In honor of Pi Day, in this blog I would like to show that the MRB constant has some meaning in our day to day lives. The first two messages are lifted from a discussion group.

I’ve written in the past of how the push for more efficient, “greener” designs are driving innovation in important industries like auto, aerospace, and power.  Over the past few years, we’ve met countless engineers around the world who are working hard to transform conventional designs to highly refined optimal designs in tune with modern realities, and some are, of course, throwing out old ideas all together and venturing into exotic power sources and radical platforms that used to be the stuff of science fiction. Last week I had one of the more interesting and enjoyable encounters with such a group of very talented green engineers.

It would be good if we could flag for admin scrutiny not just posts but also user handles.

It might help with this kind of nonsense.

Amdahl's Law is a formula for determining the theoretical speed up when parallelizing a function. For example, imagine we wanted to parallelize a function that spends 90% of its time in one algorithm. If there is a parallel version of that algorithm, how much faster would the entire function run with 2, 4 or more cores?

In our previous article we described a packed representation for sparse polynomials is designed for scalability and high performance. The expand and divide commands in Maple 14 use this representation internally to multiply and divide polynomials with integer coefficients, converting to and from Maple's generic data structure described here. In this post I want to show you how these algorithms work and why they are fast. It's a critical stepping stone for our next topic, which is parallelization.

Back in September, I posted an announcement about our plans for the new version of MaplePrimes.  Well a few months and many, many hours of development later, we are approaching the end point!

In the book Introduction to Maple by Andre Heck books.google.co.uk/books  the author manage to plot the canadian flag
in maple by using the following code:
 

restart:
with(plots):
with(plottools):

X := proc (cc) local S, R, mapleleaf, rectangles, border:

S := proc (t) options operator, arrow; 100/(100+(t-(1/2)*Pi)^8) end proc:
R := proc (t) options operator, arrow; S(t)*(2-sin(7*t)-(1/2)*cos(30*t)) end proc:
mapleleaf := plot([R, proc (t) options operator, arrow; t end proc, -(1/2)*Pi .. (3/2)*Pi], coords = polar, axes = none, color = cc, numpoints = 1000):
mapleleaf := subs(CURVES = POLYGONS, mapleleaf):
rectangles := rectangle([-5, -1], [-3, 4], color = cc), rectangle([3, -1], [5, 4], color = cc); border := plot({-1, 4}, -3 .. 3, color = black):

display([mapleleaf, rectangles, border], view = [-5 .. 5, -1 .. 4]) ;

end proc:

Ap := Array(1 .. 2, 1 .. 2):   

Ap[1, 1] := X(red):         Ap[1, 2] := X(blue):    
Ap[2, 1] := X("green"):    Ap[2, 2] := X("Orchid"):

display(Ap);

I think Maple should emphasize occupational and problem specific packages, like its TA software for teachers. Maple should have a package or set of packages for each type of engineer: electrical,hydrological, etc. Actually, Maple should promote packages for all professions that tend to need it. An abundance of packages would enable many new users to benefit from the power of maple with the experience of the advanced users who helped develop the packages.

Dear Moderator,

What is the reason that I have to request one-time password again and again?

This annoying behaviour started a few months ago.

Thanks,   Sandor

Zooming in on plots is rather annoying.  Always zooming and then having to pan the plot back into view.

Rather it would be much nicer to zoom in on a plot from the position of the pointer and not from the center of the plot.

Recently, I had to write a brief introduction to the precalculus topic "Vertical Translation of Graphs." Figure 1 ( in black, in red) says just about everything. 

But is the issue all that trivial? Although the curves are vertically separated by one unit, they don't look uniformly spaced. The animation in Figure 2 helps overcome the optical illusion that makes it seem like the black curve bends towards the red curve, even though the curves are congruent.

This is an update to my earlier post on the Rossler system, one of the simplest examples of a dynamical system in 3 dimensions that can exhibit deterministic chaos.

restart;

interface(displayprecision=10):

PDEtools:-declare(prime=t,quiet):

ross_x:=diff(x(t),t)=-y(t)-z(t):

ross_y:=diff(y(t),t)=x(t)+a*y(t):

ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):

rossler_sys:=ross_x,ross_y,ross_z;

#Find fixed points:

 Consider the sequence of divergent series in part evaluated by the following maple input.

f1 := seq((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 1/10 .. 9*(1/10), 1/10): evalf(f1);

and

f2 := `$`((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 2 .. 10): evalf(f2);

The Maple output, which is the MRB constant