Bonus
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>
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 1 | 11 | 20.91 | 100% | 91% | 18% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|
Summary
| Tournament | Edition | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| California | 2025-02-01 | 2 | 25.00 | 100% | 100% | 50% |
| Midwest | 2025-02-01 | 3 | 16.67 | 100% | 67% | 0% |
| Northeast | 2025-02-01 | 2 | 20.00 | 100% | 100% | 0% |
| Southeast | 2025-02-01 | 1 | 20.00 | 100% | 100% | 0% |
| UK | 2025-02-01 | 2 | 25.00 | 100% | 100% | 50% |
| Upper Mid-Atlantic | 2025-02-01 | 1 | 20.00 | 100% | 100% | 0% |