4 ms·
You may be referring to the https://en.wikipedia.org/wiki/Staircase_paradox https://en.wikipedia.org/wiki/Staircase_paradox. As for how a shape can have the per
by roenxi 2y ago
You may be referring to the https://en.wikipedia.org/wiki/Staircase_paradox https://en.wikipedia.org/wiki/Staircase_paradox. As for how a shape can have the perimeter of a square and area of a triangle, it just can. As you've identified, it is easy to construct. It might be more interesting to ask what combinations of perimeter and area aren't possible.
- JKCalhoun 2y agoYes, this is what I "re-invented" (I didn't know until now that it had a name). I saw it later in a math book that I flipped through on a co-workers bookshelf (but they didn't name it there either). Also, very cool, followed your link and they mentioned a 3D analog of sorts: https://en.wikipedia.org/wiki/Schwarz_lantern https://en.wikipedia.org/wiki/Schwarz_lantern
- madcaptenor 2y agoYou can always add more perimeter, so you want a lower bound on the perimeter given the area. The isoperimetric inequality (https://en.wikipedia.org/wiki/Isoperimetric_inequality https://en.wikipedia.org/wiki/Isoperimetric_inequality) says that the smallest perimeter for a given area is that of a circle.