Question
In 2023, two New Orleans high schoolers found a new way to do this task by using the law of sines. For 10 points each:
[10e] Identify this task of relating the length of the adjacent and opposite sides of right triangles to their hypotenuse. Albert Einstein and James Garfield are among the many people to have come up with ways of doing this task.
ANSWER: proving the Pythagorean theorem [or proving Pythagoras’ theorem; accept finding a proof of Pythagorean theorem]
[10m] This statement, which gives the product of the Legendre symbols of p over q times q over p, was most famously proved by Gauss, who found at least eight different proofs of this “golden theorem.”
ANSWER: law of quadratic reciprocity
[10h] Many proofs exist for Szemerédi’s theorem, which states that some subsets of positive integers contain arbitrarily long examples of these constructs. The Green-Tao theorem states that sequences of prime numbers contain arbitrarily long one of these.
ANSWER: arithmetic progressions [or arithmetic sequences]
<Leo Law, Other Science>
Summary
| 2023 Penn Bowl @ Waterloo | 10/28/2023 | Y | 4 | 22.50 | 100% | 75% | 50% |
| 2023 Penn Bowl @ FSU | 10/28/2023 | Y | 2 | 5.00 | 50% | 0% | 0% |
| 2023 Penn Bowl (Harvard) | 10/21/2023 | Y | 3 | 16.67 | 100% | 33% | 33% |
| 2023 Penn Bowl (Mainsite) | 10/21/2023 | Y | 7 | 15.71 | 86% | 43% | 29% |
| 2023 Penn Bowl (South Central) | 10/28/2023 | Y | 3 | 6.67 | 67% | 0% | 0% |
| 2023 Penn Bowl (UK) | 10/28/2023 | Y | 5 | 20.00 | 100% | 60% | 40% |
| 2023 Penn Bowl @ UNC | 10/28/2023 | Y | 3 | 6.67 | 33% | 0% | 33% |