We consider a triangle ABC, its circumscribed circle (O), of radius R, its inscribed circle (I) of centre I. We designate by α, β, γ the points of contact of BC, CA, AB with the circle (I), by A', B', C' the points of meeting other than A, B, C, of AI, BI, CI with the circle (O), by the media of BC, CA, AB.
.Establish that there is a conic (E), focus I, tangent to βγ, γα, αβ.
My code : 

restart;
with(geometry);
with(plots); _local(gamma);
_EnvHorizontalName := x; _EnvVerticalName := y;
alias(coor = coordinates);
point(A, -5, -5); point(B, 7, -1); point(C, 1, 5);
triangle(ABC, [A, B, C]); circumcircle(_O, ABC, 'centername' = OO); incircle(_I, ABC, 'centername' = Io);
line(lBC, [B, C]); sol := solve({Equation(_I), Equation(lBC)}, {x, y}); point(alpha, subs(sol, x), subs(sol, y));
line(lCA, [C, A]); sol := solve({Equation(_I), Equation(lCA)}, {x, y}); point(beta, subs(sol, x), subs(sol, y));
line(lAB, [A, B]); sol := solve({Equation(_I), Equation(lAB)}, {x, y}); point(gamma, subs(sol, x), subs(sol, y));
line(lAO, [A, OO]); intersection(Ap, lAO, lBC);
line(lBO, [B, OO]); intersection(Bp, lBO, lCA);
line(lCO, [C, OO]); intersection(Cp, lCO, lAB);
midpoint(l, B, C); midpoint(m, A, C); midpoint(n, A, B);
triangle(T, [alpha, beta, gamma]);
dr := draw([ABC(color = blue), _O(color = red), _I(color = magenta), lAO(color = black), lBO(color = black), lCO(color = black), T(color = red), alpha, beta, gamma, Ap, Bp, Cp, l, m, n], printtext = true);
display([dr], axes = normal, scaling = constrained, size = [800, 800]);
How to find the Equation of (E); Thank you.

Why is the minus sign so weak even in the bold font case? My students sometimes miss it in online tests.
How do we make the minus sign bolder?
Thank you!

mapleatha

I started using maple around 1995 on the Inverse Symbolic Calculator to discover the MRB constant and got put on this list.

Do you consider yourself to be one?

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This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics.

• Ahmes (scribe)
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There seems to be an "issue" when using a indexed name (say x[4]) as the loop index in a seq() mul() or add() command - the indexed name is assigned once the command exits!!

This never(?) happens if the loop index is not an indexed name. A bug??

See the attached which illustrates the issue for the add() command, where x[4] is assigned on exit from add(). The same thing happens if add() is replaced with seq() or mul()

Download aBug.mw

My PC is dual-booted (Win10 and Ubuntu 20.04+KDE). After creating a plot (even the simplest one) and enabling Probe Info as described in  https://www.maplesoft.com/support/help/maple/view.aspx?path=worksheet%2Fplotinterface%2Fpointprobei I do not see tooltip with cursor position. All other tooltips (Palettes, Toolbar etc.) work fine, it is only the probe Info tooltip that does not work. The same plot done while running Maple on Win10 works as expected - tooltip is visible. 

Can someone confirm whether it works for them using Linux? I wonder whether this could be Java-related problem when running on Linux KDE with compositing and using Nvidia driver (e.g. color of tooltip is white on white, or rendering does not work as expected).

I do not remember whether it ever worked on Linux. At this moment I am using Maple2021 but for testing purposes I reinstalled Maple2020 and the problem is the same.

Thanks,

Alex

Hi 

As the titel states: It is possible to create a asymptotic bode plot in maple?

I know how to do a normal bode plot with the DynamicSystem package. But is it possible to get a straight line approximation/ asymptotic bode plot instead?

I discovered the MRB constant (CMRB) while using Maple. Since then, I've found many formulas related to it, including its integrated analog the MKB constant (MKB). They're both found in Google scholar!

However, I am stuck on proving the following.

Also prove the above equation, ReMKB+NoMKB-CMRB=0.

All my similar proofs are found at

https://www.mapleprimes.com/posts/214522-Formulas-For-The-MRB-Constant?sp=214522

Dear Users!

Hope everything going find with you. I want to generate sequence of Spline[i,p], p=1…M as given bellow

restart; M := 3;
for p while p <= M do
(x-x[i])*B[i, p-1]/(x[i+p]-x[i])+(x[i+p+1]-x)*B[i+1, p-1]/(x[i+p+1]-x[i+1]);
B[i, p] := collect(%, [`$`(B[i+s, 0], s = 0 .. M)]);
B[i+1, p] := eval(%, i = i+1)
end do;
for p while p <= M do
Spline[i, p] := B[i, p]
end do

The expression for Spline[i,1] and Spline[i,2] are fine but the expressions of Spline [i,p] p>2 is not in simplified form I got the its simplification like given bellow for Spline[i,3]

Spline[i, 3]:=(x-x[i])^3*B[i, 0]/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+1]-x[i]))+(((x-x[i])*(x-x[i]))*(x[i+2]-x)/((x[i+3]-x[i])*(x[i+2]-x[i])*(x[i+2]-x[i+1]))+(x-x[i])*(x[i+3]-x)*(x-x[i+1])/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1]))+(x[i+4]-x)*(x-x[i+1])^2/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+2]-x[i+1])))*B[i+1, 0]+((x-x[i])*(x[i+3]-x)^2/((x[i+3]-x[i])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+(x[i+4]-x)*(x-x[i+1])*(x[i+3]-x)/((x[i+4]-x[i+1])*(x[i+3]-x[i+1])*(x[i+3]-x[i+2]))+((x[i+4]-x)*(x[i+4]-x))*(x-x[i+2])/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+3]-x[i+2])))*B[i+2, 0]+(x[i+4]-x)^3*B[i+3, 0]/((x[i+4]-x[i+1])*(x[i+4]-x[i+2])*(x[i+4]-x[i+3]));

I am waiting for positive respone. Please take care and thanks in advance

Please help to find the exact solution of any ODE by the >sinh or cosh method. I have attached arbitrary ODE here:

>ode:=U""+c^2*U"+k*c*U"-(3U^2+a)*U''=0

Send my matrix to word as matrix either via maple or phython

Say we have 

A:=Matrix([[0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]])

How to write this matrix to a word file in a matrix form

In general If I have a n cross n matrix  How to write this matrix to a word file in a matrix form

This a Adjacency matrix

If I have several n cross n matricies I want them to be fprintf in the same file one after other giving paragraph space with some name of the matrix at the top.

Hi, when I tried the simple example of Java OpenMaple on Mac, I can compile the code but couldn't run it. It complained about not finding libjopenmaple.jnilib. I checked that library directory, there was /libjopenmaple.jnilib but not libmaplec.dylib. Any suggestions?

> java -Djava.library.path=/Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX -classpath "$MAPLE/java/externalcall.jar:$MAPLE/java/Maple.jar:." test

Error loading libraries: java.lang.UnsatisfiedLinkError: /Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX/libjopenmaple.jnilib: dlopen(/Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX/libjopenmaple.jnilib, 1): Library not loaded: @rpath/libmaplec.dylib
  Referenced from: /Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX/libjopenmaple.jnilib
  Reason: image not found
java.lang.UnsatisfiedLinkError: /Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX/libjopenmaple.jnilib: dlopen(/Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX/libjopenmaple.jnilib, 1): Library not loaded: @rpath/libmaplec.dylib
  Referenced from: /Library/Frameworks/Maple.framework/Versions/2021/bin.APPLE_UNIVERSAL_OSX/libjopenmaple.jnilib
  Reason: image not found
    at java.base/jdk.internal.loader.NativeLibraries.load(Native Method)
    at java.base/jdk.internal.loader.NativeLibraries$NativeLibraryImpl.open(NativeLibraries.java:383)
    at java.base/jdk.internal.loader.NativeLibraries.loadLibrary(NativeLibraries.java:227)
    at java.base/jdk.internal.loader.NativeLibraries.loadLibrary(NativeLibraries.java:169)
    at java.base/jdk.internal.loader.NativeLibraries.findFromPaths(NativeLibraries.java:316)
    at java.base/jdk.internal.loader.NativeLibraries.loadLibrary(NativeLibraries.java:282)
    at java.base/java.lang.ClassLoader.loadLibrary(ClassLoader.java:2440)
    at java.base/java.lang.Runtime.loadLibrary0(Runtime.java:809)
    at java.base/java.lang.System.loadLibrary(System.java:1893)
    at com.maplesoft.openmaple.Engine.<clinit>(Engine.java:23)
    at test.main(test.java:22)
Exception in thread "main" java.lang.UnsatisfiedLinkError: 'long com.maplesoft.openmaple.Engine.getKernel(java.lang.String[], com.maplesoft.openmaple.EngineCallBacks, java.lang.Object, java.lang.Object)'
    at com.maplesoft.openmaple.Engine.getKernel(Native Method)
    at com.maplesoft.openmaple.Engine.<init>(Engine.java:44)
    at test.main(test.java:22)

Since I installed Maple 2021 I have noticed a problem with the left corner of the menu and toolbar.  See the screenshot attached. I don't know if this is a general problem in Win10 or is this a problem with my installation.

I've noticed after a creating a few documents that when save such documents as PDFs on my Mac, the drawing elements in my drawings are misalgined. Is this just a bug or is there a way to prevent this?  I've attached screenshots of the correct drawign in a document and what the result is in a pdf.

help.mw

How to solve Linear first-order PDE by the Lagrange method?

dx/(x) =dy/0=dt/0=du/3=dv/v=dw/w, where x,y,t are independent variables and u,v,w are dependent variables.

Hello

I have used Maple almost daily for the last four years, but a few days ago two students approached me with an issue I had never encountered before. However, it had happened to both of them within a few weeks.

They described the issue as follows: When they opened a random Maple document and they tried to type in simple operators (like +, - or *), Maple would instead write an odd symbol, which none of them recognised as a mathematical symbol.

As they could not find a way to solve the problem within Maple, they tried restarting their computers. When they afterwards reopened Maple, the problem was gone and the operators worked as expected again. Neither of the students has experienced the issue since.

During the last few days, I have been trying to replicate the issue myself without success. Therefore, I also don't have any screenshots to share, so hopefully my simple explanation is enough.

My questions are: Has anyone heard about this issue before? Does anyone know what might have caused it? Is there a way to replicate it and/or prevent it from happening again in the future?

I hope someone is able to clarify it a bit for me! :)

Regards,

Frederik