Classroom Capsules and Notes
Classroom Capsules and Notes brings together the best of 114 years of the short classroom materials from the MAA print publications.
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Any collection of m balls in Rn, intersecting in at most their boundaries, has at least min(m,n+1) members that can be moved without disturbing the others.
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Integers equaling the sum of the squares of their contiguous parts (a generalization of two-digit numbers which are the sum of the squares of their digits) are discussed, with several examples.
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The author discusses conditional probabilities and presents three simple hypotheses from which the classical definition of conditioning follows.
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A visual proof of the identity
(a + b)2 + (a - b)2 = 2(a2 + b2)
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The author presents an easy absolute convergence test for series based solely on differentiation, with examples.
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A bit of Euler history is presented.
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