Eureka, Or, How to Circumvent Calculus??
How the hell does the following make any kind of sense:
In mathematics, formulae form a crucial end result of many calculations. For example the problem of determining the volume of a sphere is one that requires a sigificant amount of integral calculus to solve.
Archimedes displaced water long before Newton and Liebniz invented calculus*.
*It should be noted that this blog post was written by someone who took precisely no math in college. And yet, your humble blogger seems more numerate than most?
My comment on Wikipedia's discussion page:
The reference to needing integral calculus to determine the volume of a sphere doesn't make sense, in light of Archimedes. While it makes sense to argue that integral calculus is needed to derive a formula with which to determine the volume of a sphere without dunking the sphere in water, one can nonetheless dunk a smaller sphere in water, measure the volume of water displaced, and proportionately calculate the volume of a larger sphere. So, calculus is not needed to determine the volume of any sphere. Its use is limited to creating a general formula with which to calculate a sphere's volume.
Yet more info: the density of the sphere in question doesn't matter, though density affects bouyancy. A sphere with a one-inch radius has the same volume, 4.1 cubic inches, whether it weighs one pound or one ton, though the one ton sphere is much more dense.
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