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MaplePrimes Activity

These are questions asked by Earl

Maple 15

PrimesQuestion.mw

Please let me know if this link correctly accesses my worksheet. If not, I will copy its contents into this question.

Which ODE in the worksheet, if any, provides the correct answer?

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Why do braces limit evaluation?...

Maple 15

Is there a help page which explains why braces provide the partial text evaluation in this code?

Why are ranges exceeded?...

Maple 15

eq1 := z = y*log(x): eq2 := z = y+x*log(x):

DispIntersecting := implicitplot3d([eq1, eq2], x = 0 .. 10, y = -30 .. 30, z = -40 .. 40, color = [blue, green]):

solve({eq1, eq2}, [x, y, z]);

assign(%):

DispIntersection := spacecurve([x, y, z], x = 0.1e-2 .. 10, color = red, view = [0 .. 10, -30 .. 30, -40 .. 40]):

display(DispIntersecting, DispIntersection, axes = boxed, scaling = constrained);

Why do these commands succeed?...

Maple

From a Maple Primes answer two years ago:

f(x,y) is the equation of a line through point [m,n]. The solve command finds values of a and b for which f(x,y) are lines through [m,n] and tangent to x^2 + y^2 = r^2.

f := proc (x, y) options operator, arrow; a*(x-m)+b*(y-n) end proc

solve([f(0, 0) = r, a^2+b^2 = 1], [a, b])

These commands are far from the conventional solution. Why do they provide the correct answers?

Sliding ellipse problem ...

Maple

Has anyone solved this problem from an older Putnam paper?

An ellipse sitting in the first quadrant with its major axis parallel to the x axis is tangent to the positive x and y axes.

It slides clockwise within the first quadrant while maintaining tangency to both positive axes until its major axis is parallel to the y axis.

Prove that the locus of its centre is the arc of a circle.

I have crudely animated this motion by sliding the axes around the stationary ellipse. Is there a more elegant animation which slides the ellipse against stationary axes?

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