20: Rational (Ratios)

From MC²’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?

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