a question for you? tell me the formula for the circumference of a circle ...
& most of you would come up quickly with an answer as 2πr ... easy .. right ..!
ok! now tell me the formula for the circumference of an ellipse ...
& you say what ... some think its been a long time that you practiced math or read a math/geometry book .. or many of you came up with something quickly, like πab etc. or something else, but that doesn't seem right or doesn't sound familiar ... how so ..?
so you start scratching your head .. but please don't, as you may lose a hair or two .. how about i let you google it .. no one is looking anyway .. right ..?
so you do a search on google, & the mighty google says. "there is no exact formula for the circumference of an ellipse." ... rather, there is an approx. formula, derived by an Indian genius mathematician named Ramanujan.
You say, "how's that possible. I don't remember my math teacher telling me this ..."
well, not only your math teacher didn't give you any formula, but, its likely that they didn't even mentioned this fact [that an exact calculation is not even possible; so it won't be in the exam!] ..
why? because, it's not easy for mathematicians to accept & teach that humans are unable to derive a formula for such a simple shape in geometry; so they totally skip it and don't even talk about it (human behavior!).
How's that possible that no one could solve such a seemingly simple riddle ..? of course, there is no answer to that, but i do have an opinion ...
in contrast to a circle, an ellipse is nature's domain .. some of the most complex and powerful things are built (by humans as a copy to nature's) are in elliptical shape .. think about it .. The President's room WH; colleseum in Rome ... nature, for sure, uses it for its long lasting things, e.g. there are no circular orbits in nature ... in contrast to a circle, an ellipse creates such as perfect balance, which lasts billions of years, as in the earth rotating around the Sun, or in case of other planets, all orbits are elliptical .. & its shame that all that genius men power (women included), coupled with google power (i.e. computers horse power) can't find an exact formulae for the circumference of an ellipse.
bottom-line, man is not allowed to enter in nature's domain .. other examples e (Euler's constant) & π. which can only be derived in approx. .. all that human and computer horse power can't determine the exact value of such common things that we use everyday .. btw, e is used in continuous interest rate calculations and natural log etc.
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