Recently I found a site that contains the equations to create the graphs for the
electron orbitals (s, p, d, f...) but when I use Graphing Calculator to try to
recreate the orbital graphs shown, I don't get the same results.  The site is...

http://www.uky.edu/~holler/html/orbitals_2.html

The graphs are shown by chosing the orbital in question from the left column,
the equations are shown by clicking on the equations reference on top.

I am making an assumption, which may be the problem... the graph would be of the
form r = f(theta, phi), so I pick the phi from column 1, and theta from column
2.  If I only use column 1 (the phi column) then I get shapes that look like the
0 value orbital for each state (I take the absolute value to get the other half
for some of them).  But I can't get the theta sections to work, they give me
very wierd surfaces that don't look at all like an orbital.

Okay, what am I doing wrong here?

I'm going to take the easy way out here because I've got about 49 things that
need doing before classes begin.   Have a gander at the "Mathematical Physics"
section of

<http://web.lemoyne.edu/~craigda/Physics/Sims/Files/filelibrary.html>.

I've posted a gc file that plots spherical harmonics (which is what those images
of orbitals really are.)

For a REALLY cool application check out

<http://daugerresearch.com/orbitals/index.shtml>

David




On Jan 18, 2010, at 11:21 AM, gjmcclure wrote:

> Recently I found a site that contains the equations to create the graphs for
the electron orbitals (s, p, d, f...) but when I use Graphing Calculator to try
to recreate the orbital graphs shown, I don't get the same results. The site
is...
>
> http://www.uky.edu/~holler/html/orbitals_2.html
>
> The graphs are shown by chosing the orbital in question from the left column,
the equations are shown by clicking on the equations reference on top.
>
> I am making an assumption, which may be the problem... the graph would be of
the form r = f(theta, phi), so I pick the phi from column 1, and theta from
column 2. If I only use column 1 (the phi column) then I get shapes that look
like the 0 value orbital for each state (I take the absolute value to get the
other half for some of them). But I can't get the theta sections to work, they
give me very wierd surfaces that don't look at all like an orbital.
>
> Okay, what am I doing wrong here?
>
>

David Craig


<http://web.lemoyne.edu/~craigda/>

Still working out how to relate all these different approaches to conics.
Ultimately, will be in terms of projective geometry and Dandelin spheres, I
think. Probably no other clear way to unite them all.
Will have to shuffle things around a lot.

The good news is that small-size movies are working OK.

http://home.comcast.net/~cy56/ws1/Geometry/Analytic%20Geometry/Curves/index.html

Had some non-matching subscripts for the focal parameters k relative to the eccentricities, so the major and minor axes of the ellipse and the hyperbola weren't coming out right.

Fixed below:

http://home.comcast.net/~cy56/ws1/Geometry/Analytic%20Geometry/Curves/index.html

Chris,

Can you explain projective geometry to me in a nutshell?

Steve


Christopher Young wrote:
> Still working out how to relate all these different approaches to conics.
> Ultimately, will be in terms of projective geometry and Dandelin
> spheres, I think. Probably no other clear way to unite them all.
> Will have to shuffle things around a lot.
>
> The good news is that small-size movies are working OK.
>
>
http://home.comcast.net/~cy56/ws1/Geometry/Analytic%20Geometry/Curves/index.html
>
>

The table of contents is at http://home.comcast.net/~cy56/ws1/Math/mathtoc.html
and some of the new pages are at

http://home.comcast.net/~cy56/ws1/Math/Topology/mobius1.html
http://home.comcast.net/~cy56/ws1/Math/Topology/mobiusstripswith.html
http://home.comcast.net/~cy56/ws1/Math/Calculus/implicitdifferen.html

http://home.comcast.net/~cy56/ws1/Math/Topology/index.html

The idea is to make the concept of an intrinsic test of non-orientability clear
and vivid.
I'm a little worried about how I'm constructing the "space station", via
sweeping a fixed-size rectangular frame around.

It doesn't work too well when the surface self-intersects, since the walls of
the "space station" get pinched to zero width along certain lines. Back to the
drawing board as far as space station design goes. The big question is: Is it
possible to construct a self-intersecting one-sided "surface" with thickness?

These are files made with Graphing Calculator 4, still in development. However,
they're intended to show just how much GC4 is capable of, with minimal effort
compared to something like Mathematica when it comes to vivid, interactive
graphics with straightforward, mathematical specifications.

Sorry, that link is now:

http://home.comcast.net/~cy56/ws1/Math/Topology/mobiusSpaceStn.html

The idea is to make the concept of an intrinsic test of non-orientability clear
and vivid.
I'm a little worried about how I'm constructing the "space station", via
sweeping a fixed-size rectangular frame around.

It doesn't work too well when the surface self-intersects, since the walls of
the "space station" get pinched to zero width along certain lines. Back to the
drawing board as far as space station design goes. The big question is: Is it
possible to construct a self-intersecting one-sided "surface" with thickness?

These are files made with Graphing Calculator 4, still in development. However,
they're intended to show just how much GC4 is capable of, with minimal effort
compared to something like Mathematica when it comes to vivid, interactive
graphics with straightforward, mathematical specifications.

A quick easy way to get a grid is simply to select the "checkerboard" pattern:

You can increase the fineness of the grid via the resolution slider in the lower
left corner of the window:

If you want to get individual grid lines, you can just substitute in the "t"
parameter for one of the "u" or "v" parameters, and use a variable and a
parameter list for the other parameter. Below, I multiplied the ellipsoid
function by a number slightly greater than 1 to get the lines spaced out from
the ellipsoid so that they get graphed more neatly, although that's not strictly
necessary.

Here are some tips on how to use the "t" parameter to draw lines in 2D and 3D.

First, check out the Help section relating to Two-dimensional graphs:

Here's a file with the examples above plotted:

The whole process of putting gridlines on a surface becomes a lot simpler if we
put our surface into a function. Then we can define separate parameters using
"X" and "Y" with different subscripts. In every case, we're just plotting a
vector function of the form vector(x,y,z)=vector(X,Y,function(f,X,Y)). (You can
copy that last expression directly if the following graphic doesn't show up.)

We have to watch out that GC doesn't grab expressions after the trig functions
and exponential function.
I personally would rather it wasn't quite so grabby. When typing a factor after
a trig function, be sure to enclose the trig function in parentheses so it
doesn't grab what follows as part of the argument. It's not enough just to type
an asterisk for multiplication (the way I wish GC behaved.)

If we use more closely-spaced values in our parameter lists, we can get really
nice wireframe plots. GC takes care of the shading of the lines very nicely.

In the windows version I don't think parameter lists are available. (Can
somebody using Windows let me know if you can open the file below?)

vector(x,y,z)=vector(T,k,function(f,T,k)),in(k,set(-2,-1.75,-1.5,-1.25,-1,-0.75,\
-0.5,-0.25,0,0.25,0.5,0.75,1,1.25,1.5,1.75,2))

Do any of you know if the following is possible, and if so how to do it?

I would like to embed links to .gcf files in a web site I am building. Users of
the web site can be assumed to have either GC or GCviewer on the machine they
are using to view the site. When I try to do this, clicking on the link to .gcf
file does not open the file but rather puts up a parameter list for the file the
user is trying to open.

Please help if you can.

Do any of you know if the following is possible, and if so how to do it? 

I would like to embed links to .gcf files in a web site I am building. Users of the web site can be assumed to have either GC or GCviewer on the machine they are using to view the site. When I try to do this, clicking on the link to .gcf file does not open the file but rather puts up a parameter list for the file the user is trying to open. 

Please help if you can.

Lines, Two-point to Standard Form

Chris Young

cy56@...

Begin forwarded message:

From: Walter Lee Davis <waltd@...>

Date: February 4, 2010 10:38:48 AM EST

To: freewaytalk@...

Subject: Re: [Express] Using Applescript to open a downloaded file?

Reply-To: freewaytalk@...

This is only working for you, on your particular copy of Opera -- just so you know. To make this universal, so others can have the same effect, you need to add that mime-type to the server.

Walter

On Feb 4, 2010, at 5:10 AM, Christopher Young wrote:

On Feb 3, 2010, at 5:03 PM, Christopher Young wrote:

Well, there doesn't seem to be an official mime-type for that, but you could use the catch-all application/octet-stream as the type, that just says "don't mess with me, I'm binary".

OK, I'll also try that.

With the Opera browser, I was able to add a new application, and set the mime type to "application/octet-stream". It seems to work; I can finally open files with one click!

Thanks again for the help.

Chris

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On Jun 19, 2010, at 7:44 AM, artplot101 wrote:

> Hi Chris,
>
> I have been trying to use this effect in GC. I read somewhere about it
> and have been using a formula like:
>
> z=z|z|^i2 to some effect. Maybe you've had more experience in this field? Or
has it been addressed in GC before?

Art,

Your example produces some interesting curves! I'm still wondering exactly how
it works.
I guess any exponential spiral is going to have self-similar cells in an
exponential coordinate system.
The trick would be getting the images superimposed.

Chris

http://www.josleys.com/article_show.php?id=82

Complex operations in GC are amazing. You can abuse the examples and GC
keeps on ticking. In the Julia fractal, you also can change both g(z)
and f(z). See the file Spherical Fractal01.

Art

Share your interest in the power of GC's complex number abilities.
Conformal Mapping and semi-Droste. Get the ho-hum outta your 2d graphics. See
the above subject in the FILES section. Thanks. Art

When I save a file in which I have added a text block, and then reopen the
file, the text block does not appear. What am I doing wrong?

Hallo,
o.a. Subject wird angezeigt bei der grafischen Ausgabe von M = Wurzel aus
XX+YY+ZZ  .
Es handel sich hier um den Vektor einer Schwingung. Wenn ich einen Parameter
(Phase)
ändere, funkioniert es.

Wie sieht es mit einem upgrade aus  ( z.Z. GC 3.5)?


Uwe

I always wanted a remake of Forbidden Planet so I did the ending myself.
View Forbidden Planet in the files section. Artplot

Is it possible to loop the animation?

In other words, I want the animation to run forward only and then to replay
automatically from the beginning without the slider moving backwards.

Thanks,
Beth