Evening Forum I have a interesting word problem..
What's the difference between saying "The thicker a beam is, the stronger it is." and saying "The strength of a beam varies directly as its thickness."?
any comments ?
Well "The thicker a beam is, the stronger it is" is very vague. It doesn't express the relationship between thickness and strength very precisely. For example, does it mean exponentially proportional? Increasing the thickness a LITTLE may increase the strength A LOT. This is exponential proportionality.
However, the 2nd statement is a statement of direct proportionality. If strength = S, and thickness = T, then the 2nd statement says $\displaystyle S = kT$ where k is some constant! This means that if you change S, then T change proportionally!
So all in all. The first statement does not specify how proportionally one variable changes to another, but the 2nd statement does!