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Nonsense! The Leibniz sequence is the most simple way to describe the equivalence class under multiplication by non-zero rationals of numbers that contains bot
by chalst 15y ago
Nonsense!
The Leibniz sequence is the most simple way to describe the equivalence class under multiplication by non-zero rationals of numbers that contains both pi and tau:
1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ...
which sums to equivalently pi/4 or tau/8.
The fundamental simplicity of the Leibniz sequence makes this value the only natural choice from that equivalence class. Let us call it lambda, for Leibniz.
Then the area of the unit circle is 4 lambda, the diameter of the unit circle is 8 lambda, the volume of the unit sphere is 16 lambda, the surface of the unit sphere is 16/3 lambda, etc.
Should I start selling the t-shirts?
- RuggeroAltair 15y agoI wouldn't call it nonsense. If the comparisons with the virial theorem and energy isn't enough to consider it at least as a reasonable choice, at least you should consider it as such because John Baez agrees with it. And you don't mess with John Baez ;-)
- chalst 15y agoI'm attempting irony. The tone of the manifesto is a bit breathless, putting up interesting enough considerations in a overwrought manner, with half-hearted efforts made at looking at the issues raised from more than one point of view. Draft one of my lambda manifesto shows that the only consideration of conceivable value, namely ease of defining a transcendental by means of a convergent series, leads to only one possible choice of fundamental trigonometric constant, lambda. Of course to gain widespread acceptance, I will have to cover up having written the indulgently tolerant http://www.advogato.org/person/chalst/diary/275.html http://www.advogato.org/person/chalst/diary/275.html
- RuggeroAltair 15y ago+1 for irony anyways...