| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1616.1 | A start... | CHOVAX::YOUNG | Eschew Turf | Tue May 26 1992 21:00 | 4 |
| I get
0.00000050005000876...
-- Barry
|
| 1616.2 | | GUESS::DERAMO | Dan D'Eramo, zfc::deramo | Wed May 27 1992 12:45 | 19 |
| If you write m as k^2 + i then { sqrt(m) } is
sqrt(m) - k which when multiplied by (sqrt(m) + k)/(sqrt(m) + k)
becomes i/(sqrt(m) + k) = i/(sqrt(k^2 + i) + k).
You can get {sqrt(m)} and {sqrt(n)} very close to each
other by taking i=1 so that {sqrt(m)} = 1/(sqrt(k^2 + 1) + k)
Now double both numerator and denominator to get the
(equal) value 2/(sqrt((2k)^2 + 4) + 2k). If you now take
n = (2k)^2 + 2 you see that {sqrt(n)} is very close to
that; the difference is that instead of +4 inside the
radical it has +2.
So I tried 499^2 + 1 and (2 * 499)^2 + 2 and got an
absolute difference of a little over 5.03 * 10^-10.
A computer search found a slightly smaller value which
given the above seemed obvious in hindsight.
Dan
|
| 1616.3 | the width of the first sliver of the moon | HANNAH::OSMAN | see HANNAH::IGLOO$:[OSMAN]ERIC.VT240 | Fri May 29 1992 17:06 | 16 |
|
That business of "close" square roots reminds me of something I've thought
about when contemplating the moon.
We've all noticed that slight sliver of a moon that appears the first night
after the "new moon" ("new moon" is when moon is totally invisible because sun
is so close to directly behind it as to not illuminate any of it).
What I've noticed is that from month to month, the thinness of that first
sliver differs. Some months have thinner first nights than others. Can
we predict a pattern of which months will have thinner first slivers ?
What pattern of first sliver width exists ?
/Eric
|
| 1616.4 | FYI, I have an old copy | VMSDEV::HALLYB | Fish have no concept of fire. | Mon Jun 01 1992 13:16 | 13 |
| > What I've noticed is that from month to month, the thinness of that first
> sliver differs. Some months have thinner first nights than others. Can
> we predict a pattern of which months will have thinner first slivers ?
> What pattern of first sliver width exists ?
Eric, you ol' lunatic, you've lurched into a solvable problem.
MR4SRV::ASTRONOMY talks a lot about this sort of thing from an
empirical perspective. In particular the ASTRO program written
by Tony Wachs (RIP) outputs the % illumination of the moon.
Of course it does depend on your location; ASTRO was written
for Newton MA, USA.
John
|
| 1616.5 | howling at the moon... | HANNAH::OSMAN | see HANNAH::IGLOO$:[OSMAN]ERIC.VT240 | Mon Jun 08 1992 16:17 | 4 |
|
So what's the answer, John. What are the sliver percentages for, say, the
12-13 new moons in 1992. Can you read that from the program ?
|