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A Magic Carpet Ride through Irrationality

Jeneva Clark <dr.jenevaclark@utk.edu>, University of Tennessee at Knoxville

Abstract:

Stanley Tennenbaum proved the irrationality of $\sqrt{2}$ using Carpets Theorem with square carpets, and others (myself, Conway, and Miller) have tried to generalize this proof by using triangular and pentagonal carpets. Although those families of proofs used simple tools, a.k.a. “spoons,” in this talk, I am going to try to “spoonify” this even more. I’ll prove the irrationality of $\sqrt{3}$ and $\sqrt{5}$ using only square-shaped carpets. This work extends the previous findings for grationality and opens up the possibility of more research into families of irrationality proofs.

Scheduled for: 2026-03-28 10:20 AM: Math... With a Spoon! Session #2 in Computing and Math 355

Status: Accepted

Collection: Math... With a Spoon!

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