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11 years, 10 days
East Grinstead, United Kingdom

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These are replies submitted by Ronan

Hope this helps



T := sqrt(6)*sqrt((n-1)*(-15*k^2*n+15*k^2-30*k*n+30*k-15*n+15+sqrt(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)))/(12*sigma^2*(n-1)), -sqrt(6)*sqrt((n-1)*(-15*k^2*n+15*k^2-30*k*n+30*k-15*n+15+sqrt(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)))/(12*sigma^2*(n-1)), sqrt(-(6*(n-1))*(15*k^2*n-15*k^2+30*k*n+sqrt(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)-30*k+15*n-15))/(12*sigma^2*(n-1)), -sqrt(-(6*(n-1))*(15*k^2*n-15*k^2+30*k*n+sqrt(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)-30*k+15*n-15))/(12*sigma^2*(n-1))

(1/12)*6^(1/2)*((n-1)*(-15*k^2*n+15*k^2-30*k*n+30*k-15*n+15+(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)^(1/2)))^(1/2)/(sigma^2*(n-1)), -(1/12)*6^(1/2)*((n-1)*(-15*k^2*n+15*k^2-30*k*n+30*k-15*n+15+(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)^(1/2)))^(1/2)/(sigma^2*(n-1)), (1/12)*(-6*(n-1)*(15*k^2*n-15*k^2+30*k*n+(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)^(1/2)-30*k+15*n-15))^(1/2)/(sigma^2*(n-1)), -(1/12)*(-6*(n-1)*(15*k^2*n-15*k^2+30*k*n+(1920*n*q*sigma^6-1920*q*sigma^6+225*k^4*n^2+5760*Q*n*sigma^3-450*k^4*n+900*k^3*n^2-5760*Q*sigma^3+225*k^4-1800*k^3*n+1350*k^2*n^2+900*k^3-2700*k^2*n+900*k*n^2+1350*k^2-1800*k*n+225*n^2+900*k-450*n+225)^(1/2)-30*k+15*n-15))^(1/2)/(sigma^2*(n-1))



solve(T[1], Q)




solve(T[1], q)



solve(T[1], sigma)

(-3*Q*q^2)^(1/3)/q, -(1/2)*(-3*Q*q^2)^(1/3)/q-((1/2)*I)*3^(1/2)*(-3*Q*q^2)^(1/3)/q, -(1/2)*(-3*Q*q^2)^(1/3)/q+((1/2)*I)*3^(1/2)*(-3*Q*q^2)^(1/3)/q


solve(T[1], k)


solve(T[1], n)*`~nosolution`





Hello, I only palyed with MapleSim a few years ago, so can't answer your specific question. Try this link.  There are several series on MapleSim.

Hope this helps.

@janhardo with the abs in the Maple equation the answer came out negative. I dont know how abs reacts in the fsolve command.

I notice your arctan functions have Pi/90. Have you set GE to working degrees? Radians are better for for general problem solving. That is throwing your equation for solving in Maple.

@janhardo Thanks for that. I checked it out. All I had to do was remove the absolute value from the Area equation after pasting it into Maple.


`` ``

A2 := (-R^2+4*r^2)^(1/2)*R*(-1/2)+arctan((-R^2+4*r^2)^(1/2)/R)*R^2-arctan((-R^2+4*r^2)^(1/2)*R/(R^2-2*r^2))*r^2




r := 1






fsolve(A2 = (1/2)*Pi*r^2, R)









A bit of a side line question here. I got a copy of GE the other day as it is on special offer .How did you make the overlapping area of the circles?

Read this from 2015. @ecterrab  would know if further developments have been implimented along this line.


@vv Thank you. I was not aware of msolve.

@Carl Love Originally I didn't think there would be so many solutions. So that idea went in the bin. Your line of code could will work really well.


@Kitonum Thank you. I didnt realise there would be 4000 solutions. 

 Something similar happened  around the start of the year. I suggested then that if a member with some level of status reples the OP should not be allowed without permission to delete the question.


@acer This is just an example for the question. I picked an arbitrary way of making large numbers and then extracting the data I want. I did try  a billion elements:- no hope ran all night on part 1 of your code. I have been wondering about what one would do with larger arrays. But that is not the immediate concern. It would be interesting to see how this runs on a a processor with say 16+ physical cores expecially a Ryzen.

@acer  I am using an I7-7700 4.8Ghz 64G ram on Win10. Maple 2019.0. For some reason I can't upload the maple files so it is pdfs.

I am aware of the timing variations you mentioned.




I like Threads:-Seq because it is simple for me to understand.


@tomleslie Sorry for the delay in replying to you.

Attached is a pdf of the worksheet run for 100million. 430secs parallel.!!!!

Lately I cant seem to upload maple documents. Just get a failed message.




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