Jacques,

I think that the triangle inequality implies that s-a, s-b and s-c are all positive.  Each of these differences is the sum of two sides minus the third, quantity divided by 2.  s-c is (a+b-c)/2.

(1/4*I)*sqrt((b+a-c)*(a-b+c)*(b+a+c)*(a-c-b))

The factor a-c-b above must be negative since c+b-a must be positive.  All the other factors must be positive assuming that it's not a degenerate triangle.

Somehow I sense that a ton of bricks is about to land on me but I am mischievously attracted to an expression for the area of a triangle that prominently involves the imaginary unit.

EDIT: OK, if I keep going I end up with an negative area.  Perhaps sqrt(a*b) isn't the sqrt(a)*sqrt(b).

That thing at the end of this.  I don't know how it got there and I don't know how to get rid of it.

Jacques,

This works:

A := (1/4)*sqrt(-LinearAlgebra[Determinant](M));

but I can't get this to work:

A := (I*1/4)*sqrt(LinearAlgebra[Determinant](M));

Can you help?  Here is my worksheet:

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I think that the later looks cool.  I wonder what the Wikipedia folks would like to see in their encyclopedia.

Everything works now.  Thank you.

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Jacques,

I tried the "highly symmetric form" in the MathWorks entry and it didn't work for me using Maple. Can you tell me what I did wrong?

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Acer,

You make it look easy.  Thank you.

How did you make that?

Can you upload a Maple worksheet that I can download?

I don't understand "changing periodics".

Joe,

Thank you.

Now I have another problem.  I don't understand how maximize works.  WARNING, the last line of the following Maple worksheet runs forever (at least on my PC):

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The offending line is:

maximize(y, x = 0 .. 1)

Can anybody help me understand how maximize works or do I need a faster PC?

"The Cray-3 is so fast it can execute an infinite loop in under 2 seconds!"

Thank you both.  That makes it very clear.

I'll try harder next time.  Some day, I hope to be able to think more like you.  Thanks again.

Now that Acer's Method (looks like amazing magic from where I'm at) has solved Maple's issues calculating the integral:

int(BesselJ(0, 50001*x)*x*exp((355/2)*x^2*I), x = 35/100 .. 1)

can anyone use Acer's method to produce the graph that is "...a Fresnel diffraction pattern (in Mathematica [Maple]) which gave the answer to the problem…"?

The following is a stripped down version of Dr. Dermot Hogan's "Real Life Test" from his comparison of Mathematica and Maple:

"The question was whether a particular telescope’s obstruction was 35% or 42%.

…

"With a telescope, the diffraction pattern produced by the wave nature of light when the telescope eyepiece is at focus is simple ‘Fraunhofer’ diffraction. A long way off, and you see the aperture of the telescope with the shadow of the secondary clearly obstructing it – you might call this the ‘geometric’ case. And in between is ‘Fresnel’ diffraction.

"The trouble with Fresnel diffraction is that it is tricky to compute. Indeed, before the advent of fast computers and packages like Maple and Mathematica, it just wasn’t computed. For a circular aperture, the computation involves a complex oscillatory integral with Bessel functions which can only be evaluated by numerical methods.

…

"with the eyepiece at maximum distance from the focus, the measured size of the central obstruction’s shadow was indeed 42% for a 35% physical obstruction.

... This is a Fresnel diffraction pattern (in Mathematica) which gave the answer to the problem…"

As you can see, the plot abscissa runs from 0 to 0.002.  35% of 0.002 is 0.00070 and 42% of 0.002 is 0.00082.  I'm having trouble trying to decide if that spacial pulse is 0.00082 wide (42%) and Dr. Hogan was right or is the pulse width 0.00070 (35%) or is there to much computational noise to decide or what?

I got this started by asking a stupid question about the equivalence of a definite double integral and a definite single integral.  I should have started a new thread back there somewhere and from my blog rather than from this student forum.  I hope that I haven't offended anybody.  I think that Acer's amazingly magical solution to the Maple won't and Mathematica will problem, this thread and its chaos should end soon.

I got this started by asking a stupid question about the equivalence of a definite double integral and a definite single integral.  I should have started a new thread back there somewhere and from my blog rather than from this student forum.  I hope that I haven't offended anybody.  I think that Acer's amazingly magical solution to the Maple won't and Mathematica will problem, this thread and its chaos should end soon.

I like that idea but when I tried it, it didn't work for me.  There must be some path somewhere that needs to have c:\binw added to it.  Can you tell me what file I need to edit?  TIA

I like that idea but when I tried it, it didn't work for me.  There must be some path somewhere that needs to have c:\binw added to it.  Can you tell me what file I need to edit?  TIA

I too ran Jakubi's Windows version of Acer's method and got similar results on:

Win XP 32 bits, Processor  x86 Family 15 Model 4 Stepping 4 GenuineIntel ~2793 Mhz (2 CPUs), gsl-1.8

4.532, 25488836, 56131364 BillFish ~2793 MHz

4.342, 25947504, 56464908 Jakubi's 3.00 GHz

I put libgsl.dll in the same directory as 143_acer-method-win.mws and it works.  Where is a better place to put the GSL library?  I tried c:/binw but that didn't work for me.  I got a message that said I should reinstall...

Also, why is all of Acer's Maple red?

And, why do I get a dialog box that says "The worksheet may contain features which are not compatible with the chosen format.  Continue?" when I save Acer's and your Maple after I twiddle with it?

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