Question
Doing this task numerically is referred to as doing it ‘by quadratures’. For 10 points each:
[10e] Name this task that can be performed numerically by the trapezium rule. It is equivalent to finding the area under a curve, and can be performed analytically using an anti-derivative.
ANSWER: definite integration
[10m] When this person’s namesake quadrature uses N points, it is exactly correct for polynomials of degree less than 2N. This mathematician proved the quadratic reciprocity theorem in his Disquisitiones Arithmeticae.
ANSWER: Carl Friedrich Gauss [accept Gaussian quadrature or Gauss’s law]
[10h] The simplest Gauss quadrature uses these polynomials, which are orthogonal in L2 on the interval from minus one to one. These polynomials are a subset of the ‘associated’ ones used to define spherical harmonics.
ANSWER: Legendre polynomials
Summary
| 2023 UMN COOT | 08/19/2023 | Y | 3 | 26.67 | 100% | 100% | 67% |
Data
| BHSU | Palestrina Sawayama | 10 | 10 | 0 | 20 |
| doubleplusnegfive | Our Job is Buzz | 10 | 10 | 10 | 30 |
| Jeff Weiner Fan Club | Weird Klaus Barbie | 10 | 10 | 10 | 30 |