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The downloaded worksheet below displays 3 points on the unit sphere which define a solid angle with a triangular face. The sides of the solid angle's are red arcs on the surface of the sphere and red radii which outline the planar sides within the sphere.

Three questions:

1. Is there a way to make the surfaces of the solid triangle more apparent by filling them with color?

2. Is there a way to calculate the area of the face on the surface of the sphere?

3. Is there a way to calculate the volume of the solid triangle?


Download Mechanics;

firstly apologies in advance for stuff in this question such as "triangle symbol",  my computer is pretty old. 

ok so i was confused a bit here, what i'm trying to do is write a maple procedure that computes Af for a given f contained in V . except we only need to correct the bug in the script below. This script demonstrates such a procedure in the case that omega is a square. The domain is given here as the negative set of a function F contained in V .  I have left in notes where/what i think we need to do but i dunno how to...

N:=10 ; # Global Var
Average := proc(F, f0) local f, i, j;
f := f0; # !!!!!!!!!!!!!! something is bad here...
for i to N do for j to N do
if F(i, j) < 0 then
f[i, j] := (f0[i - 1, j] + f0[i + 1, j] + f0[i, j + 1] + f0[i, j - 1])/4 ;
end if;
end do;end do;
return f;
end proc;
f0:=Matrix(N,F); # just to have something to test the procedure
Average(F,f0); # does not return the expected average, modifies f0


the necessary information we were given to produce this so far was..

Let N be a positive integer and [N] = {i contained in N | 1<= i <=N }  Let "Omega" C {(i,j) contained in [N] x [N] | 2<=i,j<=N-1} be a subset. Let V = R^([N]x[N]) be the vector space of real valued functions [N]x[N] -> R
and A, "triangle symbol":V->V (average) and "triangle symbole" (Laplacian) be the linear maps such that
[Af](i; j) = f(i; j)      if (i; j) not contained in "Omega"   OR

                             [f(i, j + 1) + f(i, j - 1) + f(i + 1, j) + f(i - 1, j)]/4 if (i,j) is contained in "Omega"

["traingle symbol"f](i,j) =  0 if (i,j) isnt contained in "Omega"   OR

                            ( f(i,j) - [f(i, j + 1) + f(i, j - 1) + f(i + 1, j) + f(i - 1, j)]/4 )    if (i,j) is contained in "Omega"

 Please and thank you for any help in advance <3


In this post we present another compact proof of this remarkable theorem without using  geometry package.
The proof uses a procedure called  Cc , which for three points returns a list of the coordinates of the center and the radius of the circumscribed circle.



local x1, y1, x2, y2, x3, y3, x, y;

x1,y1:=op(A);  x2,y2:=op(B);  x3,y3:=op(C);

solve({(x2-x1)*(x-(x1+x2)/2)+(y2-y1)*(y-(y1+y2)/2)=0, (x2-x3)*(x-(x2+x3)/2)+(y2-y3)*(y-(y2+y3)/2)=0},{x,y});


[simplify([x,y]), simplify(sqrt((x-x1)^2+(y-y1)^2))];

end proc:

Proof for arbitrary triangle:

A, B, C:=[x1,y1], [x2,y2], [x3,y3]:

A1, B1, C1, M:=(B+C)/2, (A+C)/2, (A+B)/2, (A+B+C)/3:

P1:=Cc(A,M,B1)[1]: P2:=Cc(B1,M,C)[1]: P3:=Cc(C,M,A1)[1]:

P4:=Cc(A1,M,B)[1]: P5:=Cc(B,M,C1)[1]: P6:=Cc(C1,M,A)[1]:

Cc1:=Cc(P1,P2,P3):  Cc2:=Cc(P4,P5,P6):




I'm trying to plot the 3d graph of a solid in Maple 16. The solid is generated by equilateral triangles. One vertex is  A(x,0,0), and the other one, B, moves on the circunference described by: y^2+x^2=121, z=0. The AB segment is always parallel to the Y axis and the triangles are in the yz plane. In other words, one side (of each triangle) is sqrt(121-x^2).

I tried using the spacecurve command to start plotting lines but then I didn't know how...

I've tried all sorts of different assignments for a,b and c but all still give me an error 
for root 2. 
have tried posint, int, nonnegative, positve but none work 
any help would be appreciated. 
if (a+b) > c then print (a,b,c,`are lengths of a triangle`)
#this is according to the triangle inequality theorem
elif (a+b) < c then print ...

Q3) Write a procedure, isTriangle, to determine if any three given
 numbers represent the lengths of the sides of a triangle.
The procedure should be able to deal with any input.

I have done the following and get an error

isTriangle:=proc(a,b,c::nonnegative and numeric)
if (a^2+b^2)=c^2 then print (a,b,c "represent the sides of a triangle")
end if;
end proc;
Error, unexpected string

I want to find a triangle with the vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3) knowing that the point G(1,1,1) is centroid of the triagle ABC and x1, y1, z1, x2, y2, z2, x3, y3, z3 are integer numbers, but I can not find. How do I tell Maple to do that? 


Hi all,

I wonder if there is a way to extract the upper/lower triangle entries from a matrix?

Basically, I want to creat a column vector of the none zero entries in "UpperTriangle(m);"


Also, aside, is there a way to quickly assign those entries...

I want to make triangle oAB with the angle AoB equal to 2*Pi/3. The following code is not right.

> restart:





for x1 to N do


for y1 from x1 to N do

 for z1 from y1 to N do

 for x2 to N do

 for y2 to N do

 for z2 to N do




I want to find coordinates M of the bisector of the interior angle at the vertex A of the triangle ABC.










The triangle ABC with A(4,7,5),  B(3,7,-2),  C(0,2,2) is a equilateral triangle. How do i find coordinates vertices of a equilateral triangle which their coodinates are integer numbers? Please help me. Thank you very much.

hi all

i am trying to write some code to display:

a) hexagon tiling, rather like a honeycomb in 2D

b)  equilateral triangles tiling , all space filled by said triangles. eg a series of triangles whose base is parallel to base of plot, with inverted triangles filling in the remaining spaces

c) square tiling

for a,b c I  want about 50 of each displayed (all of edge length 1) on the one plot

d)  some code...

I am playing around with Linear least squares. I have this system of equations

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