Tuesday, June 01, 2010

Outlining

  • GEOMETRY BASICS

    • Rhombic Dodecahedron (starting point)
      • inscribed cube
      • inscribed octahedron
    • Concept of Dual
      • cube - octahedron
      • cuboctahedron
    • Angle versus Frequency
      • 12-around-1: 10 * F * F + 2 (cuboctahedral numbers)
      • 12-around-0: 10 * F * F + 2 (icosahedral numbers)
      • virus morphology
      • geodesic domes and spheres
      • buckminsterfullerene
    • VE <--> Icosa (Jitterbug)
    • 25 Great Circles (VE)
    • 31 Great Circles (Icosa)
    • LCD triangles
    • Spherical Networks
      • vertex, face, mid-edge axes
      • poles as +2
      • 2*P*F*F + 2 (Coxeter paper)
    • Concentric Hierarchy
      • A & B modules
      • Mite, Sytes, Kites
      • Coupler (1)
      • Rhombic Dodecahedron and the Coupler
      • Coupler in XYZ
    • Rhombic Triacontahedron
      • toy: Ball of Whacks
      • T-E modules
      • RT volume 5
      • RT volume 7.5 (K)
      • RT volume 15 * root(2)
    • RT / RD relationship
    • Tetrahedron as Unit
      • 24 A modules
    • Unity-2
    • IVM (toothpicks)
      • two kinds of voids
      • 4 IVMs
    • Dimensions
      • 4D / 4D+


  • GEOGRAPHY BASICS

    • Time (space-time)
      • clocks
      • time-lines
      • time codes
    • adding into the future, subtracting into the past
    • time scales (geological vs. human vs. pico)
    • rates of change (ratios)
    • Space
      • Coordinate systems (including latitude/longitude, degrees)
      • Girding/griding the planet (GIS/GPS)
      • Mapping/addressing schemes
      • Length and number (ratios)
      • Area and volume
    • Objects
      • Shapes
        • spatial networks (polyhedra)
        • plane figures (triangles especially)
      • Objects organized in sets
        • types of number
        • operations with number types
        • permutations and combinations (DNA)
      • Objects organized in hierarchies
        • subtypes (rationals a subtype of real a subtype of complex)
        • geometric hierarchies
        • biological taxonomies
    • APIs: exposing objects to users
      • Fractions, Decimals, Percents (rational number type)
      • Polynomials (solving, graphing)
      • Vectors
        • adding and subtracting
        • scalar multiplication
        • dot and cross products
      • Matrices (translation, rotation, scaling)
    • Events
      • Communications
        • Symbol systems and codes
      • Energy
        • kinetic energy (units, dimensions)
        • heat energy and temperature (conversion constants)
      • Frequency (links to time)
        • color / optics (the spectrum, visible and not)
      • Rates of Change
        • velocity vectors, acceleration, slope, gradient
        • derivative
        • anti-derivative (integral)
      • Event-triggered objects
        • mouse clicks and key presses
      • Probability and Permutations