Missing Square Puzzle

This dynamic worksheet demonstrate the missing square puzzle, a paradoxical dissection discovered by an amateur mathematician named Paul Curry and popularized by Martin Gardner. The puzzle appears to show a right triangle which is cut into 4 pieces, which are rearranged to form an identical triangle with a square missing from it. Press the play button or drag the slider to see this dissection in action. See if you can figure out where the missing area goes. The first checkbox will hint at why it works, and the second checkbox will show you the missing area. You will notice that the missing square starts as a very long and skinny parallelogram, and it gradually transforms into a square as it moves into position. The area of the parallelogram remains exactly the same during the transition, although I did not find a simple way to demonstrate this visually. One can use Pick's Theorem to prove that the initial parallelogram has area 1.


David Radcliffe

Resource Type
dissection  exploration  geometry  logic  paradox  puzzle  triangle  triangles 
Target Group (Age)
11 – 19+
English (United States)
CC-BY-SA, GeoGebra Terms of Use
Derived Resources
Untitled Applet
Shared by Martin Flashman
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