[ot][ot][ot][personal] whirligig small thoughts

[Undescribed Horrific Abuse, One Victim & Survivor of Many]

[:) ?]

wedge_volume = integral(triangle_area, x=-r_sphere..+r_sphere)
triangle_area = 1/2 r_slice^2 dtheta
r_slice = sqrt(r_sphere^2 - x^2)

wedge_volume = I{-r_sphere..+ triangle_area dx
wedge_volume = I{-r_sphere..+ 1/2 r_slice^2 dtheta dx
wedge_volume = I{-r_sphere..+ 1/2 sqrt(r_sphere^2 - x^2)^2 dtheta dx
wedge_volume = I{-r_sphere..+ 1/2 (r_sphere^2 - x^2) dtheta dx

so one integral is represented, but hte other isn't. the dtheta
integral is missing.
i guess it would make sense to have put it in ....... no wait, we're
consider a differential volume, there should be only one integral.
we'll integrate dtheta later.
given rules of multiplication i think i can factor the dtheta out of
the integral?

wedge_volume = dtheta/2 I{-r_sphere..+ (r_sphere^2 - x^2) dx

i would put next step right here, but it seems other parts put it in
separate thing. [maybe in middle is