Original Math Notes
All Seasons
Episode 408: Tabu--Explore the Math
Episode 408: Tabu
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 4:
Upchurch takes in the scene.

                   UPCHURCH (cont'd)
          ... but the big money snatches tend
          to put you in contact with a higher
          class of lowlife.  If they know
          their business -- and it looks to
          me like they do -- we'll be looking
          at simultaneous movement, expected
          payoffs, bargaining strategies...
          lots of variables.

                   CHARLIE (O.S.)
          What you're talking about is
          imperfect information games.

Iterated Games »

Iterated Games
Often players in a scenario that can be modeled as a strategic-form game engage in repeated interactions with each other. In such instances, their selection of a strategy on a given "iteration" may depend on their history of previous interactions. By way of example, a player might start by playing strategy 1 and continue playing it unless the history of interactions is such that the opposing player played 0 on his/her last two turns.
Scene 9:
          Actually, Charles, you can't find
          this in any shop.  I've constructed
          my own Hero's Fountain.

OFF Charlie's look --

          ...Named for Hero of Alexandria.
          The Greek mathematician and
          engineer.  Once we get the pressure
          right, the water will start to flow
          under its own power.

Linked Sliders »

Linked Sliders
Heron's formula (also called Hero's formula) gives the area of triangle in terms of a triangle's side lengths a, b, and c as sqrt((a + b + c)(-a + b + c)(a - b + c)(a + b - c))/4. Triangles having rational sides and area are known as Heronian triangles.
Scene 19:
          I think what he's trying to say is
          Pierce has violated his own rules of
          corporate Game Theory.  It's standard
          Minimax -- like a tug of war --

Profit Maximization in Perfect Competition »

Profit Maximization in Perfect Competition
A perfectly competitive firm with rising marginal costs maximizes profit by producing up until the point at which marginal cost is equal to marginal revenue. The marginal revenue for a perfectly competitive firm is the market price determined by the intersection of the supply and demand curves, as shown in the panel on the left. The panel on the right shows the orange price line intersecting the purple marginal cost curve at the profit maximizing quantity, Qmax.
Scene 21:
          If we had a DTMF decoder --
              (off David)
          Dual-tone multi-frequency -- touchtone.

          Because you couldn't have said that
          in the first place.

          It wouldn't have been as much fun.

Touch Tones »

Touch Tones
Dial and listen to the touch tones. Press the composed number to listen to its tone sequence. Numbers can be stored and retrieved from the menu.
Scene 57:
          ...Perhaps not an altogether bad
              (off her look)
          The charged particles of the solar
          wind need heat and combustion to
          escape the gravitational pull of the
          sun.  From tumult comes freedom.

          You have a way of making my
          neurosis sound so... cosmic.

Charged Particle in Uniform Electric and Magnetic Fields »

Charged Particle in Uniform Electric and Magnetic Fields
The path of a charged and otherwise free particle in uniform electric and magnetic fields depends on the charge q of the particle and the electric and magnetic field strengths E and B.
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