Interactive Computations

Use the free Wolfram *Mathematica Player* to interact with the math
behind NUMB3RS.

INT. EPPES' HOUSE / LIVING ROOM - NIGHT CHARLIE and AMITA are playing poker. He's wearing his best pajamas. She's got a sexy Teddy under a silk robe. Charlie lays down his cards. CHARLIE Beat three sixes. AMITA puts down her cards. AMITA Flush. All hearts. CHARLIE But... you should have folded. AMITA I was feeling lucky. CHARLIE Lucky? There was a less than 18 percent probability you'd complete the flush.

This Demonstration generates random poker hands.
Each of the 2598960 different possible poker hands will get one of the ten possible rankings, from royal flush to
nothing.

ALAN picks up the cards, shuffles absently. ENTER CHARLIE VISION: The cards shuffle in slow motion. Equations are parsed into the flipping cards. The deck is cut. THE ACE OF DIAMONDS. EXIT VISION. CHARLIE (to Amita) If we can construe each murder as a separate Markov Chain. What if we tried to shuffle them together? AMITA Analyze precipitating events and potential motives... Find any commonalities.

Suppose that if it is sunny today, there is a 60% chance it will be sunny tomorrow and that if it is not sunny today,
there is a 20% chance it will be sunny tomorrow. If we assume today's sunniness depends only on yesterday's sunniness
(and not on previous days), then this system is an example of a Markov chain, an important type of stochastic process.

Charlie is in the living room with FIVE OR SIX GRADUATE STUDENTS. There's a CHALKBOARD from the garage. CHARLIE I think with that we'll call it a night. And thanks again for dealing with the last minute change in venue. Alan enters through the front door. Is a little surprised by the parade of STUDENTS exiting. CHARLIE My Tuesday evening graduate topology seminar. ALAN In our living room. CHARLIE We usually meet in my office, but I'm kinda locked out at the moment.

Costa's minimal surface is
described as a torus with three points removed.
How is this done? The points are literally removed from 3D-space and flung to infinity. Here is a Demonstration of
specifically where on the torus the points are removed and how the torus turns itself inside-out when the resulting ends
of the surface are flung to infinity.

CHARLIE There's a classic problem in combinatorics. The Travelling Salesman Problem... ENTER VISION: A VINTAGE 50s GUY WITH A VACUUM CLEANER in front of a SUBURBAN HOME. CHARLIE The Salesman must visit a specific set of cities... A MAP OF THE US. A ROUGH OCTAGON OF CITIES ARE HIGHLIGHTED. CHARLIE Each leg of the trip has a different cost... THE CITIES ARE CONNECTED BY RAIL LINES. A PRICE APPEARS FOR EACH CONNECTION. CHARLIE And he must figure out the most routes that minimizes the total expense.

The traveling salesman problem asks
for the shortest route by which a salesman can visit a set of locations and return home. Drag the points to change the
locations the salesman visits to see how the route changes.