Fibonacci Cones, Type 2.

Here we make cones each of which has a circumference which is a Fibonacci number. Invert the cone and it is a funnel shape. Example 3 was the first diagram made, and there was a mistake but I include it to show working out.

Notice the obvious relationships:-

Radius F(n) - Radius F(n-1) = Radius F(n-2)

or Radius F(n) + Radius F(n=1) = Radius F(n-2)

Collapse the cones to make a series of concentric circles

---- Theoretical Fibonacci Ripples.

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Example 2 shows shapes with higher Series numbers. Out of the corner of my eye I notice more relationships:-

fib no 1597 is approx 1.6 x 1000; half = 0.8 and so on, along rhs of page.

........0.8, 1.3, 2.1, 3.4, 5.5, 9, 14.5, 23.......

This looks like 1/10 of series ......8, 13, 21, 34, 55, 144, 233.

Another Equation presents itself! The mind maps the design and sees a pattern.

Our Equation is F(n) / 200 almost = F(n-11)

eg F24 = 46368, half = 23184; this is almost 233 x 100, ie F13.

Also F32 = 2178309, half = 1089309.5; this is almost 10946 x 100, ie F21

We can make all kinds of cones or ripples with radius, diameter or circumference being Fibonacci numbers.