The Total Gravity of N Layers

xxxxxxxxxx

 

1

var('D,G,i,N')

2

Vi(D,i)=4/3*pi*((D+i)/2)^3-4/3*pi*((D+i-1)/2)^3

3

v(D,i)=Vi(D,i).expand().simplify().factor()

4

pretty_print('the volume of the i-th layer:')

5

pretty_print(v(D,i))

6

P(D,G,N)=sum(v(D,i)*G/i,i,1,N)

7

pretty_print('the total gravity of N layers:')

8

pretty_print(P(D,G,N).factor())

9

from sage.plot.plot3d.shapes import Sphere

10

def display_shell(D,G,N):

11

    g=Graphics(); s=Sphere(D,color='gray',frame=false)

12

    layers=sum([Sphere(D+i,opacity=G/i) for i in [1..N]])

13

    st='<center>D=%d, G=%.2f, N=%d => P=%f</center>'

14

    pretty_print(html(st%(D,G,N,P(D,G,N))))

15

    (g+s+layers).show()

16

display_shell(7,.75,10)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

---

Messages