Pythagorean Theorem By Plane Tessellation

(Proof 27)

From [Frederickson, p. 35] we learn of a proof by tessellation different from that by Friedrichs. As other proofs that superimpose two plane tessellations, this, too, furnishes a whole 2-parameter family of various dissections of squares on the legs of a right triangle that combine into a square on its hypotenuse.

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(In the applet the skewed tessellation is draggable.)

Note that Perigal's dissection could be as easily obtained from the present proof as from that by Friedrichs. To see that just combine all squares of the same size in (natural) quartets to double their sides.


  1. G. N. Frederickson, Hinged Dissections: Swinging & Twisting, Cambridge University Press, 2002

Related material

Plane Tessellations

  • Dancing Squares or a Hinged Plane Tessellation
  • Dancing Rectangles Model Auxetic Behavior
  • A Hinged Realization of a Plane Tessellation
  • A Semi-regular Tessellation on Hinges A
  • A Semi-regular Tessellation on Hinges B
  • A Semi-regular Tessellation on Hinges C
  • Escher's Theorem
  • Napoleon Theorem by Plane Tessellation
  • Parallelogram Law: A Tessellation
  • Simple Quadrilaterals Tessellate the Plane
  • Pythagorean Theorem a la Friedrichs
  • Pythagorean Theorem By Hexagonal Tessellation
  • Hinged Greek Cross Tessellation
  • Pythagorean Theorem: A Variant of Proof by Tessellation
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