Michigan State University/University of Delaware High School Tournament: Round 5 Tossups

Ming Dynasty [or Empire of the Great Ming

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Ming Dynasty [or Empire of the Great Ming]

4. It opens with a list of people who taught the author important lessons, and notes that “very little is needed to make a happy life” and “The things we want in life are empty.” For 10 points each:
[10] Name this guide for self-improvement which the author “addressed to himself,” a work of ancient philosophy largely written on a military campaign.
ANSWER: Meditations [or “Ta eis heauton”]
[10] Meditations was a work by this Roman philosopher who succeeded Antoninus Pius as the last of the Five Good Emperors.
ANSWER: Marcus Aurelius Antoninus Augustus
[10] Marcus Aurelius belonged to this school of philosophy founded by Zeno of Citium. It focused on using reason to overcome destructive emotions.
ANSWER: Stoicism [or word forms such as “stoics”]

5. The Ulam spiral depicts patterns in the distribution of these numbers, and the sieve of Eratosthenes finds all of these numbers below a given value. For 10 points each:
[10] Name this class of integers whose members are divisible only by one and themselves.
ANSWER: prime numbers
[10] Cantor used his diagonal argument to prove the uncountability of the set of these numbers, which cannot be represented as a ratio of integers.

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