Is Zero a Square Number?
Date: 02/16/2000 at 10:47:33 From: Janie Cates Subject: Is zero a square number? I would like to know whether or not zero is considered to be a square number. I have found some sources that say it is. and others that say it isn't. Please let me know so that I can tell my students.
Date: 02/16/2000 at 11:11:18 From: Doctor TWE Subject: Re: Is zero a square number? Hi Janie - thanks for writing to Dr. Math. This depends on the way you (or your source) define the term "square number." Some sources define a square number as any number that is the square of an integer. By this definition, zero is indeed a square number, because 0 = 0^2 and zero is an integer. Others define a square number as any number that is the square of a natural (or counting) number. The natural numbers are the set of all integers greater than or equal to one. Since zero is not considered a natural number (and no other natural number squared equals zero), zero would not be considered a square number using this definition. This second definition has more of a "geometric" interpretation. Imagine measuring the area of a square that is n units on a side. If n = 0, you don't really have a square to begin with - you have nothing. In ancient times mathematicians didn't count zero (or even have a symbol for it) because they used numbers to represent physical measurements, and a physical object couldn't have a measurement of zero. I hope this helps - if you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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