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Circle Disk: Redundant?

Sometimes, I will argue about something in mathematics...and any patient listeners respond: "Get a Life!"

For example, I am always troubled by the task "Find the area of a circle with radius 5." Why?

Because, from Euclid on, a circle has been defined as the set of points a fixed distance (i.e. the radius) from a center point. Thus, a circle is a curve, and has an area of 0! (Note: For the purists, a circle as a set of points has measure zero.)

That is, we should change the task to "Find the area of a circular disk with radius 5."

Now, that task is reasonable and do-able.

And, despite my pleas for the past 40 years, few have listened. Yet, I am not alone in my quest....I hope.

Then, Julio Gonzalez Cabillon, distinguished math historian, throws in some counter elements. In 1998, he wrote: "In current mathematical English, 'circle' is splitting into 'circle' (the curve) and 'disc' (the plane region)...a terminology which I don't like. perhaps I am old-fashioned, but I prefer 'circumference' and 'circle' (resp.) as we use them in Spanish!"