Packet D: Bonus 20

Answer the following about the intersection between algebraic topology and breakfast foods, for 10 points each.
[10e] A common joke holds that a coffee mug is the same as this surface since they are homeomorphic. Donuts and bagels are shaped like this surface.
ANSWER: torus [or tori; accept S-one cross S-one]
[10h] This type of map is often visualized as flattening a stack of pancakes, the union of which is the preimage of a neighborhood in the base. Up to equivalence, a simply connected space has only one of these maps.
ANSWER: covering maps [or covers; accept covering projections or covering spaces; accept universal covers]
[10m] The Borsuk–Ulam theorem gives an algebraic topology proof of the ham sandwich theorem, which concerns one of these subspaces that “cuts” n objects in half. These affine subspaces have dimension one less than the full space and generalize a two-dimensional analog.
ANSWER: hyperplanes [prompt on planes]
<TM, Other Science> | Packet-D_CWRU-A_Iowa_Toronto-A_WashU-A

HeardPPBE %M %H %
1120.91100%91%18%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Cambridge ANYU C10101030EHM
Chicago AWashU B1001020EM
Chicago CChicago B1001020EM
Georgia Tech CGeorgia Tech D1001020EM
Harvard ADartmouth A1001020EM
Haverford ACornell B1001020EM
MIT AHarvard B1001020EM
MissouriChicago D100010E
Oxford ACambridge B1001020EM
UC Berkeley AUCSD10101030EHM
UCLAClaremont B1001020EM

Summary

TournamentEditionMatchHeardPPBE %M %H %
California2025-02-01✓225.00100%100%50%
Midwest2025-02-01✓316.67100%67%0%
Northeast2025-02-01✓220.00100%100%0%
Southeast2025-02-01✓120.00100%100%0%
UK2025-02-01✓225.00100%100%50%
Upper Mid-Atlantic2025-02-01✓120.00100%100%0%