Original Math Notes
All Seasons
Episode 415: End Game--Explore the Math
Original Math Notes
Episode 415: End Game
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 8:
Solar panels and 'sunflower system' gear surround them.
                   PROFESSOR BILL WALDIE
          Blame Mother Earth.  To maximize
          efficiency, ideally we'd install
          solar panels on the roof at the same
          angle as our latitude, parallel to
          the earth' s axis--

          Here we're at 34 degrees, 8 minutes.
                   PROFESSOR BILL WALDIE
          ... Yet the slope of your roof is a
          gentle, eye - pleasing 22.5 degrees --

          -- so we lose efficiency.
                   PROFESSOR BILL WALDIE
          Angling the panels upward is one
          solution, we're also looking at
          mechanizing the mounts to follow the
          Sun -- a 'sunflower system' --
          keeping the hardware to a minimum.

Solar Panel of NASA's Phoenix Mars Lander

The Phoenix Mars Lander has two circular solar panels that are deployed like the opening of a fan after landing.
Scene 16:
Colby enters to find Charlie poring over the silo blueprints.

          Is that a silo?

          ...Cylindrical granary.  My dad's
          having it put in the backyard.

Minimizing The Surface Area of a Cylinder with a Fixed Volume »

A common optimization problem faced by calculus students soon after learning about the derivative is to determine the dimensions of a twelve-ounce can made with the least material, that is, the problem is to find the dimensions of a cylinder with a given volume that minimizes the surface area. Use the slider to adjust the shape of the cylinder and watch the surface area fluctuate about the minimum of the surface area function.
Scene 19:
Amita crosses back to Charlie, who now looks over at Larry
sitting on a desk, gazing out the window, a lost look --

          Paradise lost.  Larry, we've been
          spending 20 hours a week together,
          working on the Higgs Boson project.
          I know something's wrong.  You were
          in a tailspin long before you
          punched out a monk.

          ...It's the Higgs.

          What're you talking about?

          Much as I bristle at references to a
         'God Particle,' I must confess
          discomfort at the prospect of its
          discovery, the prospect that this
          'seeing into the mind of God' may
          prove to be no more than another
          blind alley in the search for a Grand
          Unified Theory.

          You won't know until you get there.

Combining Quarks into Hadrons

The "particles" setter summarizes the component particles of the standard model: quarks, leptons, gauge bosons, and the putative Higgs particle. The fact that isolated quarks have never been observed is referred to as quark confinement. Baryons and mesons, known collectively as hadrons, exist as combinations of quarks. Baryons, including the proton and neutron, consist of quark triplets. Mesons combine a quark with an antiquark. There also exist antibaryons, made of antiquark triplets.
Scene 32:
Porter reaches for his OJ, knocks his burrito onto the
ground.  He bends down, picks it up, looks at it.  Disgusted.

                   CLAY PORTER (cont'd)
          If I talk to you two anymore, I'll
          lose the rest of my breakfast.

Porter tosses his food in the trash, goes to his motorcycle.
David and Colby toss their food, get in the car, start it up.
Porter pulls away.  David and Colby follow, hear a POP! The
car pitches.  They jump out, take a look...  They see a flat
tire, HOMEMADE TIRE SPIKES on the ground.

Hyperbolization of a Dodecahedron

This Demonstration shows how to "hyperbolize" a dodecahedron (and other Platonic solids).
Scene 65:
Alan spreads out a new blueprint.  Charlie and Amita look --

          ...A windmill?

          Wind turbine is the precise term.

                   PROFESSOR BILL WALDIE
          Generates 1000 watts at 11 meters per
          second, an easy 5 kilowatts per day.
          Goodbye grid.

          That sounds great.

Windmill Model

The windmill model consists of a pole, a shaft, four blades, and a spinner. You can control the rotation of the blades, the height of the shaft, the length of the blades, and the direction of the whole assembly.
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