solve for x
- Thread starter Perdurat
- Start date
i have a gutfeeling that Mario's monster and the rabbit [math](\sin\left(\frac{\pi x}{2}\right)=\frac{4x}{\pi})[/math] share a common ancestor, Thales?I asked wolframalpha to solve the equation. It responds by changing the solve command to the plot command. That's telling, something.
View attachment 38323
"do not reinvent the wheel" wouldn't be a one liner if such endeavour wouldn't occure often...
back to the drawing board:
[math]y=\sin x[/math]moving around to match
[math]y=x^{2}[/math]for -1<=x<=1
yields:
[math]y=-cos(x/2)+1[/math]going down the rabbit hole and finding one:
[math]\sin\left(\frac{\pi x}{2}\right)=\frac{4x}{\pi}[/math]chopping its head and adding an additional function
[math]y=\sin\left(\frac{\pi x}{2}\right) (a), y2=\frac{4x}{\pi} (b),x=y^{2} (c)[/math]points of intersects of (a) and (b):
(0,0): the origin, lets call it R0
(0.6695,0.8907): what the post is all about, lets call it R1
points of intersects of (a) and (c):
(0.6169,pi/4): interesting
gazing at:
[math]y=-cos(x/2)+1[/math]to be continued...
back to the drawing board:
[math]y=\sin x[/math]moving around to match
[math]y=x^{2}[/math]for -1<=x<=1
yields:
[math]y=-cos(x/2)+1[/math]going down the rabbit hole and finding one:
[math]\sin\left(\frac{\pi x}{2}\right)=\frac{4x}{\pi}[/math]chopping its head and adding an additional function
[math]y=\sin\left(\frac{\pi x}{2}\right) (a), y2=\frac{4x}{\pi} (b),x=y^{2} (c)[/math]points of intersects of (a) and (b):
(0,0): the origin, lets call it R0
(0.6695,0.8907): what the post is all about, lets call it R1
points of intersects of (a) and (c):
(0.6169,pi/4): interesting
gazing at:
[math]y=-cos(x/2)+1[/math]to be continued...
Attachments
"Clowns to the left of me,
Jokers to the right,
Here I am stuck in the middle with you" (Stealers Wheel)
it appears to me by wanting to reference the problem to something fundamental (x-axis, y-axis,...), the solution hides in plain sight...
the bigger picture:
with a tiny bit more developped programming skills, than those required to "make the screen say hello world"
with mathematical skills, well lets just say I was humbled by a rabbit...
i want to write a program...
of cource there is no such thing as human error, which leaves me in a tight spot, since I would be the one to write the program:
(a scalable fourier transform)
a hint from the cpu manual suggests that under the hood a cordic algorythm is used to provide for a sin/cos function
the goofing around with desmos x^2 vs sin x was just to get an idea of the penalty in accuracy it would suffer if x^2 would be used in stead of a proper sin(x) function
the taylor series :
[math]\cos\left(x\right)=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-...[/math]awfully looks like (rabbit snippet):
[math]y=-\cos\left(\frac{x}{2}\right)+1[/math](i am an idiot)
even a bit as (monster snippet):
[math]4854321355161000\pi^{32}+296652971704320\pi^{34}+11611416821760\pi^{36}[/math]but then googling the 69672960 constant, pointing to (see attached), i kept a copy for a rainy day
thanks "Mario Ramanujan"
let the thread die in peace
,
Jokers to the right,
Here I am stuck in the middle with you" (Stealers Wheel)
it appears to me by wanting to reference the problem to something fundamental (x-axis, y-axis,...), the solution hides in plain sight...
the bigger picture:
with a tiny bit more developped programming skills, than those required to "make the screen say hello world"
with mathematical skills, well lets just say I was humbled by a rabbit...
i want to write a program...
of cource there is no such thing as human error, which leaves me in a tight spot, since I would be the one to write the program:
(a scalable fourier transform)
a hint from the cpu manual suggests that under the hood a cordic algorythm is used to provide for a sin/cos function
the goofing around with desmos x^2 vs sin x was just to get an idea of the penalty in accuracy it would suffer if x^2 would be used in stead of a proper sin(x) function
the taylor series :
[math]\cos\left(x\right)=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-...[/math]awfully looks like (rabbit snippet):
[math]y=-\cos\left(\frac{x}{2}\right)+1[/math](i am an idiot)
even a bit as (monster snippet):
[math]4854321355161000\pi^{32}+296652971704320\pi^{34}+11611416821760\pi^{36}[/math]but then googling the 69672960 constant, pointing to (see attached), i kept a copy for a rainy day
thanks "Mario Ramanujan"
let the thread die in peace
,
Since you have figured out all this information by your own, I think that we have a new natural born Genius here. You deserve a big applause
and you have been promoted to Perdurat Ramanujan.If you don't know this fact about me, I will tell you about it now: Fourier series, Fourier Transform, Laplace Transform, Z Transform, Taylor series, her child McLaurin series along with their mother Power series are all my friends.
Srinivasa Ramanujan was a great Indian mathematician. I am and many others are inspired by him, but we don't deserve to be called Ramanujan because he invented formulas from scratch while we are playing fancy by using the technology to simplify some other people complicated expressions for us. And we say YES we did it while in fact we have achieved ZERO.
Cheers,
-Mario, not Dan's student
