ʃdxdydz UδV + ʃdσ U [dV/dώ] - 4πU’’’ = ʃdxdydz VδU + ʃdσ V [dV/dώ] - 4πV’ .... (3')
I have no idea what this equation tells us, and could never have learnt mathematics to the level needed to solve it! It is rather elegant aesthetically, though a mathematician would say it is "elegant" technically.
- It is attributed to (discovered by)? the British mathematician George Green (1793 - 1841). I found it quoted as decoration on a mug I saved from clearing out my section's "tea-boat" room at work; the mug also carying a drawing of the wind-mill that refers to Green being from a family of millers in the Nottinghamshire village of Snienton.
Hazarding a guess at what it is about....
It is Calculus. That's a start. It refers the leading Integrals to (x, y, z) Differences, suggesting three dimensions. I don't know the significance of U but V is often short for Volume. The 4pi terms make me think of Solids of Revolution. The apostrophes and the suffix (3') shows it is only one of a set of equations or identities within the particular study...
So I hazard a guess that it is on the relationships between mathematically-regular, compound-curved, surfaces and the volumes they enclose.
It only really comes alive when you plug actual values into it, when presumably if the LHS ends up =, say, 42 then the RHS will also = 42!
So there you are, if we had no numbers. Geo. Green's equation could not exist, let alone do anything! Though we'd not be able to talk about it like this, either.....
This post was edited by Durdle at December 26, 2018 5:21 PM MST