continued fractions - 2024 Chicago Open

Question

To solve indeterminate equations, Gauss introduced special bracket notation for approximating these expressions. When the private key in RSA is small, it can be exposed using these expressions in Wiener’s attack. The limit of these expressions’ geometric means almost always converges to Khinchin’s constant. (15[2]-5[2])A bijection between quadratic surds and the periodic class of these expressions (15[1])is given by Minkowski’s (-5[1])question-mark function. Loch’s theorem produces asymptotics for these expressions’ convergents, which are subject to Legendre’s (15[1])theorem in (*) Diophantine approximation. It’s not a decimal expansion, but while there are two of these expressions for every (-5[1])rational number, every irrational number can be written (10[1])uniquely as an infinite one (10[2])of these (-5[1])expressions. (10[1]-5[1])For 10 points, name these sequences that express a real number in terms of an infinite iteration of sums and reciprocals. ■END■ (10[4]0[3])

ANSWER: continued fractions [accept finite continued fractions or infinite continued fractions or terminated continued fractions or convergents of continued fractions; prompt on convergents until read by asking “of what objects?”; prompt on fractions]

<JC, Other Science (Math)>

= Average correct buzz position

Back to tossups

Buzzes

Player	Team	Opponent	Buzz Position	Value
Michael Hunding	SAYYID QUTB, DRIVING THE LONGEST CAR YOU’VE EVER SEEN THROUGH TAHRIR SQUARE	genAI this, genAI that, have you found your 真爱 yet	43	-5
Vincent Du	A Nervy Liberal Nanny Hence	LMM's LLM MLM	43	-5
Anderson Wang	I’ll take a quiet 10 / A handshake of CO (Chicago Open)	The Dyatlov Passement incident	43	15
Alex Akridge	We Need New Names	Punished "Venom" BHSU	43	15
Conor Thompson	Galvanized Square Steen and Eco-Friendly Wood Vermeer	Lying on a Mattress at Lou’s Apartment in Pilsen, Chicago	55	15
Eric Bobrow	Read slowly: A A A A A A A A A A A A A A A Read quickly: A	NJTRANSit (and bobby, i guess)	59	-5
Iain Carpenter	Are You There, Chat? It's Me, Margaret	The Oldest Men in the World	74	15
Arya Karthik	Charlotte's Moderately Successful Team	Lisan al-Quib	93	-5
Swapnil Garg	it's the great pumpkinification objection, charlie brown	The Empire Bikes Back	101	10
Aidan Mehigan	First Cause, First Cause, make me young!	var merchants	106	10
Richard Niu	AMOGH QUIZ HACK? 英雄联盟 400 PPG 24 TUH	There are buzzable clues everywhere for those with eyes to see	106	10
Rasheeq Azad	Mindgoblin of Little Hobbes	Berkeley Mafia and the Chicago Boy	108	-5
Billy Busse	BHSU B	sticking out your guyot for the ridge push; you're so seafloor spread, you're so fracture zone	109	10
Jorrest Weintraub	The Jeam Team	when you look this good, you don’t have to know anything	109	-5
Natan Holtzman	Lisan al-Quib	Charlotte's Moderately Successful Team	131	10
Kevin Wang	genAI this, genAI that, have you found your 真爱 yet	SAYYID QUTB, DRIVING THE LONGEST CAR YOU’VE EVER SEEN THROUGH TAHRIR SQUARE	131	0
Eric Mukherjee	LMM's LLM MLM	A Nervy Liberal Nanny Hence	131	10
Kevin Ye	Berkeley Mafia and the Chicago Boy	Mindgoblin of Little Hobbes	131	10
Fierro Grey	NJTRANSit (and anwen, I guess)	Les Missourables	131	0
June Yin	Les Missourables	NJTRANSit (and anwen, I guess)	131	0
Sky Hong	NJTRANSit (and bobby, i guess)	Read slowly: A A A A A A A A A A A A A A A Read quickly: A	131	10

Summary

Tournament	Edition	Exact Match?	TUH	Conv. %	Power %	Neg %	Average Buzz
2024 Chicago Open	07/28/2024	Y	15	80%	27%	40%	96.75