MaplePrimes - Newest Comments

Constructing a family of planes

Rouben Rostamian — Fri, 02 Oct 2026 01:22:50 Z

This website still fails to display uploaded worksheets. Is anyone looking after this?

I will write L for the line that you have called the axis of the bundle.

Let a be a (nonzero) vector along L, and let p the position vector of a given point on L.

Pick an arbitrary nonzero vector s which iis not parallel to a. Any such vector will do. Then the vector b = a x s would be orthogonal to a, and the vector c = a x b would be orthogonal to both a and b.

Normalize the vectors a, b, and c, that is, divide them by their own lengths. Then for any angle θ, the unit vector d = b cos θ + c sin θ is in the plane of b and c, and therefore perpendicular to a. It follows that a parametric equation for the planes spanned by a and d and going through the point p is
r = p + u a + v d.
where u and v are the parameters of the plane. As θ varies, you obtain the bundle of planes that you are looking for.

See the attached worksheet for a worked-out example. The following illustration is extracted from that worksheet. The point p and the vector a are shown in black.

Download mw2.mw

That is a nice work

lemelinm — Thu, 01 Oct 2026 15:52:04 Z

@sand15 Since finding maximum (or minimum) on 3D functions can be sometrime tricky. For example f(x,y)=sin(x)*cos(x). I think that the user could have to give the point and the planes that he want.

Byt the way, see what the new software ExaktAI from our friend Edgardo can do when I used it with maple as computing engine and save it as maple document.:

plot3d(sin(x)*cos(y), x = -10 .. 10, y = -10 .. 10)

We see the grid and as the mouse move, we wee lines that shows the plane, if I underestand correctly the result. It is nice. It was save as a maple document. But when I opened it in Maple 2026, the magic was gone. Too bad. It should be a plot,options

Thank you for taking the time to answer me.

That looks like what I want

lemelinm — Thu, 01 Oct 2026 15:41:46 Z

@Carl Love Thank you for taking the time to answer me.

Nice!

lemelinm — Thu, 01 Oct 2026 15:40:34 Z

@C_R Thank you for taking the time to answer me. I love the use of zgradient. I will use that command more:

colorscheme = ["zgradient", ["blue", green, "yellow", "red"], zrange = 0 .. 1]

But I do want the effect Matlab style.

fixed

dharr — Wed, 30 Sep 2026 21:36:53 Z

@salim-barzani

i think file is not update!

salim-barzani — Wed, 30 Sep 2026 19:03:01 Z

@dharr i checked but the file is same , i didnt see any fsolve command !