ratios.

So: pi: ratio of the circumference of a circle to its diameter.

Rate:

A rate is a special form of ratio￼ where the the two terms are in different units. ￼￼￼

a circumference￼ and a diameter, despite both being “of a circle”, is it possible that we are using the wrong units for circumference?

this would make sense because the shape of the “line” of a circumference￼￼￼ is different from the shape of the line of the diameter:

The underside of a curve is different from the outer side of a curve.

but there is no difference between the underside of a straight line and the outer side of a straight line.

i’m stating something obvious probably: it sounds like this is what calculus deals with – but perhaps a rate is needed instead of a basic ratio.

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