I would suggest p-addic numbers, wich i find fascinating, and are understandable by a high school student (perhaps not otrogradsky's therorem, but..)
The definition of the distance btw p-addic number is the most difficult thing, but what a joy when you realize that there can be other...
I don't agree. there's a true base-one system.
A positional system is a convention for describing numbers with signs.
The usual convention is that 0 is the number zero, 1 is the number 1, 2 is the number two and so on, and that in base b any number is a sum of a*b^i terms with 0<= a < b
but...
Thank you very much, pervect.
If i understand, the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position, but as long particles follow geodesics (no acceleration), this is the same as if gravity were propagating at infinite speed.
So...
Right, of course, but my "prime predicate" function has a real argument, not integer, and my hope was that i could use some tricks of real function analysis (eg a transform of some kind) to obtain a new expression for pi(x)
but the concept raises an interesting question : what can you say about a number wich has a periodic development in base pi ?
such as a = 1.0101010101(base pi) = pi+pi^3+pi^5+...
it is tempting to name those numbers "rationals in base pi"
However, they look like p-adic numbers, because of...
Just a question from a begginer :
In the simulation of a solar or (galactic) system, when you calculate the position of a planet P at time t+dt, you only know the position of the other bodies in the system at time t, so you calculate the distance d between P and any other body Q at time t...
Yet another formula for pi(x) (prime number counting function)
start with wilson's therorem : p is prime iff p divides (p-1)! + 1
let G(x) be the gamma function
then p is prime iff sin(pi*(G(x)+1)/x) = 0
let f be the function x -> sin(pi*(G(x)+1)/x)
Since f(x) = sin(pi*G(x)/x+pi/x) and...
wrong. you CAN go directly up the wind. This is because the boat stands at the interface btw water and air.
the max speed of the boat will be s=w.e/(1-e), where w is the wind speed and e is the efficiency of the system (windmill+water propeller)
So if e=80% you go 3 times the wind speed and...