Liu Hui's Exhaustion Method

Author

Eric W. Weisstein
August 30, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Constants/LiuHuisExhaustionMethod.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/LiuHuisExhaustionMethod.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

Successive regular polygons inscribed in a circle illustrate Liu Hui's exhaustion procedure.

GraphicsRow[Table[Graphics[{{Directive[LightDarkSwitched[Darker[StandardGray, 0.55], Lighter[StandardGray, 0.55]], AbsoluteThickness[1], Dashed], Circle[]}, {FaceForm[None], EdgeForm[Directive[RGBColor[0.18, 0.42, 0.68], AbsoluteThickness[2]]], Polygon[CirclePoints[n]]}, Text[Style[StringJoin[ToString[n], "-gon"], FontFamily -> "Times", 13], {0, -1.25}]}, Axes -> False, PlotRangePadding -> {{Scaled[0.03], Scaled[0.03]}, {Scaled[0.18], Scaled[0.03]}}], {n, {6, 12, 24, 48}}]]