Friday, November 7, 2014

Platonic Solids


  1. Your Extended Fibonacci chart and research here shows the ‘added angles’ of platonic solids are at potentially meaningful intervals in the Fibonacci doubling sequence. But how do you search out the meaning of the interval?

    What if the answer is connected to the way Richard Feynman uses QED to ‘add angles’ to determine the probability amplitude of traveling photons? His technique goes hand-in-hand with measuring the length of arrows. See e.g., Feynman, QED: The Strange Theory of Light and Matter, p. 61.

    Therefore, imagine the extended Fibonacci goes from number-to-number like it is measuring out the length of something material like light (Fibonacci numbers = QED arrows). But if so, where is Feynman’s ‘imaginary stopwatch’ that provides the angle calculation (the direction the arrows point)? Perhaps Feynman's stopwatch is actually a Fibonacci spiral, such that the clock/spiral begins in your column 1 (1, 1, 2, 3, 5, 8…) and then when you get to row 12 in the extended Fibonacci table, it is like reaching 12 on a clock – you start a new cycle again from the top (but now you’re in row 2 (2, 2, 4, 6, 10…) because the Fibonacci progression is a spiral, not a circle).

    And then in QED the physicists always square the results of their total arrow length calculation to match experiment (that is, to match probabilities actually observed). Chad, might this be where your ‘3-torus model in a cube’ and the Russellian view comes into play for the Extended Fibonacci to match experiment/reality (referring to your post “Three Torus Model of Micro”, 2/5/13).

    So in a nutshell, the extended Fibonacci in a 2-d model emphasizes the number 9. It makes me think perhaps ‘9’ is at the top of a spiral clock in the 2-d model; and the probability of a platonic solid materializing in the Fibonacci spiral is a function of length and angle. If this can be shown with a reliable equation, it should assist the 3-d applications as well.

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  3. This works for exterior angles also. The sum of exterior angles of any polygon is 360 degrees, so here are the exterior angle sums for each of the platonic solids in Row 12 of your Extended Fibonacci Table:

    Icosahedron (7200) at column 50
    Dodecahedron (4320) at column 30
    Octahedron (2880) at column 20
    Cube (2160) at column 15
    Tetrahedron (1440) at column 10