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Re: Can you reproduce the 3D graph in the ticalc.org logo?
Michael Chmutov  Account Info
(Web Page)

after looking at the 'cool graphs' section on technoplaza...

Reply to this comment    7 June 2003, 00:48 GMT


Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
Barrett Anderson  Account Info
(Web Page)

are you sure? i couldn't find the EXACT graph anywhere at technoplaza.net

Reply to this comment    7 June 2003, 06:28 GMT

Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

If there are some of you who don't know what they're talking about, click the link (if the filter didn't kill it), or click here, just paste the sections of the link together.
http://www.technoplaza.net/
graphs/index.cgi?
displaygraphs=1&howmany=15
&type=5&ppequ=1&ss=1

There is one that looks like a variation of the one at the ticalc.org logo, so that could be played around with...

Reply to this comment    7 June 2003, 17:25 GMT


Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
Michael Chmutov  Account Info
(Web Page)

I was talking about the "A Raindrop in Water". It turned out to be a little different, which I didn't realize until now, but I would guess it can be modified, although I haven't tried it myself.

Reply to this comment    8 June 2003, 03:54 GMT


Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

It does look very similar... maybe it uses the same... idea to get the ripple effect, only... different.

Earlier, I was thinking of (x^2+y^2)^.5 and sin/cos, so I had the right idea, I guess...

Reply to this comment    8 June 2003, 17:22 GMT

I look at all the lonely fnords.
RCTParRoThEaD_ Account Info
(Web Page)

no. have a nice day.

Reply to this comment    7 June 2003, 01:50 GMT

Re: Can you reproduce the 3D graph in the ticalc.org logo?
Frank A. Nothaft  Account Info
(Web Page)

Yeah.

It said how to somewhere on here at some time...

I'm working on updating QuadForm in a way that could blow some peoples minds...

Reply to this comment    7 June 2003, 04:31 GMT

Re: Can you reproduce the 3D graph in the ticalc.org logo?
nyall Account Info
(Web Page)

The graph looks like it is symetric around the z-axis: The further you go out from the z-axis the smaller it gets, but it is still wavy, so I think it is an exponentially decreasing sinusoid (or cosinusoid)

To see this in 2d graph y(x) = A*e^(-B*x) * cos(C*x)
Pick reasonable values for the Constants.

but instead of x we have distance from the z axis, so replace the xs in the above 2d formula with the distance formula to get:

z(x,y) = A*e^(-B*sqrt(x^2+y^2))* cos(C*sqrt(x^2+y^2))

And if you think about it some more the square root operators would not be needed to get radial symetry.


Any other theories?

Reply to this comment    7 June 2003, 07:13 GMT


Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
Ryan Kearney  Account Info
(Web Page)

this may sound stupid but whats the e?

Reply to this comment    7 June 2003, 08:46 GMT

Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
Soth  Account Info
(Web Page)

2.78.... or something vaguely similar.
It is a value which engineering uses a fair bit.

Reply to this comment    7 June 2003, 12:03 GMT


Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
JcN  Account Info

e = the sum of 1/n! where n starts at 0 and continues on to infinity in incriments of 1. Also, you can solve for e from this equation:

e^(imaginary pi) = -1

I'd solve for e, but I'm too lazy :P

Reply to this comment    8 June 2003, 07:37 GMT

Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
Soth  Account Info
(Web Page)

Very interesting, learn something new every day.

Something I am trying to figure out is that a couple weeks ago I was walking through some local 'park land' to get to uni, and someone had randomly written
e^i(pi)=-1 (obviously with the right symbols)
on the path in chalk.

Why? Was it his idea of revision?

Reply to this comment    8 June 2003, 13:03 GMT


Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

Heh, that's funny, today outside of church, on the bench, I wrote "3.1415926535..." I would have done all that I knew (it's now over 150), but it takes a long time to make precise little marks on wood. It will probably become unoticable in a few days anyway.

So, why does e^(i*PI)=-1?
Hm...
ln(e^(i*PI))=ln(-1)
i*PI=ln(-1)
i*PI=ln(1)+i*PI
i*PI=i*PI

Oh.... It all makes sense now! I never got that before... :) Wow...

Reply to this comment    8 June 2003, 17:47 GMT


Re: Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
nyall Account Info
(Web Page)

Um I think your proof may be circular?

Your simplification of ln(-1) into ln(1)+i*pi is probably based on the origional identiy you are trying to prove.

The proof I was tought for eulers identity is based on taylor expansions.

Reply to this comment    9 June 2003, 04:13 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

Nah, I've just always seen on my calc (in rectangular mode) that ln(x)=ln(-x)+pi*i (if x is less than zero)... I could be wrong, but that was my observation. Then, I remembered that, and it came up in the formula... I don't see WHY you'd add pi*i, but oh well :)

Reply to this comment    9 June 2003, 22:37 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
nyall Account Info
(Web Page)

Here is the precise formula:

Ln(complex_number) = Ln(abs(complex_number)) + i*angle(complex_number)

The first part: Ln(abs(complex_number)) is real valued.
The second part: i*angle(complex_number) is imaginary


I would not consider using this advanced formula as proof of the euler formula to be a valid proof.

Reply to this comment    9 June 2003, 23:00 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

Well, then I had the right idea... I just tested numbers like

ln(-2) ln(-8.9) ln(-9) ...

I think I might try to remember that...

Reply to this comment    10 June 2003, 01:54 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
nyall Account Info
(Web Page)

Wait never mind. I remembered the proof for ln(complex) = ln(abs(complex)) + i*angle(complex)

It is simple, convert the imaginary number to polar form: r*e^(i*angle) I hope you know what the polar form is.

Apply the ln function to this to get

ln(r*e^(i*angle))

Use a ln() identity:

ln(r) + ln(e^(i*angle))

And simplify the second ln()

ln(r) + i*angle

where r is abs(imaginary number) which is sqrt(real^2+imag^2)

Reply to this comment    10 June 2003, 16:10 GMT


Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

DARN, you beat me to saying it! LOL

You could also put in

(1+1/x)^x in for Y1 and at the homescreen type

Y1(999999999)

and you'll get an approximation of e... of course, you could also just hit the e (or e^) key on your calculator ;-)

To the best of my knowledge, it goes like 2.71828182846... (is that right?)

Reply to this comment    8 June 2003, 17:25 GMT


Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
JcN  Account Info

Yup, that's what my TI-89 told me.

Reply to this comment    9 June 2003, 06:44 GMT


Re: Re: Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
no_one_2000_  Account Info
(Web Page)

That's all I knew :) LOL

Reply to this comment    9 June 2003, 22:37 GMT

Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
Frank A. Nothaft  Account Info
(Web Page)

Its the natural log.

Reply to this comment    7 June 2003, 15:37 GMT


Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
BlackThunder  Account Info
(Web Page)

No it isn't, it's the base of the natural log.

Also known as 2.718281828459...

Reply to this comment    7 June 2003, 20:23 GMT

Re: Re: Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
VoidedProgrammer  Account Info
(Web Page)

Even more techinically, its Leonhard Euler's number, hence e.

VP

Reply to this comment    11 June 2003, 11:05 GMT


~:~
slimey_limey  Account Info
(Web Page)

Or the natural log of 1.

Reply to this comment    13 June 2003, 21:29 GMT


Re: ~:~
Soth  Account Info
(Web Page)

log |1| = 0
regardless of base.

it just so happens to be log |15.154....|
(but that is just log |e^e| so it is quite meaningless).

Reply to this comment    14 June 2003, 01:26 GMT


Re: Re: Re: Can you reproduce the 3D graph in the ticalc.org logo?
RCTParRoThEaD_ Account Info
(Web Page)

yep, that sounded stupid. ^_^

Reply to this comment    9 June 2003, 05:35 GMT

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