On Sunday, January 7, 2018 at 4:12:32 AM UTC+2, Archimedes Plutonium wrote:
> Alright, many years ago, perhaps a decade ago, I remember doing the Log spiral, golden mean log spiral
> and was curious about the arclength in quarter circles. Of course, if it is a quartercircle then we apply 3.14159.... to determine arclength, but what do we apply if it is not a circle or part of a circle for that of say a log spiral or a ellipse.
>
> Anyway, to cut a long story short.
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> I hypothesized way back when that the Easiest explanation of the number 2..71828... is that it is the number for ellipse and for log spiral arclength..
>
> When you have a circle, the number 3.14159.... relates the diameter to the arclength
>
> When you have a ellipse, the number 2.71828... relates the diameters to the arclength
>
> So here, I want to develop this conjecture.
>
> At the time I offered this conjecture years back, I made the comment that the world's first geometrical explanation of 2.71828..... is it is the pi of ellipses. Whereas the rest of the world wants to home in on the calculus value of 2.71828.... never a geometry explanation of that number.
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> Further, another conjecture
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> Now in topology, they easily dream up that if you sit upon a circle and squash it evenly you can form a ellipse. But most of Topology is just fairy tale math, where imagination rules and ruins true thinking.
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> In New Math, no curves actually exist but are strung together tiny straight line segments. So, can we sit on say a 100 regular polygon and expect to form anything symmetrical after we sat on it.
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> So here, I offer another Conjecture:: You cannot bend a circle into a ellipse, and conversely, you cannot bend a ellipse to be a circle, not when mathematics is discrete points and all figures are tiny strung together straightline segments.
>
> AP