{{{id=26|
# Copyright 2009, P. Lutus
# Released under the GPL (http://www.gnu.org/copyleft/gpl.html)
///
}}}
{{{id=0|
#auto
# reset() # commented out for now -- ticket 7255
# special equation rendering
def render(x,name = "temp.png",size = "normal"):
if(type(x) != type("")): x = latex(x)
latex.eval("\\" + size + " $" + x + "$",{},"",name)
var('a d v R r y L')
forget()
assume(R >= 0)
assume(r >= 0)
assume(L >= 0)
assume(y >= 0)
///
}}}
{{{id=50|
var('a d v R r y L')
///
(a, d, v, R, r, y, L)
}}}
{{{id=23|
#auto
acaps(y,R) = pi*(2*R-y)*y
render(a == acaps(y,R),"equ_area_caps.png","large")
///
}}}
{{{id=3|
#auto
vcaps(y,r,R) = integrate(acaps(y,R)*r/R,y)
render(v == vcaps(y,r,R),"equ_vol_caps.png","large")
///
}}}
{{{id=35|
plot(vcaps(y,10,10),(y,0,20),figsize=(4,3))
///
}}}
{{{id=36|
render(latex("$v\_{sphere} = \\frac {4}{3}\pi r^3 $"),"equ_sphere_volume.png","large")
///
}}}
{{{id=37|
vcaps(20,10,10)
///
4000/3*pi
}}}
{{{id=24|
#auto
dcyl(y,R) = 2*sqrt((2*R-y)*y)
render(d == dcyl(y,R),"equ_dia_cyl.png","large")
///
}}}
{{{id=28|
plot(dcyl(y,10),(y,0,20),figsize=(4,2.5))
///
}}}
{{{id=29|
#auto
vcyl(y,R,L) = ((integrate(dcyl(y,R),y)) * L).full_simplify()
render(v == vcyl(y,R,L),"equ_vol_cylinder1.png","large")
///
}}}
{{{id=30|
plot(vcyl(y,10,1),(y,0,20),figsize=(4,3))
///
}}}
{{{id=32|
render(latex("$\int cos(x) dx = sin(x) + C $"),"equ_integration_constant.png","large")
///
}}}
{{{id=33|
render(latex("$v\_{cyl} = \pi R^2 L $"),"equ_cylinder_volume.png","large")
///
}}}
{{{id=7|
%auto
vcyl(y,R,L) = ((integrate(dcyl(y,R),y) + pi*R^2) * L).full_simplify()
render(v == vcyl(y,R,L),"equ_vol_cylinder2.png","large")
///
}}}
{{{id=34|
vcyl(20,10,10)
///
1000*pi
}}}
{{{id=31|
plot(vcyl(y,10,1),(y,0,20),figsize=(4,3))
///
}}}
{{{id=25|
%auto
vfull(y,r,R,L) = (vcaps(y,r,R,L) + vcyl(y,R,L)).full_simplify()
render(v == vfull(y,r,R,L),"equ_vol_full.png","large")
///
}}}
{{{id=40|
render(latex(v == pi * R^2 * L + 4/3 * pi * R^3 * r/R))
///
}}}
{{{id=41|
N(pi * 31 * 13^2 + 4/3 * pi * 13^2 * 7)
///
21414.1427244192
}}}
{{{id=43|
N(vfull(26,7,13,31))
///
21414.1427244192
}}}
{{{id=17|
plot(vfull(y,5,10,10),y,0,20,figsize=(4,3))
///
}}}
{{{id=47|
///
}}}
{{{id=48|
render(latex("$\\frac {y} {(3x)} $"),"equ_simplify_target.png","Large")
///
}}}
{{{id=49|
render(latex("$\\frac {y} {3x} $"),"equ_simplify_mathematica.png","Large")
///
}}}
{{{id=45|
render((y/(3*x)).full_simplify(),"equ_simplify_fail.png","Large")
///
}}}
{{{id=46|
///
}}}