Sici spiral, create graphic

[AlfredFlaßhaar]

Between Christmas and New Year's I want to "play" with curves on graphs in Mathcad 14. I am particularly interested in the graphical representation of the Sici spiral (or named after Nielsen). It is represented parameterized in the Cartesian x-y coordinate system by x=Si(t) and y=Ci(t) with t>0. The Si and Ci functions are found in Mathcad on the f(x) menu. But they don't work in the diagram, even though I followed the instructions from the "Help". That's why I didn't attach a test file here. What am I doing wrong?

Kind regards, Alfred Flasshaar

[Werner_E]

As the help states, Si() and Ci() are symbolic only functions. They cannot be evaluated numerically and plotting requires numeric evaluation.

[Werner_E · Accepted solution]

Of course you can redefine the function and evaluate the necessary integrals numerically that way:

[AlfredFlaßhaar]

thank you very much 🙂

[AlfredFlaßhaar]

In MathCad 14, can the drawing of the spiral be represented as the movement of a "drawing" symbol/dot in slow motion?

[Werner_E]

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@AlfredFlaßhaar wrote:

In MathCad 14, can the drawing of the spiral be represented as the movement of a "drawing" symbol/dot in slow motion?

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You mean an animation where a dot travels along the spiral?

Something like this?

Mathcad file attached

 

[Werner_E]

... or would you rather prefer some kind of pencil drawing the curve

For a constant speed we would need a different parameterization

 

[AlfredFlaßhaar]

Thanks for the educational animations in all the answers. So far I have only used Mathcad for calculations. Learned something again.

[AlfredFlaßhaar]

In the attached animation file with the pen, what does "disable Frame=200 before generating animation" mean? What to do when creating the animation?

The first animation with the moving dot works well.

[Werner_E]

Animations in Mathcad are quite simple. When you animate, all that happens is that a variable FRAME is looped. Start and end value can be set in the animation popup window - in case of my animations you should chose 0 for "From" and the value you assigned for my variable MAXFRAMES in the "To" field.

All that Mathcad does is to calculate the sheet (or at least the area you had chosen for animation) for every value of FRAME, takes a pic and appends all to an avi movie. Its up to you to use FRAME so that the animation shows what you want.

Now for your question: By default, when you edit your sheet, FRAME has the value 0. Is is only incremented when you start the creation of an animation. In the worksheet you refer to there is not much to be seen when FRAME=0, so I manually set FRAME to a higher value to be able to see if the plot does what I intend it to do. To be able to set it right next to the plot I used a global assignment. If you don't delete or disable this assignment, FRAME is not iterated by the animation and you will see no change.

BTW, the codec used by Mathcad for the avi-file is very old and (at least in the past) this forum refused movies which used that codec (at those time the forum even refused Mathcad files so they had to be zipped zu be able to upload them - at least this is fixed in the meantime).

So to be of use here, the movie would have to be converted by some program. But the animations you see in my and Luc's posts are just animated gifs - so you can't pause them or watch them frame by frame. I use an online converter to do the job of turning the avi into a gif.

[AlfredFlaßhaar]

With this detailed answer everything is now clear. The animations work. It is interesting to observe the evolution of the curves. Now I can also "play" with other parameterized functions. I would also like to thank Luc and wish you a peaceful and healthy New Year.

[Werner_E]

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@AlfredFlaßhaar wrote:

With this detailed answer everything is now clear. The animations work. It is interesting to observe the evolution of the curves. Now I can also "play" with other parameterized functions. I would also like to thank Luc and wish you a peaceful and healthy New Year.

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You are welcome!

As the arc length of this curve basically is simply is a*ln(t), we can easily make an animation with a constant pencil speed.

 

A peaceful and happy 2023 to all readers!

[LucMeekes]

Or like this...

Success!
Luc

[AlfredFlaßhaar]

I would like to deal with this type of animation. Could I get a file please?

[LucMeekes]

Here you are.

I let FRAME run from 0 to 270 to create the animation.

Success!
Luc