HIGHEST LEVEL OF MATH
- Thread starter HEAVYMETALGANGSTER
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i have always thought that knot theory sounded hard which i guess is part of topology. seems like it might be interesting though.
and calculus based physics is actually really easy.
call position as a function of time x(t)
call velocity as a function of time v(t)
call acceleration as a function of time a(t)
a(t) = dv/dt - acceleration is the rate of change of velocity
v(t) = dx/dt - velocity is the rate of change of position
and you can integrate a(t) to get v(t), and you can integrate v(t) to get x(t)
(this is for rectilinear motion)
of course there is other stuff, like Work = ∫F dx
and calculus based physics is actually really easy.
call position as a function of time x(t)
call velocity as a function of time v(t)
call acceleration as a function of time a(t)
a(t) = dv/dt - acceleration is the rate of change of velocity
v(t) = dx/dt - velocity is the rate of change of position
and you can integrate a(t) to get v(t), and you can integrate v(t) to get x(t)
(this is for rectilinear motion)
of course there is other stuff, like Work = ∫F dx
you should check out this book called Chaos in Wonderland: Visual Adventures in a Fractal World by Clifford A. Pickover. it is a weird book and like half of it is some pointless story, but there is some interesting info in there. you can even make your own fractals with the equations he has in there at the end
yeah you mean the Fibonacci sequence which is also related to phi aka the golden ratio.
the ratio of successive numbers in the sequence approaches phi
1,1,2,3,5,8,13,etc.
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.67
8/5 = 1.6
13/8 = 1.625
the ratios alternate being above and below the value of phi of around 1.618 and it gets closer as you keep going. and a spiral made from proportions using the golden ratio does have fractal qualities as it will look the same no matter how zoomed in or zoomed out you are on it.
the ratio of successive numbers in the sequence approaches phi
1,1,2,3,5,8,13,etc.
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.67
8/5 = 1.6
13/8 = 1.625
the ratios alternate being above and below the value of phi of around 1.618 and it gets closer as you keep going. and a spiral made from proportions using the golden ratio does have fractal qualities as it will look the same no matter how zoomed in or zoomed out you are on it.
lol not pi....phi. different stuff. pi pops up in nature too, but phi is very common.
just for clarification
pi = π = about 3.14 (cant get the symbol to look right its two small vertical lines with a wavy line on top)
phi = ɸ = about 1.618
but yeah they are different things. both are transcendental numbers though.
pi = usually pronounced "pie", phi = usually pronounced "fee"
and just my opinion, phi and e are way cooler transcendental numbers than pi. pi is cool but it just seems kinda arbitrary, like thats how a circle has to exist in 2 dimensions and pi just happens to be part of it.
phi comes out of this ratio
e (around 2.718) is an awesome number and comes from
also the derivative of e^x = e^x which is cool and e is the only number that does that
just for clarification
pi = π = about 3.14 (cant get the symbol to look right its two small vertical lines with a wavy line on top)
phi = ɸ = about 1.618
but yeah they are different things. both are transcendental numbers though.
pi = usually pronounced "pie", phi = usually pronounced "fee"
and just my opinion, phi and e are way cooler transcendental numbers than pi. pi is cool but it just seems kinda arbitrary, like thats how a circle has to exist in 2 dimensions and pi just happens to be part of it.
phi comes out of this ratio
e (around 2.718) is an awesome number and comes from
also the derivative of e^x = e^x which is cool and e is the only number that does that
