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One of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines or fiscal frauds. Each conversation is in two parts--an introductory essay which provides a gentle introduction to the topic and a second section that delves deeper and requires study by the reader. The topics themselves are extremely appealing and include, for example, Pick's theorem, Simpson's paradox, Farey sequences, the Frobenius problem, and Benford's Law.
Giancarlo Travaglini Universita di Milano-Bicocca, Italy.
Integer points, polygons, and polyhedraSimpson's paradox, Farey sequences, and Diophantine approximationA coin problem and generating functionsPythagorean triples and sums of squaresBenford's law, uniform distribution and normal numbersSums and integralsIndex