The Staircase Paradox
The staircase paradox: a staircase path from corner to corner always has length 7, no matter how many tiny steps. But in the limit it looks exactly like the diagonal, which has length 5. Perplexity climbs to infinity.
Transcript
[1] [A rectangle path] "Length: 7" "Perplexity: 0%"
[2] [Two steps] "Length: 7" "Perplexity: 5%"
[3] [Four steps] "Length: 7" "Perplexity: 18%"
[4] [Eight steps] "Length: 7" "Perplexity: 31%"
[5] [A straight diagonal] "Length: 5" "Perplexity: ∞%"
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2019-10-08-the-staircase-paradox/ (CC BY-NC 4.0)