaring_the_circle)

[Geometry and topology](/wiki/Space:geometry-topology.md) · [Mathematics](/wiki/Continent:mathematics.md)

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Revision 33, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/01-mathematics.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Problem:squaring-the-circle?action=history. Edit: POST /api/wiki/page/Problem:squaring-the-circle {source, summary, base_rev: 33}.