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#26 Re: This is Cool » [Fractal Spirograph] Fractal Roulette » 2012-07-22 23:23:07
Can you add a way to halt the drawing so we can see how the wiggles are formed.
The animations are animated GIFs (not Flash videos).
Use a GIF animation software to see the static frame images.
Did you find the wheel ratios by trial and error?
Yes.
#27 Re: Help Me ! » Easier Proofs for the Basic Limit Laws? » 2012-07-02 01:38:37
is an arbitrary number, then is an arbitrary numberIs (*) (the statement in the first quote) a correct assumption?
It is correct (but informal) since the following two statements are equivalent.
If so, then are these arguments valid proofs?
#28 Re: Help Me ! » A troubling sum » 2012-06-28 11:07:39
Hi benice
The second link doesn't apply here.
Hi! See the second link if you're interested in how to obtain the infinite product
#29 Re: Help Me ! » A troubling sum » 2012-06-28 04:13:18
Can anyone help me with the sum
http://math.stackexchange.com/a/143157
http://en.wikipedia.org/wiki/Basel_prob … he_problem
#30 Re: Help Me ! » Need help in understanding haar wavelet transformation » 2012-06-11 16:12:42
I did not understand that how did he consider values of B , V , H and D.
Split W4 into two 2x4 block matrices P and Q.
#31 Re: Help Me ! » Relations and Functions: Domain and range of special functions » 2012-06-01 20:13:04
But what do you mean when you say that since x∈R-Z so the equation 0<x-[x]<1.
( [x] ≤ x < [x]+1 for all x∈R ) and ( x = [x] iff x∈Z )
=> [x] < x < [x] + 1 for all x∈R-Z
=> [x] - [x] < x - [x] < [x] + 1 - [x] for all x∈ R-Z
=> 0 < x - [x] < 1 for all x∈R-Z
#32 Re: Help Me ! » Relations and Functions: Domain and range of special functions » 2012-05-31 03:15:30
(1)
Now for Range, what should I do?
Notice that [x] ≤ x < [x]+1 for all x∈ R.
x ∈ R-Z
=> 0 < x-[x] < 1
=> 1/(x-[x]) > 1
=> f(x) = 1/sqrt(x-[x]) = sqrt(1/(x-[x])) > 1
(2)
|x| = -x if x ∈ [-2,0] or x if x ∈ (0,2]
=> f(|x|) = -x-1 if x ∈ [-2,0] or x-1 if x ∈ (0,2] ... (a)
f(x) = -1 if x ∈ [-2,0] or x-1 if x ∈ (0,2]
=> |f(x)| = |-1| = 1 if x ∈ [-2,0] or |x-1| if x ∈ (0,2] ... (b)
(a) and (b)
=> g(x) = f(|x|) + |f(x)| = -x-1 + 1 = -x if x ∈ [-2,0] or x-1 + |x-1| if x ∈ (0,2]
=> g(x) =
-x if x ∈ [-2,0];
0 if x ∈ (0,1);
2x - 2 if x ∈ [1,2].
#33 Re: This is Cool » [Dynamic Spirograph] Circle Rolling around Rolling Circle » 2012-05-16 20:36:18
i have geogebra but how do you make that?
#34 Re: This is Cool » Funny Math Pictures in Ancient Art Style » 2012-05-14 00:44:26
Prehistoric drawings and ancient mythologies.
Thank you for these pics. They look like Aliens!
#36 Re: This is Cool » Funny Math Pictures in Ancient Art Style » 2012-05-14 00:33:36
No,two faces on the pic above looked like smiling tiger faces to me.
I see. Thank you.
#37 Re: This is Cool » Funny Math Pictures in Ancient Art Style » 2012-05-14 00:24:21
There are tigers in your pics as well.
Did you mean the faces between two adjacent characters?
#38 Re: This is Cool » Funny Math Pictures in Ancient Art Style » 2012-05-14 00:13:14
Hi anonimnystefy;
Yes, some characters look like owls. Another owl picture can be found here.
You can also visit this page to learn how to draw an owl (or other animals) with circles.
#40 This is Cool » Funny Math Pictures in Ancient Art Style » 2012-05-13 07:53:03
- benice
- Replies: 18
Some people told me that these math pictures look like the art of ancient civilizations.
My sister said that the visual style is like children's graffiti works.
#41 Re: This is Cool » Find an equation showing special graph » 2012-05-02 14:27:17
Hi,benice;
I review the sites and infer that the earliest one is before 2011-07-29 09:35:26 (+8). But the site you gave just show "9 months ago", when the equation was flooding, so I don't know whether that is the original one.
The original post was submitted on 28 Jul 2011. (Look at the upper right corner of the comment page.)
We tried to plot it, only to found it abused "sqrt" so there is no plot. I tried to correct but gave up later because of the complex numbers (complex, not "i").
Plot each component separately:
f1(x,y) = ((x/7)^2) * sqrt( sign(abs(x)-3) ) + ((y/3)^2) * sqrt( sign(y+3*sqrt(33)/7) ) - 1
f2(x,y) = abs(x/2) - ((3*sqrt(33)-7)/112)*(x^2) - 3 + sqrt(1 - (abs(abs(x)-2)-1)^2) - y
f3(x,y) = 9*sqrt( sign((1-abs(x))*(abs(x)-0.75)) ) - 8*abs(x) - y
f4(x,y) = 3*abs(x) + 0.75*sqrt( sign((0.75-abs(x))*(abs(x)-0.5)) ) - y
f5(x,y) = 2.25*sqrt( sign((0.5-abs(x))*(abs(x)+0.5)) ) - y
f6(x,y) = 6*sqrt(10)/7 + (1.5-0.5*abs(x))*sqrt(sign(abs(x)-1)) - 6*(sqrt(10)/14)*sqrt(4-(abs(x)-1)^2) - y
#43 Re: This is Cool » How to draw the US Flag mathematically? » 2012-05-02 04:20:22
I just want to know how to "Drawing a US Flag using Inequalities" and draw "Monster Cow".
Hi Sumasoltin,
Flag of the United States:
1. Plot using Graph:
http://padowan.dk/forum/viewtopic.php?id=549.
2. Plot using GeoGebra:
http://www.geogebra.org/forum/viewtopic.php?f=2&t=24109.
The formulas for the Monster Cows are not public.
I will email benice from his site about it and ask permission.
Hi bobbym,
Thank you for your email.
#44 Re: Help Me ! » Limits - Proofs » 2012-03-21 01:06:40
a)
You can prove the contrapositive:
If lim(x⇒a)f(x)g(x) exists, then lim(x⇒a)g(x) also exists.
Assume that lim(x⇒a)f(x)g(x) exists.
Since lim(x⇒a)f(x)g(x) and lim(x⇒a)f(x) both exist and lim(x⇒a)f(x) is nonzero,
it follows that lim(x⇒a)g(x) [ = lim(x⇒a)f(x)g(x)/f(x) ] exists.
#45 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-27 02:18:55
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)]}
Deterministic?
#46 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-26 10:06:25
Are f(t) and g(t) random functions?
f and g are arbitrary deterministic (non-random) functions.
#47 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-25 16:41:33
just wondering,you wrote there three formulas ....
The third one is a general formula.
#48 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-22 14:32:47
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)
#49 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-22 14:06:53
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
#50 Re: This is Cool » Cool graphs using the sgn(x) function!!! » 2012-02-21 10:21:48
hi benice
thank you!
now i just need to find the general formula.
y = 0.5 (a sgn(x + 1) + b sgn(x - 1))