The Tao of Gaming

Boardgames and lesser pursuits

May Links

Written by taogaming

May 16, 2021 at 6:49 pm

Posted in Linky Love

8 Responses

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  1. The LBJ books are excellent, but you don’t need me to tell you that. However, Coke Stevenson, I am advised by historians, gets treated better than he deserves.

    Fred Bush

    May 16, 2021 at 10:31 pm

    • I’ve seen that criticism, and he certainly seems racist based on other sources.

      I started the Caro book and what impressed me is how much more I learned in the first 20 pages compared to one year of Texas History (granted, in 7th grade).


      May 17, 2021 at 1:11 pm

  2. The story of how that solo happened (no rehearsal!) is pretty good too:


    May 17, 2021 at 1:42 pm

  3. Seems like you could use that cake proof to show that just about any infinite series of that type sums up to 1/2. If you get 40% of each slice and I get 40%, we’ll each get the same amount and the cake will eventually be gone. Same with 30%. So dad needed to add a bit more information to make that proof valid.


    May 20, 2021 at 7:38 pm

    • Well, yes. Assuming I did this right:

      r = 0.4 (your 40%)
      s = 1 – 2 * r (the remaining middle portion

      Then the series is r + rs + rs^2 + …

      This becomes r * (1 /(1-s), which is 1/2.

      Of course, the beauty is that when r = 1/3, s = 1/3 and the figure is pleasing to the eye.

      But regardless, the figure does show how 1/3 + 1/9 + … equals 1/2.


      May 21, 2021 at 9:08 am

  4. If the procedure is to cut up the unassigned portion using a consistent ratio it will fill up the area completely with any value from > 0 to 0.5. In fact you could make a visual proof for any of them by adjusting the cut lines in or out as appropriate. Only the 1/3 matches up with a standard geometric series though.

    Mark Delano

    May 21, 2021 at 1:12 pm

    • Well, you get r (1 + s + s^2 + …) where s = 1 – 2 r, which equals 1/2. Close enough to a geometric series for govt work. Using r = 1/3 is the most pleasing to the eye, I think.

      Joe J. Rushanan

      May 22, 2021 at 9:55 am

      • I was trying to get standard to do a lot more work than I should have. Point taken though.

        Mark Delano

        May 24, 2021 at 2:57 pm

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