So this is a long snake ruler coiled in the radial marking circle. The radial marker steps around the circle and a descending market on the radial counts Bayes spaces on the coiled snake. counts spaces on the snake. When a new space is discovered, the stamp will stamp the most accurate measurement of the integer. Each space on the snake getting three 'adjustments', in units of 1/x,1/y,1/z, x y z relatively prime.
No marker appears three times in a row, the most accurate marker will often appear twice.
Moreover, he pointed out that {\displaystyle x^{2}+y^{2}+z^{2}=3xyz+4/9}, an approximation of the original Diophantine equation, is equivalent to {\displaystyle f(x)+f(y)=f(z)}
with f(t) = arcosh(3t/2).[6] The conjecture was proved[disputed – discuss] by Greg McShane and Igor Rivin in 1995 using techniques from hyperbolic geometry.[7]
Our flat circle has become a salad bowl The splitting of the hyperbolic angles is the splitting of a fixed bandwidth channel. those are relative number of bit assigned. The angles follow the old Fibonacci, notice.
How does this work? This optimum ratio estimates the most irrational number as one counts around the edge of the salad bowl/ That means there is no predictable error and the current estimate is the best possible. It is an optimum self sampled system. The sum squares between bandwidth X plus bandwidth Y should be close to bandwidth square Z, within 3/2. That condition is why we have curved paper.
If you spiral down the side of the salad bowl, every space must have three marks, that is the maximum and minimum accuracy. This is another concept of coloring. This is factional approximation, we are half a simple behind, 3/2 when we are used to 2D and 2.
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