We are inclined to think it trivial to characterize "size of circle" as "diameter". In fact, it is not trivial to see the invisible "diameter" and to define the size of a circle by using "diameter". This way of characterization is what human beings created. This is an element of our culture.
- Meaning of "Diameter"
- "Diameter" is introduced for the purpose of representing "size of circle". (On the other hand, "radius" is a structual element of "circle".)
- Diameter as a chord
- Diameter can be defined as a chord that passes through the center.
- Diameter can be characterized as "the longest chord".
- This is proved by using "Triangular Inequality" :
- Getting/Measuring Diameter
- As an application of the characterization of "Diameter" :
"Diameter is the longest chord."
we can get a diameter of a circle as follows :
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