A lemma is a small theorem which is used to prove a larger theorem.

Suppose that we are going to wrap an 11 gauge wire around a 3/8 inch mandrel. How much wire do we need to go around once?

OK. What do we know? We know that 3/8 inch is .375 inches and that the wire diameter is .091 inches. We also know that the circumference of a circle C = πd where d is the diameter of the circle and π is 3.14.

So what is this diameter? It has to take into account the diameter of the wire. It certainly looks to me like that diameter is .375 + .091 + .091= .557 and that the circumference is .557π = 1.75 inches. That is, it takes 1.75 inches of 11 gauge wire to wrap around a 3/8 inch rod one time.

Here is my thinking. It has changed since I started writing this so I might be wrong. 1.75 inches is the circumference of the rod plus two wire diameters so it is the outside circumference of the wire wrapped around the rod.

If we measure around the outside of the wire we get our answer. And anything less is not going to meet up.

John

## 2 comments:

Is figuring this out what one would call a dilemma?

For sure.

As the days go on I feel like I understand it better and better.

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