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How to Free Your Inner MathematicianNotes on Mathematics and Life$
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Susan D'Agostino

Print publication date: 2020

Print ISBN-13: 9780198843597

Published to Oxford Scholarship Online: April 2020

DOI: 10.1093/oso/9780198843597.001.0001

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Divide and conquer, just like Riemann sums in calculus

Divide and conquer, just like Riemann sums in calculus

Chapter:
(p.89) 14 Divide and conquer, just like Riemann sums in calculus
Source:
How to Free Your Inner Mathematician
Author(s):

Susan D'Agostino

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198843597.003.0015

“Divide and conquer, just like Riemann sums in calculus” offers a basic introduction for how to estimate—with any desired non-zero margin of error—the area of an irregular shape. For an initial underestimate, readers are encouraged to draw a large rectangle that fits inside the irregular shape and then use the grade school formula to calculate the rectangle’s area: area equals length times width. To refine this underestimate, readers learn to draw multiple smaller rectangles inside the shape whose areas they also sum. An analogous method is provided for overestimates. The discussion concerning how to obtain underestimates or overestimates with any desired margin of error is illustrated with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to consider dividing and conquering in all challenges they face in mathematics or life. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Keywords:   divide and conquer, Riemann sum, calculus, estimate area, irregular shape

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