4 ms·

All the symmetrical watch faces and code to generate them

23 points by jgrahamc 6y ago

jlbnjmn 6y ago
I like this. Thanks for sharing. Are those decimals or seconds?
- saagarjha 6y ago
  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.
userbinator 6y ago
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.)
- saagarjha 6y ago
  Just over once a minute if you assume the seconds hand is in the middle of the three?
- jgrahamc 6y ago
  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.
- smabie 6y ago
  It's just LaTeX, I believe. it's kind of strange that it's just a image when it could be typeset with mathjax instead.
mkl 6y ago
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.
deleted 6y ago
[deleted]
dingaling 6y ago
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 6y ago
  I actually own one of those, but they are rare and not something most people see.
aaronax 6y ago
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.
- jgrahamc 6y ago
  Here you go: https://imgur.com/a/fnt4677 https://imgur.com/a/fnt4677

23 points by jgrahamc 6y ago

jlbnjmn 6y ago

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

saagarjha 6y ago
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.

userbinator 6y ago

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.)

saagarjha 6y ago
Just over once a minute if you assume the seconds hand is in the middle of the three?
jgrahamc 6y ago
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.
smabie 6y ago
It's just LaTeX, I believe. it's kind of strange that it's just a image when it could be typeset with mathjax instead.

mkl 6y ago

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.

deleted 6y ago

[deleted]

dingaling 6y ago

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 6y ago
I actually own one of those, but they are rare and not something most people see.

aaronax 6y ago

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.

jgrahamc 6y ago
Here you go: https://imgur.com/a/fnt4677 https://imgur.com/a/fnt4677