Original Math Notes
All Seasons
Season 5
Episode 506: Scan Man
Evolution of a smoothed parametrized fractal
Evolution of a smoothed parametrized fractal
Scene 2:
          I'm not sure an Error Correcting Code 
          is gonna get you there --
            (off tense looks)
          -- That is what you're using, right?

          ...And have been for weeks.

Golay Code »

Golay Code
When the Voyager spacecraft took pictures of Saturn and Jupiter, they used Golay code to encode the data for transmission. Each 24-bit block of data could have up to three errors, and the computers here on Earth could fix these errors. The Golay code is thus an error-correcting code. It was originally published in 1949 with Marcel Golay's half-page paper, "Notes on Digital Coding." Today, this paper is considered one of the most remarkable papers ever published, with deep, deep connections to group theory, graph theory, number theory, combinatorics, game theory, multidimensional geometry, and even particle physics.
Scene 23:
            (slides a statement across) 
          Bank statements don't lie --

          I have 511,108 dollars and 23 cents.
          Tomorrow it'll be 511,114 dollars and
          17 cents.  Compounded daily.  At our
          preferred introductory rate.

Compound Interest Table »

Compound Interest Table
Compound interest tables are useful for looking up interest compounded at various rates.
Scene 25:
Charlie eyes the box: "QUANTITY: 150" In his palm are the 3
paper clips he plucked out. 

          What's 364 squared?


          The square root of 7?

          2.645751311106 --

Number Theory Tables »

Number Theory Tables
A book of mathematical tables will contain listings for some of the functions listed in this Demonstration. For example, tables of square numbers and cubic numbers are included. If you are curious to find out more about a particular sequence, put a list of the first few terms into the The On-Line Encyclopedia of Integer Sequences, or take a look at the corresponding MathWorld link.
Scene 42:
          You mentioned Fractal Analysis...?

Charlie holds her look, the fence-mending begins...

          It came to me staring at a poster of 
          a drip painting on Emerson's wall... 
          how he sees the world -- whether in
          an abstract painting, or a barcode,
          or in the way he arranges seemingly
          random clutter in his apartment --

          -- it's all part of a larger design,
          a fractal pattern...

          ...shapes repeating within the same
          object -- like a snowflake.

Fractal Curves »

Fractal Curves
Fractal curves can be generated from an initial curve (often a regular polygon) and one or more replacement curves. Repeatedly, each line is replaced by a properly scaled copy of one of the replacement curves. The buttons show the first iteration of the replacement curve used. The fractal illustrated above is known as the Koch snowflake.
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