
All the symmetrical watch faces and code to generate them - jgrahamc
https://blog.jgc.org/2020/06/all-symmetrical-watch-faces-and-code-to.html
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mkl
I like thinking about this kind of thing graphically:
[https://www.desmos.com/calculator/mlsp0u98go](https://www.desmos.com/calculator/mlsp0u98go)

The hands are symmetrical where the minute hand coincides with a backwards-
going hour hand, and the minute hand goes 12 times as fast.

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userbinator
This reminds me of an old algebra textbook I have from the beginning of the
20th century, which had a series of similar problems relating to the angle of
clock hands.

I also found the nicely typeset explanation rather pleasing to look at --- it
reminds me of old maths books as well --- but the explicit multiplication
symbols are a bit odd, as is the lack of simplification; here's how I was
taught to show the work:

    
    
        H(h, m) = 360 - M(h, m)
        30h + m/2 = 360 - 6m
        6m + m/2 = 360 - 30h
        13m/2 = 30(12 - h)
        m = 60(12 - h)/13
    

_If I modify my program to show the location of the second hand you can see
that perfect symmetry between hour and minute hands gets messed up by its
presence._

...which then leads to the next question, "at what times are the hands
equidistant from each other?" (That's a bit of a trick question.)

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jgrahamc
I deliberately used the explicit \times symbol in the LaTeX because I figured
that anyone who had a hard time do that mathematics themselves might also have
a hard time with things like 30h instead of 30 x h. I belaboured the
simplification a bit hoping to help the reader.

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aaronax
It is a bit disturbing to see the second hand drawn as the shortest hand in
the graphic of three hands. My mind is well-trained that the shortest hand
should be the hour!

I couldn't find or think of any convention for styling the second hand except
that it should normally be thinner, and presumably full length.

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jgrahamc
Here you go: [https://imgur.com/a/fnt4677](https://imgur.com/a/fnt4677)

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dingaling
That's a cool little personal project, but I did smile wryly at the typical
programmer focus on one specific subset of the problem space. He didn't
consider watches with analogue 24-hour faces...

~~~
jgrahamc
I actually own one of those, but they are rare and not something most people
see.

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jlbnjmn
I like this. Thanks for sharing. Are those decimals or seconds?

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saagarjha
Seconds; you can see the seconds hand in the second (no, it’s unintended) set
of clocks. Generally I’d prefer using a colon to separate both to avoid this
kind of confusion.

