• Buffon's Needle Problem for the Taxicab Geometry: or Why $\pi = 4$

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    • Keywords


      Geometric probability, taxicab geometry, Buffon's needle problem.

    • Abstract


      We revisit the famous Buffon's needle problem, one of the first problems in geometric probability. Only now, the plane upon which we toss our needles is not Euclidean, as it was for Buffon, but instead has the simple but fascinating taxicab geometry. We find that we get the exact same solution as Buffon did, except that now $\pi = 4$! As a bonus, we get nice introductions to basic probability theory and geometry.

    • Author Affiliations


      Alan McRae1

      1. 2963 Brownsburg Tpke, Raphine VA 24472 USA
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