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swimsuit addict

Fun with birthdays, and primes

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Today was a birthday swim morning at Riverbank for one of my lanemates. Two friends and I put on our festive flowery swim caps and did the following set to celebrate:

800 lcm warmup (400s, 200k, 200p, photo op)

43 x 50 @ whenever-lane-space-permitted intervals (usually 5-10 sec. rest, with a few chat/calculation breaks), with all FR except prime numbers = non-free
[I did BK for the non-free lengths, and sprinted the triangular numbers and kicked the cubes just for good measure.

200 warmdown

This set really brought out my high-school-math-team-geek tendencies. Since all my sprints but one ended up being free, I wondered if 3 were the only prime triangular number. It seemed like that had to be so, but it took me a few 50s to work out a proof. After the set was over we noticed that our ages were all now prime—I wondered if this had happened before (the answer is yes, it was in fact the fourth time during our lifetimes). It would be nice to think we’ll be around to celebrate the next occurrence, but that's a ways off—I would be competing in the 105-109 age group by then!

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Comments

  1. pool tourist's Avatar
    Triangular?
  2. andrewmalinak's Avatar
    Oh I miss you guys. Save me a spot in your lane the week after Memorial Day?
  3. pwb's Avatar
    I love it when math and swimming come together. Prime numbers are great for devising sets, but even more magical for ages. I always make sure to remind my daughters when they are in the 'Prime' of their life.

    I saw and loved the photo op pic on FB. That was a prime picture.
  4. ekw's Avatar
  5. swimsuit addict's Avatar
    Quote Originally Posted by pool tourist
    Triangular?
    Triangular!
    Triangle numbers are generated by adding 1+ 2 + 3 + . . ., up to however high you want to go. So yesterday's set should have had 8 sprints in it (1,3,6,10,15,21,28,36), with progressively more rest in between each. But I only came up with the sprinting idea on #6, so I missed the first two.

    (They're called triangular because they are the number of dots you can use to form a filled-in equilateral triangle--think marbles on a Chinese checkers board--the same way squares are called squares because they're the number of dots you can use to form a filled-in square. The sequence is probably more familiar to swimmers as the totals of increasingly longer pyramid sets.)
  6. swimsuit addict's Avatar
    Quote Originally Posted by andrewmalinak
    Oh I miss you guys. Save me a spot in your lane the week after Memorial Day?
    Woohoo! Absolutely, we'll save you a spot. Can't wait to see you and hear all about your upcoming great swim adventure!
  7. swimsuit addict's Avatar
    Quote Originally Posted by pwb
    I love it when math and swimming come together. Prime numbers are great for devising sets, but even more magical for ages. I always make sure to remind my daughters when they are in the 'Prime' of their life.

    I saw and loved the photo op pic on FB. That was a prime picture.
    Quote Originally Posted by ekw
    Thanks! It was such a fun morning!
    My husband thinks that swimmers develop good math skills because of all the complicated sets we do--he claims that runners (his sport) would just be befuddled and amazed by all the various intervals and distances involved. I know as a kid I used to calculate what percentage of a set I had done after each repeat or each lap, and other masters swimmers have admitted that they still do this.