Inconsistency

What is a Diamond?

(Archive Question of the Week) Having discussed various issues involving categorizing shapes, let’s take a look at a very different shape question, which didn’t fit into the last post. Is “diamond” appropriate? The word “diamond” is not a formal mathematical term; some people take it as equivalent to “rhombus”, while others equate it to “kite”, …

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Ranges of Inverse Trig Functions

(Archive Question of the Week) We have had a number of questions over the years about inverse trig functions and their ranges. For today’s question, I have chosen one from 2011, which will link to a number of others that I will not quote in detail.

Is a Square a Rectangle? Classifying Shapes

We get many questions about classifying shapes, from both elementary and high school students (or their parents or teachers). They often have trouble with the very idea of classifying items by applying definitions, and also with the fact that definitions can vary, both between everyday and technical usages, and from one textbook to another.

What is the Median, Really?

From time to time we get questions about finding the median in statistics. Some are entirely routine; but the three I want to discuss today take us gradually deeper into a morass of ambiguity. A recurring theme of my experience in Ask Dr. Math has been that definitions are not always what they seem – …

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