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  "body": "\n## Summary\n\nA curve of constant width is the boundary of a plane [[convex body|437FSG3419]] with this property.\nEvery two parallel supporting lines of the body are at the same distance, called the width.\nThe circle is the simplest example, but there are many others, such as the Reuleaux triangle.\nCurves of constant width are a classical source of extremal problems in plane convex geometry.\nAll of them with a given width have the same length, but their areas differ.\n\n## Explanations\n\n### L1 human\n\nPut the shape between two parallel rulers that touch it on opposite sides.\nIf the distance between the rulers is the same however the shape is turned, the boundary of the shape is a curve of constant width.\nA coin with this property could roll smoothly between two boards, which is why such shapes can serve as rollers.\nA circle of radius $1$ has constant width $2$.\nA square does not: its width is $1$ across the sides and $\\sqrt{2}$ across the corners.\n",
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