Original Math Notes
All Seasons
Season 6
Episode 602: Friendly Fire
Homotopy of an algebraic surface
Homotopy of an algebraic surface
Scene 6:
          I didn't know you did any work down
          What is this, 11-dimensional

Gravitational Wave Polarization and Test Particles »

Gravitational Wave Polarization and Test Particles
This Demonstration shows how test particles move when a gravitational wave passes them. The wave is perpendicular to the plane of the particles. The two polarizations are "plus" polarization and "cross" polarization, 45° apart since gravitons are spin-2 particles.
Scene 28:
Larry's lost in the moment. He stares out the window.

          Two solid rocket boosters, each
          providing 12.5 million newtons of
          thrust at liftoff.
          For every action there is an equal
          and opposite reaction.

          Sir Isaac Newton.

          Arguably the greatest scientist who
          ever lived. Yet he spent a much
          greater part of his life writing
          interpretations of the bible than
          he ever did on the laws of physics.

A beat. The screen changes as the shuttle begins to approach
outer space. 

Launching a Rocket »

Launching a Rocket
The launch of a spacecraft is fundamental to all space activity. As a rocket flies it loses mass, because most of its mass is fuel (pure hydrogen and oxygen) that provides the propulsive force. This Demonstration shows the dynamics of an ideal rocket from launch time to measured burn-out time, based on Newton's laws and Tsiolkovsky's rocket equation. Specify the rocket parameters and launch with the trigger.
Scene 30:
          Charlie, this is incredible.

          My confidence interval is ninety
          The shooting began here.

Colored lines (ballistics) red/robbers, blue/FBI.  

Confidence and Prediction Bands »

Confidence and Prediction Bands
Drag the points or alt-click the plot to add or subtract points from the dataset. The least-squares regression line for the dataset is shown, as well as the option to include confidence or prediction bands with a confidence level that you can adjust with the slider.
Scene 48:
          It's Larry's work.

          Theoretical physics, cosmology...

          -- string theory, supersymmetry...
            (looks at them)
          It's all here.

Bohm Trajectories for Quantum Particles in a Time-Dependent Linear Pot »

Bohm Trajectories for Quantum Particles in a Time-Dependent Linear Pot
The time-dependent probability density associated with this Gaussian wave packet is Gaussian for all times. The de Broglie–Bohm formulation of quantum mechanics, also known as the quantum theory of motion, is a single-valued theory in configuration space with one possible velocity for a given position at a particular time.
Wolfram: Creators of Mathematica, Leaders in Math & Computation
Compute expert-level answers—Wolfram|Alpha