Original Math Notes
All Seasons
Season 6
Episode 603: 7 Men Out
Roulette-wheel construction
Scene 9:
          I'm not going into a tailspin, Earth
          is. Icarus-like, we're soon fated to
          tumble from orbit and be engulfed by
          the sun in a vaporous death.

          What did I miss? Should we turn on
          Larry King?

          The Royal Astronomical Society has
          recalculated the demise of Earth,
          shortening its lifespan significantly.

          ...We've still got another 7.59
          billion years.

Red Giant Stars and the Death of the Sun »

Our Sun is a middle-aged star fusing hydrogen in its core into heavier and denser helium. As the Sun ages, the helium builds up, eventually leaving no hydrogen fuel. The fusion of hydrogen generates energy that counteracts gravity, so in about 5 billion years the Sun's core will start to collapse. It will heat up, with the remaining fusion reaction taking place at a faster rate in a shell of hydrogen gas surrounding the core. The extra energy produced will push the outer layers of the Sun outward; they will cool and take on a reddish hue. The Sun will engulf the current orbits of Mercury, Venus, Earth, and perhaps even Mars as it becomes a red giant star. A strong stellar wind will result in large mass loss for the Sun as it blows away its outer layers.
Scene 17:
The grainy nanny-cam video of the Russian Roulette game plays
as... Don, Nikki, Charlie and Larry watch.

          Russian Roulette.  Legend has it
          Russian officers, starving at the
          front, resorted to wagering their
          lives for a crust of bread.

Pascal-Like Triangles Made from a Game »

The triangle of fractions has properties that makes it very similar to Pascal's triangle suppose two adjacent fractions in the same row are a/b and c/d. Then the fraction below them is (a + c)/(b + d), which is how the fractions a/b and c/d are added in the Farey sequence.
Scene 21:
          What makes a man do this?

          "The Gambler's Ruin."  Doubling down,
          chasing losses...  A 1000 dollar wager
          fast becomes a six-figure debt, and a
          man begins to see no way out.

The Gamblers Ruin »

The gambler starts with an i unit stake and the casino or house starts with c units. They repeatedly play a game for which the gambler has a fixed probability p of winning and the winner gets 1 unit from the loser.
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