The arc actually does line up with 1.4142 (sine 45's cosecant ratio). Incredible ratio relations to 1.4142 which is the arc ratio that hits the drag circle dead on with the fib circles.ie. The fib circles have a center and 2 drag points. To make the arc land precisely on one of the drag circles you need the 1.4142 ratio. The related ratios should be related to 1.4142...1.413 is slightly off. The difference isn't much anyway, but I DISCOVERED THE PROPER 1.4142 RATIO SINCE THIS WAS FIRST POSTED.

If "A"=1.413 then A/4=.35325 AND A/2=.7065 AND A*1.5=2.12~ AND A*1.75=2.47 AND A*2=2.826 AND A*3=4.24

Do you get the idea. All the points that are touched are relational to one ratio 1.413 which is the original ratio for the ellipse to cover the 5 key brushed points. All other incredible hits are derived from that ratio. So this means you have possibilities of predicting from ONE ratio that generates other values.

I thought it might be related to the cosecant ratio for sine 45 1/sine 45=1.4142 but the value is sightly smaller.

If "A"=1.413 then A/4=.35325 AND A/2=.7065 AND A*1.5=2.12~ AND A*1.75=2.47 AND A*2=2.826 AND A*3=4.24

Do you get the idea. All the points that are touched are relational to one ratio 1.413 which is the original ratio for the ellipse to cover the 5 key brushed points. All other incredible hits are derived from that ratio. So this means you have possibilities of predicting from ONE ratio that generates other values.

I thought it might be related to the cosecant ratio for sine 45 1/sine 45=1.4142 but the value is sightly smaller.

andvs

2 years ago

you have an interesting analysis, but little explanation for mere mortals :). it saddens me

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