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Quote by: iahag  Tell yuo the truth Praxius Im absolutely amazed by sheres and circles and expnonential functions with regard to the physical world. I came across a very interesting mathematical simplicity regarding spheres and the natural exponential. They both exhibit a unique, similar, but not identical property.
Define a circle
A 2 dimensional object whose rate of change of area is equal to its perimetre (hint, theres only one solution for such an object).
Define a sphere
A 3 dimensional object whose rate of change of volume is equal to its surface area (again, only one solution).
From a philosophical standpoint, it seems somewhat mystical that there is only one such solution for each case, and that, the universe reproduces such shapes everywhere. Indeed, one can analyse a system and conclude thats its most natural state is in a sphere - I just find the coincidences so appealing.
Define the natural exponential function
The NEF is an implicit function whose rate of change with respect to a distinct, stand alone variable is proportional to the function itself. - Its called the natural function for a reason. There is only one such solution.
What gets more interesting is that this function, when placed on an argand diagram, formulates a circle across a real and an imaginary dimension. Coincidence? Or simply a mathematical inevitability? Are circles the key to other dimensions?
I ponder on.
Wow, Ive gone completely off the tracks of topic! |
Good points.... another aspect is the Big Bang theory. If the Universe was created by the Big Bang, then the universe would have been created at a central point and expanded in an equal sphere-like explosion. As eons go by, everything in the universe passes further and further from one another....... eventually as I mentioned before, the universe would counter it's own gravity and momentum to start pulling back on itself, in an equal amount (Sphere) and cause the Big Squish, possibly producing yet another Universe.
Is the Universe alive? I say yes..... It moves, it produces, it sustains life on various planets, and sustains other unknowns. Everything inside the universe works together to make the Universe, such as our own internal systems. The Universe is in a sense, one big Atom of existance, and we live inside it.
Now think about what's outside our Universe.