Question

Joseph Liouville (“zhoh-ZEFF l’yoo-VEEL”) proved a theorem that classifies all of these functions in a Euclidean (“yoo-CLID-ee-in”) space of degree 3 or higher. For 10 points each:
[10h] Name these functions that exist between any simply connected open subset of the complex plane and the unit disk. These functions have the property of constancy of dilation at every point in their domain.
ANSWER: conformal maps [or conformal mappings or conformal transformations; prompt on biholomorphic maps or holomorphic maps or bijective holomorphic maps by asking “a holomorphic function that is a bijection is what other type of function?”] (The sentence about the complex plane and the unit disk refers to the Riemann mapping theorem.)
[10m] Liouville’s theorem states that conformal maps are all higher dimensional analogues of transformations named for this mathematician. A number theoretic function named for this mathematician outputs one on square-free positive integers with an even number of prime factors.
ANSWER: August Ferdinand Möbius [accept Möbius function]
[10e] Conformal maps preserve these values between curves. Polar coordinates specify points using a distance and one of these values.
ANSWER: angles

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Data

TeamOpponentPart 1Part 2Part 3Total
Chicago BUC Berkeley A10101030
Chicago CFlorida B0101020
Claremont ANYU A001010
Columbia AWUSTL B0101020
Columbia BFlorida A10101030
Cornell AJohns Hopkins A10101030
Harvard AChicago A001010
Indiana APurdue A0101020
MIT ADuke A0101020
Michigan APenn State A001010
Minnesota AMaryland A10101030
North Carolina AImperial A10101030
Northwestern AMinnesota B001010
Ohio State AMcGill A0101020
Penn AVanderbilt A001010
Rutgers AHouston A0101020
South Carolina AYale B001010
Stanford ABrown A10101030
Texas AYale A0101020
UC Berkeley BRutgers B10101030
WUSTL AToronto A001010