- #1

- 535

- 72

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter geoffrey159
- Start date

- #1

- 535

- 72

- #2

- 3,893

- 1,460

If you divide the number of seconds in twelve hours by eleven, you get the period between passings. You can then use that to specify the ten times, down to the second, when such passings occur.

ie the time of the ten passings is

noon + ##k\cdot\frac{12\cdot60\cdot 60}{11}## seconds, for ##k\in\{1,2,...,10\}##

There are of course another ten such times between midnight and noon. They are the same times with

- #3

- 535

- 72

spoiler

- #4

- 263

- 180

Yes

- #5

- 462

- 138

What would you answer at the nearest second ?

At the nearest second I would answer "Well..." because one second is to fast to come up with a better answer.

- #6

- 3,379

- 944

On the other hand Dad's mechanical clock compared to a Caesium 133 based atomic clock is so wildly innaccurate that you might as well call it random.

- #7

- 535

- 72

An alternative answer is the following: there are 60 equal angular sections on the watch. Every hour, the hour needle crosses exactly five angular sections, and between two consecutive hours, it crosses an additional 1/12 of what crosses the minutes needle. A relationship between time ##h : m## and the positions ##x_h## and ##x_m## (in number of angular sections) of the needles is

##x_m = m \quad## and ##\quad x_h = 5(h \text{ mod } 12)+ x_m/12##

The problem consists in finding the pairs ##(h,m)## such that ##x_h = x_m##.

This happens whenever ##m = \frac{5\times 12 \times (h \text{ mod } 12) } {11} ##.

The fractional part of ##m## must be converted in seconds by multiplying it by 60.

So the exact times of needles alignments are :

## h## hours, ##\lfloor \frac{5\times 12 \times (h \text{ mod } 12) } {11} \rfloor ## minutes, and ## 60\times ( \frac{5\times 12 \times (h \text{ mod } 12) } {11} - \lfloor \frac{5\times 12 \times (h \text{ mod } 12) } {11} \rfloor)## seconds.

So if you want to see a needle eclipse, take a look at your watch at 1:05:27 !!!

Share: