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janhardo

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@janhardo Indeed, i was not sure if...

janhardo 700
July 27 2020
0 0

@janhardo 

Indeed, i was not sure if the answer from Rouben was correct, but i saw today that geometry has also his interest.
I took over  the example from dr John Val and assume that his work is correct done ( but that was not the case)

 

@tomleslie ThanksThat's a ingen...

janhardo 700
July 26 2020
0 0

@tomleslie 

Thanks

That's a ingenious way to look at this with the use of similar triangles
Scaling of the coordinates that's the idea  
It was a excercise meant for highschool students to learn vector calculations, but its solved on a quicker way.

@tomleslie ThanksWell done, looks n...

janhardo 700
July 26 2020
0 0

@tomleslie 

Thanks

Well done, looks not so complicated with the geom3d package , compared with the original calculation!
Checking this is a little bit more complicated , because its done with standard vector calculation :  direction vector ,normalvector ,etc

You could do this calculalton on the same way as in the example with maple too, but tha needs more insicht in vector calculations.
and how to perform this in maple

Author is http://www.johnval.nl/school/wiskunde/  see linear algebra pdf ( end of it)

Must again look to the reasoning of Rouben:   The ratio of the areas of the rectangles EFGH and SJIK equals (ML/NL)^2.
This remains true even if you replace the rectangle EFGH by any convex shape.
   
 

@Rouben Rostamian  ThanksAs i studi...

janhardo 700
July 25 2020
0 0

@Rouben Rostamian  

Thanks

As i studied the example it is 76 +2/25  as answer for the the green area.

It was dr. John Val who did the math , so i did not check his answer

@Rouben Rostamian   Thanks This m...

janhardo 700
July 25 2020
0 0

@Rouben Rostamian  

Thanks

This must be the calculated answer  : 76 + 2/25 for the green area

Its not done in 5 minutes this vectorcalculations  

 

 

@Rouben Rostamian Thanks  The ra...

janhardo 700
July 25 2020
0 0

@Rouben Rostamian

Thanks 

The ratio is 25/144  ~ 1/6 , the calculated answer is : 76 + 2/25 for the green area.
2 by 4 gives 8 is area => x 6  green area  : about 48
So this ratio is not working then. 

@Carl Love Interesting but complica...

janhardo 700
July 25 2020
0 0

@Carl Love 

Interesting but complicated to follow, what  solutions strategy is followed ?
I do see a implicit differentation and put from this together 3 linear equations 

 

@Carl Love  Thanks The derivation ...

janhardo 700
July 24 2020
0 0

@Carl Love 
Thanks

The derivation by  hand was correct, because you formula u(x,y) is the same!

Suppose if you fill in  for f(x) = cos(x) and f(y) =y^2  you get a true equation

@Carl Love ThanksThe mathematical d...

janhardo 700
July 24 2020
0 0

@Carl Love 

Thanks

The mathematical derivation was rather lengthy to follow , but the general solution is

u[x,y] = e^-y.f(x)+g(y) ..all functions of this form substituted in the PDE are true.

As exercise i try to do this now in Maple, to check this  

The idea is to get a impression of the importance of PDE's in this modern world : applications

@ecterrab ThanksInteresting to know...

janhardo 700
July 24 2020
0 0

@ecterrab 

Thanks

Interesting to know more how the PDE can be possibly solved
I did one PDE:  u[x,y]  = - u[x] by hand following: a long calculation to arrive at the general analytical solution equation.
 

This could be a big question  http...

janhardo 700
July 22 2020
0 0

This could be a big question 

https://mathworld.wolfram.com/SingularMatrix.html 

Plane chance and vertical lines...

janhardo 700
July 21 2020
0 0

@janhardo 


 

> 

  restart;
  with(plots):
  with(ArrayTools):
  doPlot:= proc( A )
           local rooster, p1;
            rooster:= plot3d
                       ( 0, 0..op([2, 1, 2], A),
                         0..op([2, 2, 2], A),
                         grid= [op([2, 1, 2],
                         A)+1,
                         op([2, 2, 2],
                         A)+1], style=wireframe,
                         color= COLOR(RGB, .15$3),
                         thickness= 0
                       );
            p1:=spacecurve({[[0,0,0], [0,0,0.5]],[[1,0,0], [1,  0,0.5]],               [[0,1,0], [0,1,0.5]], [[1,1,0], [1,1,0.5]]}, color=black):
            display
                 (  rooster, p1, [ seq
                     ( seq
                       ( plot3d
                         ( A[i,j],
                           x=i-1..i,
                           y=j-1..j,
                           shading=zhue,
                           style=surface,
                           axes=normal,
                           view=[ 0..op([2, 1, 2], A),
                                  0..op([2, 2, 2], A),
                                  min(0, A[..,2] )..max(A[..,2])
                                ]
                         ),
                         i=1..Size(A,1)# 1..5
                       ),
                       j=1..Size(A,2)
                     )
                   ],
                   scaling=constrained,
                   size=[1000, 1000]
                 );
          end proc:
  T1:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ]
             ]
           );
   T2:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ],
              [ 1.5,  1  ],
               [ 1.75, 2  ],
               [ 2,    2.5]
             ]
           ):
  T3:=Array( [ [ 0.5, -1, 3, 4  ],
               [ 1,    2, 4, 6  ],
               [ 1.5,  1, -4, 4 ],
               [ 1.75, 2, 5, 2  ],
               [ 2,    2.5, 2, 2]
            ]
          ):
  doPlot(T1);
  doPlot(T2):
  doPlot(T3):

Matrix(2, 2, {(1, 1) = .5, (1, 2) = -1, (2, 1) = 1, (2, 2) = 2})

  

 
> 

with(plots):
> 

 

> 

p1:=polygonplot3d([[1,1,5],[2,1,5],[2,3,5],[1,3,5]]):
> 

p2:=polygonplot3d([[2,3,2],[3,3,2],[3,4,2],[2,4,2]]):
> 

p3:=spacecurve([[0,0,0],[3,0,0],[3,4,0],[0,4,0],[0,0,0]],color=black):
> 

display({p1,p2,p3},axes=normal,orientation=[-16,78]);

 
> 

p4:=spacecurve({[[1,1,0],[1,1,5]],[[2,1,0],[2,1,5]],[[2,3,0],[2,3,5]],[[1,3,0],[1,3,5]],[[2,3,0],[2,3,2]],[[3,3,0],[3,3,2]],[[3,4,0],[3,4,2]],[[2,4,0],[2,4,2]]},color=black):
> 

display({p1,p2,p3,p4},axes=normal,orientation=[-16,78]);
> 

 

 

 

 

New proc for this existing procedure doPlot

- planes are now made with polygonplot3d .. or use exising plane with borderlines 
-vertical line segments


How to do this ?
Input doPlot is a
T1:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ]
By input this array for example a plane 0.5  has for z = 0.5
For every plane you get 8 points , and must generate this for plotting vertical lines between the points.

 

 

 

> 

 


 

Download arrplot3-1_laatste_tom_leslie1.mw

@vv  He is from Holland  Andr&...

janhardo 700
July 20 2020
0 0

@vv 
He is from Holland  André Heck .. me too. 
For some books: aging is no problem and agree with you.

I bought recently : introduction to Maple from André Heck ,the first edition and brandnew for  8 USD
Got the impression that this book is dated : Maple V release 2 ?

I am interesed in this bookversion, but is it somewhere to find used? 

 

@Carl Love  Seems that the package...

janhardo 700
July 20 2020
0 0

@Carl Love 

Seems that the package is not freely  without copyright issues, so removed links to the package.
5 LAMP commands not working in Maple:  
Drawlines,Drawplanes, Backsolve,Matsolve, Inverse
As i undertstand the coding from this package is not the best one at the moment ( 20 years back)
Is there another free Maple package for maple programming training purposes?
 

 

@Carl Love  What the command for i...

janhardo 700
July 19 2020
0 0

@Carl Love 

What the command for instance Drawlines ( )  excactly does, it is not explained in the section: commands in this module( see worksheet link)
The book text gives more explanation for the  command Drawlines: plot the lines without first having to solve each equation for y

No plotting and there is a error message

Interesting to know this code works?    
 

 

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