Tuesday, November 27, 2007

exp and sin/cos similarity

It is known to exist deep. They can be expressed on through another. Harmonic oscillation degenerates into exp attenuation. It seems, I have finally comprehended it.

Any two magnitudes are related as sin and cos if the one is a growth of another. The exponent is a speed of change of itself.

In other words, I believe that a=sint and b=cost follows from the system
(1) a′(t) = b(t)
(2) b′(t) = k * a(t)

like f = e^x follows from the f(t)′ = f(t).

The angle Phi in exp(i*phi) signifies the balance between self-dependence and interdependence. Moving from zero (e^0) to in the imaginary cycle we shift to two-variables (e^i=sin) system and moving further we return to single-variable (e^(i*i)=e^-1)

Disclaimer: I'm a profane in the math. The philosophy must be taken as a prompt to study it.

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