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One can combine two identical rectangles to form a larger rectangle which is a scaled version of the smaller pieces -- this is the case for two A5 pages combining to A4 page.

Are there any other polygons with that property? What if we allow disconnected "puzzles"?

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  • $\begingroup$ Another example is 45-45-90 triangle $\endgroup$
    – Radost
    Commented Dec 11, 2022 at 21:24
  • $\begingroup$ Depends on the exact definition of the property, I guess... You can combine 4 identical triangles to form a larger triangle similar to them all. Also works for 4 identical rectangles. $\endgroup$
    – colt_browning
    Commented Dec 11, 2022 at 21:24
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    $\begingroup$ Generally, see en.wikipedia.org/wiki/Rep-tile $\endgroup$
    – colt_browning
    Commented Dec 11, 2022 at 21:27
  • $\begingroup$ It appears these are other 'simple' ones mathoverflow.net/questions/184668/rep-tiles-of-order-2 $\endgroup$
    – Radost
    Commented Dec 13, 2022 at 18:22

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