4 thoughts on “A Round Squared Clock”

  1. Looking at that clock I just realized – each square increases by an odd number that goes up by 2 each time – 3, 5, 7, 8, 11 and so on. Is that a thing everyone knew except me? Math wasn’t interesting enough to pay attention to in high school. (And we didn’t have a round squared clock.)

    • Yup (but I liked math), and it’s easy to see why it happens.

      Start with 1:

      Then make a 2×2 square:
      By doing this, you added 1 row, 1 column, and 1 for the corner (total: 3).

      Keep going, to 3×3:
      You added 2 rows, 2 columns, and 1 for the corner (total: 5)

      Each time you expand the square, you have to add 2 more than what you added previously because you previously added 1 row and 1 column to the square. So for the next one, 4×4, you have to add 3 rows, 3 columns, and 1 for the corner (total: 7).

      Ta da!

      • That’s really neat. If I’d had you for a math teacher I might had paid more attention! I just remember a sub who taught us how to multiply by 15 (which I remember) and by 12 (which I don’t) and a few other really useful tricks. All the rest of Gr. 9 to 12 math is a blur, except that the words sine and cosine still give me hives.

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