Wikipedia:Reference desk/Archives/Mathematics/2019 August 21

= August 21 =

Has this formula ever been used before in some way or form?
$$v={C_m+({(C_e - C_m) \cdot {D_g \over {C_m \div 4}})} \over 2} \div t$$ -- MrHumanPersonGuy (talk) 10:13, 21 August 2019 (UTC)
 * $$v$$ = velocity (i.e. rate of expansion)
 * $$C_m$$ = circumference at the meridian (i.e. where the spheroid's cross-section is most oblate)
 * $$C_e$$ = circumference at the equator (i.e. where the spheroid's cross-section is least oblate)
 * $$D_g$$ = geodesic distance from a given surface point to the nearest of either two surface points closest to the spheroid's center
 * $$t$$ = time taken for a circular phenomenon to encase the entire spheroid
 * And what is this formula supposed to produce? Ruslik_ Zero 20:09, 21 August 2019 (UTC)
 * To put it this way; if a gray-goo type mass spawns somewhere on a planet and it was known when it would encase the entire planet, then this formula could be used to figure out the average speed of the mass's outward expansion across the planet's surface. -- MrHumanPersonGuy (talk) 22:37, 21 August 2019 (UTC)


 * One might naïvely expect (a) that the antipodal point was the last to be affected and (b) that for an oblate spheroid, the shortest route between antipodal points was along a meridian. In which case


 * $$v = \frac{C_{m}}{2 t}$$


 * which is similar, but not the same. catslash (talk) 22:41, 21 August 2019 (UTC)
 * Though (a) could be incorrect. A pair of points, just (roughly) east and west of the antipodal point might be the last affected (supposing that the wavefronts converging on the antipodal point from the north and south were convex when they met there). catslash (talk) 22:51, 21 August 2019 (UTC)