Items tagged with center



In some cases when dealing with vectofields an such the are integral has to be expressed in terms of r(t).

the general form for r is r^2=(r*cos(t)-a)^2+(r*sin(t)-b)^2, When I solve this in maple it seems like I get the inverse of the desired result.

If I knew that was always the case I could just inverse my result to get the right expression for r, but im not sure if it only applies for this particular cas or all cases.

I would be happy if anyone took a quick look and suggested a way to obtain the desired solution for any center (a,b) for the circle.



Expression for radius, circle centred at (a,b)

RA := r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2

r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2


isolate(r^2 = (r*cos(t)-a)^2+(r*sin(t)-b)^2, r)

r = (1/2)*(a^2+b^2)/(cos(t)*a+b*sin(t))


eval(%, [a = -1, b = 0])

r = -(1/2)/cos(t)


plot3d([-2*x, x^2+y^2], y = -sqrt(-x^2-2*x) .. sqrt(-x^2-2*x), x = -2 .. 0, color = [green, red], orientation = [0, 0, 0])


(1/2)*Pi <= t and t <= 3*Pi*(1/2)

(1/2)*Pi <= t and t <= (3/2)*Pi


0 <= r and r <= -2*cos(t)

0 <= r and r <= -2*cos(t)


Area_off_center = int(r, [r = 0 .. -2*cos(t), t = (1/2)*Pi .. 3*Pi*(1/2)]); 1; Area_at_center = int(r, [r = 0 .. 1, t = 0 .. 2*Pi])

Area_off_center = Pi


Area_at_center = Pi






I would also happily like to know how I can solve for the range r can take, obviously in the example i´m working with here r starts at 0, but that is not always the case i guess.


Thank you, your help is much apperciated

I have some triangles ABC with vertices

1) A(-13,-5,5), B(-5,11,-11), C(-3,-9,15) has centre of out circle is (3, 3, 3), orthocentre (-27, -9, 3) and centroid (-7, -1, -3). 

2) A(-6,6,-1), B(-5,-1,-3), C(2,10,7) has centre of out circle is (1, 2, 3), orthocentre (-11, 11, -3) and centroid (-3, 5, 1). 

How can I write a program to find a triangle with integer coordinates of vertices, centroid, orthocenter and center of the triangle in geometry 3D? 

The application center has undergone some changes.  I usually like to see if things are working properly.

There are currently problems with searching maplesim models.  Doing an advanced search under maplesim5 does not bring up all maplesim 5 models, such as

- Flow dynamics in liquid connected tanks
- Double glazed windows

The next issue is with regards to phantom applications that are there but not linked.  For example:  Advanced...

After making a search for applications in the applications center, they are ordered in some crazy unknown way. 

They do not appear to be ordered alphabetically by author, nor by title and also they have no date published attached to the searched list. 

Searching for all titles by product Maple 16, we find that TEST APPLICATION created July 31 is actually listed behind Robert Lopez's Classroom Tips and Techniques: Slider-Control of Parameters in Numeric...

Ive tried this for hours and can't get it to work. Any help would be greatly appreciated. I need to 

find a 10 significant figure approximation to the 10th derivative of

evaluated at x = -2.

Ive tried using this maple command:


Of 4000 daily visitors of the site pages Russian Maple ApCent (during the examination session) 3800 - Russian students, and only 100 - Ukrainian. Sad.
Dynamics of visits:
June 2010 - 44.656 (35,000 for one day! - Unified state examination in mathematics (EGE) 

i need to calculate the radius of an arc. i have that the chord lenght is 96 inches and the distance between the chord and the arc is 6 inches perpendicular from the center of the chord. assuming that i am working with a circle.... how do i calculate the radius of the circle????

At there seems to be a quite
interesting contribution by Rob Corless, Erik Postma and David Stoutemyer.

It would be helpfull and interesting to provide the according paper as well (through a link?).
Hope this message is read by Eric Postma.


PS: I wanted to drop an according message at the center as comment, but failed to log in,

Page 1 of 1