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  Elena, Liya

  "Researching turkish song: the selection of the main element and its graphic transformations",

   Russia, Kazan, school #57

The setting and visualization of the melodic line of the song
> restart:
> with(plots):with(plottools):
> p0:=plot([[0.5,9],[1,7],[2,9],[4,11],[6,9],[7,11],[8,7],[10,9],[12,9],[14,9],[16,7],[16.5,9],[17,7],[18,9]],color=magenta):p1:=plot([[18,9],[20,11],[22,9],[23,11],[24,9],[26,11],[28,11],[29.5,8],[30,11],[32,9],[33.5,8],[34,9],[36,7],[37.5,5],[38,9],[40,7],[42,5],[44,5],[46,4],[47,5],[48,2],[50,4],[51,5],[51.5,4],[52,2],[54,4],[56,4],[56.5,5],[57,4],[58,5],[60,7],[62,5],[64,7],[66,5]],color=cyan):
> p2:=plot([[66,5],[68,5],[69,5],[70,4],[71,5],[71.5,4],[72,2],[73,4],[74,5],[75,7],[76,5],[78,4],[78.5,7],[80,5],[82.5,4],[83.5,4],[84,2],[86,4],[88,4],[90.5,4],[91.5,4]],color=red):
> p3:=plot([[91.5,4],[92,2],[94,4],[96,4],[96.5,9],[97,7],[98,9],[100,11],[100.5,9],[101,11],[102,9],[104,11],[106,9],[108,9],[109,9],[109.5,9],[110,7],[111,9],[112,7],[113,7],[114,9],[116,11],[116.5,9],[117,11],[118,9],[119.5,11],[120,9],[122.5,9],[124,9],[124.5,9],[125,11],[125.5,9],[126,11],[128,9],[129,7],[130,9],[132,11],[132.5,9],[133,11],[134,9],[136,11],[136.5,9],[138.5,9],[140,9],[140.5,9],[141,11],[141.5,9],[142,11],[143,7],[143.5,7],[144,9],[144.5,9],[145,7],[146,9],[148,11],[148.5,9],[149,11],[150,9],[151.5,11],[152,9],[154.5,9],[156,9],[156.5,9],[157,11],[157.5,9],[158,11],[160,9],[161,7],[162,9],[164,11],[164.5,9],[165,11],[166,9],[168,11],[168.5,9],[171.5,9],[172,9],[172.5,9],[173.5,11],[174,9],[174.5,11],[175,7],[175.5,7],[176,9],[176.5,9],[177,7],[178,9],[180,11],[180.5,9],[181,11],[182,9],[183.5,11],[184,9],[186.5,9],[188,9],[188.5,9],[189,11],[189.5,9],[190,11],[192,9],[192.5,9],[193,7],[194,9],[196,11],[196.5,9],[197,11],[198,9],[200,11],[201.5,9],[202,11],[203,9],[203.5,8],[204,9],[205,7],[205.5,9],[206,11],[207,9],[208,7],[209,8],[209.5,7],[210,9],[211,7],[212,5],[213,5],[213.5,5],[214,9],[215,7],[216,5],[217,5],[217.5,5],[218,7],[219,5],[220,4],[221,4],[221.5,4],[222,7],[223,5],[224,4],[225,4],[227,4],[227.5,4],[228,2],[230,4]],color=blue):
> p4:=plot([[230,4],[232,4],[232.5,5],[233,4],[234,5],[236,7],[236.5,5],[237,5],[238,9],[240,7],[242.5,5],[244,5],[245,5],[246,4],[246.5,5],[247,4],[248,2],[250,4],[250.5,7],[251,5],[252,4],[254,4],[254.5,7],[255,5],[256,4],[258,4]],color=brown):
> p5:=plot([[258,4],[259,4],[260,2]],color=green):
> plots[display](p0,p1,p2,p3,p4,p5,thickness=2);

 

 

The selection of the main melodic element in graph of whole song. The whole song is divided into separate elements - results of transformationss0:=plot([[7,11],[8,7],[10,9],[12,9],[14,9],[16,7],[16.5,9]],color=blue):
> s1:=plot([[118,9],[119.5,11],[120,9],[122.5,9],[124,9],[124.5,9],[125,11],[125.5,9]],color=blue):
> s2:=plot([[134,9],[136,11],[136.5,9],[138.5,9],[140,9],[140.5,9],[141,11],[141.5,9]],color=blue):
> s3:=plot([[150,9],[151.5,11],[152,9],[154.5,9],[156,9],[156.5,9],[157,11],[157.5,9]],color=blue):
> s4:=plot([[166,9],[168,11],[168.5,9],[171.5,9],[172,9],[172.5,9],[173.5,11],[174,9]],color=blue):
> s5:=plot([[182,9],[183.5,11],[184,9],[186.5,9],[188,9],[188.5,9],[189,11],[189.5,9]],color=blue):
> s6:=plot([[250,4],[250.5,7],[251,5],[252,4],[254,4],[254.5,7],[255,5],[256,4]],color=blue):
> plots[display](s0,s1,s2,s3,s4,s5,s6);
> s:=plots[display](s0,s1,s2,s3,s4,s5,s6):

 

Animated display of grafical transformation of the basic element (to click on the picture - on the panel of instruments appears player - to play may step by step).m0:=plot([[7,11],[8,7],[10,9],[12,9],[14,9],[16,7],[16.5,9]],color=blue):
> pm:=plot([[118,9],[119.5,11],[120,9],[122.5,9],[124,9],[124.5,9],[125,11],[125.5,9]],color=red,style=line,thickness=4):
> iop:=plots[display](m0,pm,insequence=true):
> plots[display](iop,s0);

> m0_t:=translate(m0,110,0):
> m0_r:=reflect(m0_t,[[0,9],[24,9]]):
> plots[display](m0,m0_r,insequence=true);
> m0r:=plots[display](m0,m0_r,insequence=true):

> pm0:=plots[display](pm,m0):
> plots[display](pm0,m0r);

> m0:=plot([[7,11],[8,7],[10,9],[12,9],[14,9],[16,7],[16.5,9]],color=blue):
> pn:=plot([[134,9],[136,11],[136.5,9],[138.5,9],[140,9],[140.5,9],[141,11],[141.5,9]],color=blue,thickness=3):
> iop:=plots[display](m0,pn,insequence=true):
> plots[display](iop,s0);

> m0_t1:=translate(m0,126,0):
> m0_r1:=reflect(m0_t1,[[0,9],[24,9]]):
>
> plots[display](m0,m0_r1,insequence=true);
> m0r1:=plots[display](m0,m0_r1,insequence=true):

> pm01:=plots[display](pn,m0):
> plots[display](pm01,m0r1);

 

> pm2:=plots[display](pn,pm,m0):
> plots[display](pm0,m0r,pm01,m0r1);

> pt_i_1:=seq(translate(pm,5*11*i,0),i=0..4):
> plots[display](pt_i_1);

> pm_i:=seq(translate(pm,5*11*i,0),i=0..4):
> plots[display](pm_i);
> iop1:=plots[display](pm_i,insequence=true):
> plots[display](iop1,s0);

 

> pm_i_0:=seq(translate(m0_r,5*11*i,0),i=0..4):
> plots[display](pm_i_0);
> iop2:=plots[display](pm_i_0,insequence=true):
> plots[display](iop2,s0);

 

 

 

 

 

 

I never expected that the reflected light direction of sun from moon in the sky would be so dificult to imagine ...

at the following article mentioned :

we derive an equation for the magnitude of the moon tilt illusion that can be applied to all con gurations of sun and moon in the sky.

THE MOON TILT ILLUSION

 

since the calculations contains many steps and high level mathematical formula , there is no way rather to recourse to maple (powerful math assistant )

I hope there was adaptations between a lots of functions and predefined schema of maple and this problem so that the calculations and visualization facilitated several times ?

your effort will be a graet present for all the people of the world that look to the moon crescent everytime !

 

Consider the well-known Euler's formula  

 eix = cos x + i sin x   

When we calculate that for  x = π  we get:

eiπ = cos π + i sin π   or

eiπ = −1 + i × 0   (because cos π = −1 and sin π = 0)  or

eiπ = −1  or  eiπ + 1 = 0

It seems absolutely magical that such a neat equation combines  5  fundamental constants: e ,  i ,  π , 1 , 0

The purpose of this post - to give a simple visualization of equality  eiπ = −1  (statical and animated) by expanding  eiπ  in a series of complex numbers. These numbers we represent as vectors in the plane. We will see that the partial sums of this series are broken lines like a spiral, twisting around the point -1 steadily approaching to it.

Euler procedure has one required parameter  n is positive integer - the number of displayed terms of the series  for  eiπ  

Optional parameter  a  is any symbol (by default  a=NULL). We use this option if  instead of a static spiral want to see an animated spiral. 

Procedure code can be found in the attached file  Euler.mw

 

Examples of use.

The first example shows  8 terms of the series (broken line of 8 units):

Euler(8);

                

 

 

The terms of the series where  n> = 10  on the same plot can not be seen as very small. In this case, we use  the second plot with magnification of  100 : 1 .  

The second example:

Euler(14);

 

 

 

In the third example, we see an animated broken line. It's  first 9 units represented  on the left plot, and then for n> = 10 on the right plot:

Euler(13, a);

  

 

Euler.mw

Hello.

When I click to start simulation button maple start counting but after that don't open visualization. When I open visualization manually, there aren't results of simulation. Program don´t show any error. It does not work with my models and examples to. Thanks for your help.

Hello,

I use for the 3D visualization the component CAD geometry with STL files.
My STL files are created from CATIA with parts mesured in mm.
In MapleSim, in order to keep mm, I have, of course, to set "mm" in the inspector tab of the components "CAD geometry".
But, I have also to put the scale factor to 0.001.
I don't understand why I should to set it to 0.001 because :
- the CADs from CATIA are in mm.
- and the option in the inspector tab of the components "CAD geometry" is also in mm.
Would you have some precisions about the scale factor for the "CAD geometry" element ?

Thank you for your help.

Where was this graphic of a mountain crater used in Maple?  The top left graphic from here http://www.maplesoft.com/products/maple/features/Visualization.aspx#

I haven't seen it used in any webinars nor have I seen it in the application center.  5 points to anyone who can find it :)

 

Hello everybody,

 

my question concerns the visualizing possibilities of maple:

can maple visualize complex functions? (f(z): C->C)

If so, which possibilities do i have und what is the command for it? Maybe as a coulour diagram, as a vector field (f(x): R^2->R^2) , or as mapping of sets (e.g. curves, grids into new curves and curved lines)?

 

 

 

Thanks in advance

regards

Nikita

 

PS: I am using maple 18.

Hello,

Concerning the 3D visualization of my multibody systems, in the visualization windows, i can see both :
- the display of geomtry of the elements which has been defined as simple forms (as cylindrical geometry)
- the display of the geometry of the elements where the display of the geometry has been defined with CAD.

However, concerning the 3D animation, i have only see the components where the display of the geometry is defined as simple forms (as cylindrical geometry).

Have you some ideas why I can not see the elements which has been defined with CAD ?

For your information, the CAD geometries have been defined with STL files and, in the CAD geometry component, I let the box "Transparent" empty.

Thank you for your help

In this work we show you what to do with the programming of Embedded Components applied to graphics in the Cartesian plane; from the visualization of a point up to three-dimensional objects and also using the Maple language generare own interactive applications for touch screen technology in mobile devices techniques. Given that computers use multicore and designed algorithms that solve calculus problems with very good performance in time; this brings programming to more complex mathematical structures such as in the linear algebra, analytic geometry and advanced methods in numerical analysis. The graphics will show real-time results for the correct use of the parallel programming undertook to bear the procedural technique is well suited to the data structure, curves and surfaces. Interaction in a single graphical container allowing the teaching and / or research the rapid change of parameters; giving a quick interpretation of the results.

 

FAST_UNT_2015.pdf

Programming_Embedded_Components_for_Graphics_in_Maple.mw

Atte.

L.Araujo C.

Physics Pure

Computer Science

 

 

 

Hi, we recently put together a web video on how memes spread on the internet using several visualizations generated from Maple 18:

http://youtu.be/vEhAkEPwESI

Found the new ability to specify a background image for plots to be very helpful.

Hello,

In my model, it seems that I have parameters which are not evaluated.

Indeed, I'm not sure that the parameters defined with relations as you can see in the printscreen are evaluated.

 

One point which helps me to debug my model is to follow the evaluation of the construction of my model with the 3D visualization.

Questions :
1) How can I do to be sure that my parameters are evaluated ?

2) Is it possible to launch the update of the 3D visualization even if I still have some bugs in my model ?

Thank you for help.

Following @acer 's challenge to create some more examples for the Rosetta Code project, I've put together some code that constructs Stem-And-Leaf plots here.

I've also attached a new mathapp ( StemAndLeafDisplay.mw ) that contains the code as well as an interactive example for Stem-Plots. This MathApp is also viewable online on the MapleCloud here.

This older post may also be of interest for anyone looking to make a stem and leaf plot with decimals.

Well-known problem is the problem of placing eight shess queens on an 8×8 chessboard so that no two queens attack each other. In this post, we consider the same problem of placing  m  shess queens on an  n×n  chessboard. The problem has a solution if  n>3  and  m<=n .

Work consists of two procedures. The first procedure  Queens  returns the total number of solutions and saves a complete list of all solutions (global variable  S ). The second procedure  QueensPic  shows the user-defined solutions from the list  S  on the board. Formal argument  t  is the number of solutions in each row of the display. The second procedure should be used in the standard interface, rather than in the classic one, since in the latter it may not work properly.

Queens := proc (m::posint, n::posint)

local It, K, l, L, M, P;

global S, p, q;

It := proc (L)

local P, k, i, j;

M := []; k := nops(L[1]);

for i in L do

for j to n do

if convert([seq(j <> i[s, 2], s = 1 .. k)], `and`) and convert([seq(l[k+1]-i[s, 1] <> i[s, 2]-j, s = 1 .. k)], `and`) and convert([seq(l[k+1]-i[s, 1] <> j-i[s, 2], s = 1 .. k)], `and`) then M := [op(M), [op(i), [l[k+1], j]]]

fi;

od; od;

M;

end proc;

K := combinat:-choose([`$`(1 .. n)], m);

S := [];

for l in K do P := [];

L := [seq([[l[1], i]], i = 1 .. n)];

P := [op(P), op((It@@(m-1))(L))];

S := [op(S), op(P)]

od;

p := args[1]; q := args[2];

nops(S);

end proc:

 

QueensPic := proc (M, t::posint)

local m, n, HL, VL, T, A, N;

uses plottools, plots;

m := p; n := q; N := nops(args[1]);

HL := seq(line([.5, .5+k], [.5+n, .5+k], color = black, thickness = 2), k = 0 .. n);

VL := seq(line([.5+k, .5], [.5+k, .5+n], color = black, thickness = 2), k = 0 .. n);

T := [seq(textplot([seq([op(M[i, j]), Q], j = 1 .. m)], color = red, font = [TIMES, ROMAN, 24]), i = 1 .. N)];

if m <= n and 3 < n then

A := seq(display(HL, VL, T[k], axes = none, scaling = constrained), k = 1 .. N), seq(display(plot([[0, 0]]), axes = none, scaling = constrained), k = 1 .. t*ceil(N/t)-N);

Matrix(ceil(N/t), t, [A]);

display(%);

fi;

end proc:

 

Examples of work:

Queens(5, 6);  

S[70], S[140], S[210];

QueensPic([%], 3); 

                                                                            248

[[1, 5], [2, 3], [3, 6], [4, 4], [6, 1]], [[1, 3], [2, 5], [4, 1], [5, 4], [6, 2]], [[2, 1], [3, 4], [4, 2], [5, 5], [6, 3]]

 

Two solutions of classic problem:

Queens(8, 8); 

S[64..65];

QueensPic(%, 2);

                                                                                      92

[[[1, 5], [2, 8], [3, 4], [4, 1], [5, 7], [6, 2], [7, 6], [8, 3]], [[1, 6], [2, 1], [3, 5], [4, 2], [5, 8], [6, 3], [7, 7], [8, 4]]]

 

 

Queens_problem.mw

Here is a solve problem based on theoritical analytic approach, http://math.stackexchange.com/q/460365/8581. May I ask make me hints in which I can visualze the region f maps. In the question we are speaking about $f(E)$, so I am thinking about a plot illustaring $f(E)$. Thanks for the time and any hints.

Hi,

A right click on the visualization CAD geometry icon, attaching an STL file, activates a pop up list of options. One of the options is "make rigidbody". The units are for the MKS system. I must be doing...

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