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  "body": "\n## Summary\n\nA Pythagorean field is a [[field|04C5ZBG1WT]] in which every sum of two squares is again a square.\nThe name comes from the [[Pythagorean theorem|0VP3A1290K]].\nIn such a field, a right triangle with legs in the field has a hypotenuse in the field.\nReal closed fields and algebraically closed fields are Pythagorean, but $\\Q$ is not.\n\n## Explanations\n\n### L1 human\n\nIn the rational numbers, the right triangle with legs $1$ and $1$ has hypotenuse $\\sqrt 2$, which is not rational.\nA Pythagorean field is a field where this never happens: $\\sqrt{a^2 + b^2}$ always lies in the field.\nThe real numbers have this property, and so do the complex numbers.\n",
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