Skip to main content

All the symmetrical watch faces (and code to generate them)

If you ever look at pictures of clocks and watches in advertising they are set to roughly 10:10 which is meant to be the most attractive (smiling!) position for the hands. They are actually set to 10:09.14 if the hands are truly symmetrical.

I wanted to know what all the possible symmetrical watch faces are and so I wrote some code using Processing. Here's the output (there's one watch face missing, 00:00 or 12:00, because it's very boring):




The key to writing this is to figure out the relationship between the hour and minute hands when the watch face is symmetrical. In an hour the minute hand moves through 360° and the hour hand moves through 30° (12 hours are shown on the watch face and 360/12 = 30).

The core loop inside the program is this:
  for (int h = 0; h <= 12; h++) {
    float m = (360-30*float(h))*2/13;
    int s = round(60*(m-floor(m)));
    int col = h%6;
    int row = floor(h/6);
    draw_clock((r+f)*(2*col+1), (r+f)*(row*2+1), r, h, floor(m), s);
  }
h is the hour number, m the number of minutes past the hour and s the number of seconds past the minute. As you can see, the loop looks at the hours 0 to 12 and then calculates the minutes and seconds using this formula:
    float m = (360-30*float(h))*2/13;
    int s = round(60*(m-floor(m)));
The s part is simple, it's just the decimal part of m turned into seconds. m is the interesting calculation and gives the number of minutes past the hour h (expressed as a decimal to also capture the seconds). Here are the details of how m is calculated from h.

If you look back at the watch face above it's not actually showing 10:09.14, it's showing 10:11.39. I think this is in part because it puts the second hand in a pleasing location. 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.

 

Comments

Davebakedpotato said…
Love it! One further reason for using 10:10 (especially vs 1:50) is that the hour and minute hands form a 'tick' - another positive affirmation that you should definitely buy the watch. :)
Emma Jasmine said…
Good post..

Popular posts from this blog

Making an old USB printer support Apple AirPrint using a Raspberry Pi

There are longer tutorials on how to connect a USB printer to a Raspberry Pi and make it accessible via AirPrint but here's the minimal one that's just a list of commands and simple instructions. 1. Install Raspbian on a SD card 2. Mount SD card on some machine and navigate to / . Add a file called ssh and set up wpa_supplicant.conf for WiFi access. Now you have headless and don't need a keyboard or monitor. 3. Boot. Login. sudo raspi-config . Change password. 4. Connect printer via USB cable 5. Then execute the following sequence of commands to set up CUPS and make it accessible on the network. sudo apt-get update sudo apt-get full-upgrade sudo apt-get install cups sudo usermod -a -G lpadmin pi sudo cupsctl --remote-any sudo systemctl restart cups 6. Visit http://raspberrypi:631/admin and add the local printer. Make sure "sharing" is enabled on the printer. 7. Then make sure AirPrint is set up sudo apt-get install avahi-daemon sudo reboot Printer should work

How to write a successful blog post

First, a quick clarification of 'successful'. In this instance, I mean a blog post that receives a large number of page views. For my, little blog the most successful post ever got almost 57,000 page views. Not a lot by some other standards, but I was pretty happy about it. Looking at the top 10 blog posts (by page views) on my site, I've tried to distill some wisdom about what made them successful. Your blog posting mileage may vary. 1. Avoid using the passive voice The Microsoft Word grammar checker has probably been telling you this for years, but the passive voice excludes the people involved in your blog post. And that includes you, the author, and the reader. By using personal pronouns like I, you and we, you will include the reader in your blog post. When I first started this blog I avoid using "I" because I thought I was being narcissistic. But we all like to read about other people, people help anchor a story in reality. Without people your bl

Your last name contains invalid characters

My last name is "Graham-Cumming". But here's a typical form response when I enter it: Does the web site have any idea how rude it is to claim that my last name contains invalid characters? Clearly not. What they actually meant is: our web site will not accept that hyphen in your last name. But do they say that? No, of course not. They decide to shove in my face the claim that there's something wrong with my name. There's nothing wrong with my name, just as there's nothing wrong with someone whose first name is Jean-Marie, or someone whose last name is O'Reilly. What is wrong is that way this is being handled. If the system can't cope with non-letters and spaces it needs to say that. How about the following error message: Our system is unable to process last names that contain non-letters, please replace them with spaces. Don't blame me for having a last name that your system doesn't like, whose fault is that? Saying "Your