Broken Bamboo Problem

Author

Eric W. Weisstein
August 30, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Problems/BrokenBambooProblem.nb.

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

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

Figure

The original and broken positions of a bamboo stalk form a 3-4-5 right triangle.

Module[{a = 3, b = 4, c = 5, cs, dx = 3., theta}, cs[t_] := {Cos[t], Sin[t]}; theta = ArcTan[b, a]; Graphics[{{RGBColor[0.18, 0.42, 0.68], Circle[{0, b}, 0.4, {theta - Pi/2, Pi/2}]}, {LightDarkSwitched[Darker[StandardGray, 0.55], Lighter[StandardGray, 0.55]], AbsoluteThickness[2], Line[0.3*{{0, 1}, {1, 1}, {1, 0}}], {Dashed, Line[{{0, b}, {0, b + c}}]}, Line[{{0, b}, {a, 0}}], Line[{{0, b}, {0, 0}, {a, 0}}]}, {RGBColor[0.72, 0.24, 0.18], PointSize[0.018], Point[{{0, 0}, {0, b}, {a, 0}}]}, Text[Style["c", FontFamily -> "Times", FontSlant -> Italic, 15], {0, b} + (c/2)*cs[Pi/2], (-dx)*cs[Pi]], Text[Style["b", FontFamily -> "Times", FontSlant -> Italic, 15], {0, b/2}, {dx, 0}], Text[Style["a", FontFamily -> "Times", FontSlant -> Italic, 15], {a/2, 0}, {0, dx}], Text[Style["c", FontFamily -> "Times", FontSlant -> Italic, 15], {a, b}/2, (-dx)*cs[theta]]}]]