# Proof without Words: The Sum of a Positive Number and Its Reciprocal Is at Least Two (four proofs)

by Roger B. Nelsen (Lewis and Clark College)

This article originally appeared in:
Mathematics Magazine
December, 1994

Subject classification(s): Inequalities | Algebra | Algebra and Number Theory
Applicable Course(s): 4.3 Number Theory | 3.7 Discrete Math

Four geometric demonstrations of an inequality: the sum of a positive number and its reciprocal is at least $$2$$

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Capsule Course Topic(s):
Number Theory | Numbers With Special Forms or Properties