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#51 2012-02-22 01:46:49
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Hi anonimnystefy;
That is not correct. It is defined for 0.
Sign[0] = 0.
Here is how it is defined in Wikipedia.
http://en.wikipedia.org/wiki/Sign_function
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#52 2012-02-22 07:46:05
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi bobbym
really.oh well.we can take it one the same interval just excluding the zeors of the functions.so for the last function which has three parts we would look at it just over the R\{-1,1}
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#53 2012-02-22 08:06:54
- benice
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Re: Cool graphs using the sgn(x) function!!!
anonimnystefy wrote:
found it:The function
Hi anonimnystefy;
It's a nice expression!
Here is another expression: y = 0.5 sgn(x) (1 + sgn(abs(x) - 1)).
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#54 2012-02-22 08:38:00
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi benice
thank you! 
now i just need to find the general formula.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#55 2012-02-22 09:21:48
- benice
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Re: Cool graphs using the sgn(x) function!!!
anonimnystefy wrote:
hi benice
thank you!
now i just need to find the general formula.
y = 0.5 (a sgn(x + 1) + b sgn(x - 1))
Last edited by benice (2012-02-22 10:00:20)
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#56 2012-02-23 08:11:23
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi benice
thanks for that formula as well.but i wanted the formula which will give the three lines at hights of a,b and c,respectively.
if you find anything let me now.once again,thank you for the formulas.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#57 2012-02-23 08:25:33
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi benice
i think i found one,but i don't know if it works for all heights and distances:
where a,b and c are the heights i mentioned and d and e are the distances of the breakings in the interval or in other words, d and e are the points where the sgn(x) function breaks according to our 'definition'.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#58 2012-02-23 13:06:53
- benice
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Re: Cool graphs using the sgn(x) function!!!
anonimnystefy wrote:
hi benice
i think i found one,but i don't know if it works for all heights and distances:
where a,b and c are the heights i mentioned and d and e are the distances of the breakings in the interval or in other words, d and e are the points where the sgn(x) function breaks according to our 'definition'.
Assume d < e.
x<d
=> y = 0.5[(a+c) + (b-a)(-1) + (c-b)(-1)] = 0.5[a+c-b+a-c+b] = a
d<x<e
=> y = 0.5[(a+c) + (b-a)(1) + (c-b)(-1)] = 0.5[a+c+b-a-c+b] = b
x>e
=> y = 0.5[(a+c) + (b-a)(1) + (c-b)(1)] = 0.5[a+c+b-a+c-b] = c
Last edited by benice (2012-02-23 13:09:21)
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#59 2012-02-23 13:32:47
- benice
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Re: Cool graphs using the sgn(x) function!!!
Hi anonimnystefy;
You can use the sgn function to generate curves with dashed line:
x = sgn(cos(32t)) cos(t)
y = sgn(sin(32t)) sin(t)
x = sgn(cos(512t)) [cos(t) + sin(2t)]
y = sgn(sin(512t)) [sin(t) - sin(2t)]
x = sgn(cos(nt)) f(t)
y = sgn(sin(nt)) g(t)
Last edited by benice (2012-02-23 13:35:57)
My Gallery of Math Art: benice equation
#60 2012-02-25 05:25:54
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi benice
now those are some nice graphs.thanks for sharing that.
just wondering,you wrote there three formulas,and there are two graphs.which formula is for which graph?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#61 2012-02-26 01:29:01
- John E. Franklin
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Re: Cool graphs using the sgn(x) function!!!
what is this "sgn" function? Can you provide a definition of it.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#62 2012-02-26 07:11:07
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Hi John;
A few examples will do the trick:
sign(0) = 0
sign(+5) = 1
sign(+.3) = 1
sign(-2) = -1
sign(-200.34) = -1
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#63 2012-02-26 09:21:09
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
hi JEF
it's called the sign function.and as its name says,it gives us the "sign" of the number.for positive numbers it returns 1, for negative -1 and for 0 it returns zero.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#64 2012-02-26 15:41:33
- benice
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Re: Cool graphs using the sgn(x) function!!!
anonimnystefy wrote:
just wondering,you wrote there three formulas ....
The third one is a general formula.
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#65 2012-02-26 20:13:01
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
Hi benice
I don't know why I didn't notice it.
Are f(t) and g(t) random functions?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#66 2012-02-27 09:06:25
- benice
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Re: Cool graphs using the sgn(x) function!!!
anonimnystefy wrote:
Are f(t) and g(t) random functions?
f and g are arbitrary deterministic (non-random) functions.
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#67 2012-02-27 11:02:29
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
Deterministic?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#68 2012-02-27 11:29:39
- John E. Franklin
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Re: Cool graphs using the sgn(x) function!!!
thanks for the examples (bobby) and definition (anom).
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#69 2012-02-27 11:31:54
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
You're welcome! 
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#70 2012-02-27 13:15:12
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Hi John E. Franklin;
Your favorite programming language might have that command built in.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#71 2012-02-28 00:44:48
- anonimnystefy
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Re: Cool graphs using the sgn(x) function!!!
Hi bobbym
And that is?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#72 2012-02-28 01:18:55
- benice
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Re: Cool graphs using the sgn(x) function!!!
Hi anonimnystefy;
Here is a more general formula:
f(x) = 0.5 {f1(x) + f3(x) + sgn(x-a)[f2(x) - f1(x)] + sgn(x-b)[f3(x) - f2(x)]}
anonimnystefy wrote:
Deterministic?
http://en.wikipedia.org/wiki/Deterministic_system
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#73 2012-02-28 02:45:10
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Hi anonimnystefy;
And that is?
Sometimes Sgn, Signum or Sign.
While python and C++ do not, mathematica, maple, delphi, Maxima and VB do.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#74 2012-03-21 17:03:18
- afridinazneen
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Re: Cool graphs using the sgn(x) function!!!
I have gotten some good information here.
#75 2012-03-21 17:11:26
- bobbym
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Re: Cool graphs using the sgn(x) function!!!
Hi;
Welcome to the forum!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.