Time, Gentlemen, Please!

[grip at netcom.com]

On Fri, 4 Oct 1996, Henry Musikar wrote:

> 10:10 isn't quite perfect, because the hour hand is past ten at that 
> time. 8:20 is the same. I don't think our man/boy would make that mistake. 
> I have heard the "Time Lincoln was Shot" theory, and I like it. Anyone want 
> to take a stab, just for s&g's, at the actual symmetrically perfect 
> times? 

Sure. Just e-mail the s&g's to me. :)

Let T be the time in minutes after noon/midnight; H be the angle of the 
hour hand at time T; and M be the angle of the minute hand at time T. 
(Angles measured in degrees.) Then you have the relationship that M = 6T 
and H = T/2. You also have that M = N(360) - H, where the N indicates the 
next Hour time. So for 12:55, for example, N =1, so 6T = 1(360) - T/2.
Solving for T gives a value of 55 minutes and a fraction more than 23 
seconds. For 1:50 N = 2 and T = 110 minutes and about 46.2 seconds. This 
is 1:50:46.2. At 10:10 then, if my analysis is correct, the time of 
symmetry should be close to 10:09:13.85.

grip