Similar to the work of Philip Swift regarding the Bitcoin Pi Cycle Top, I’ve recently come across a similar mathematically curious ratio that corresponds to Bitcoin cycle bottoms. This ratio was extracted from skirmantas’ Bitcoin Super Cycle indicator. Cycle bottoms are signaled when the 700D crosses above the 137D (because this indicator is closed source, these moving averages were reverse-engineered). Such crossings have historically coincided with the January 2015 and December 2018 bottoms. Also, although yet to be confirmed as a bottom, a cross occurred June 19, 2022 (two days prior to this article)
The original pi cycle uses the doubled 350D and the 111D . As pointed out this gives the original pi cycle top ratio:
350/111 = 3.1532 ≈ π
Also, as noted by Swift, 111 is the best integer for dividing 350 to approximate π. What is mathematically interesting about skirmanta’s ratio?
700/138 = 5.1095
After playing around with this for a while I realized that 5.11 is very close to the product of the two most numerologically significant geometrical constants, π and the golden ratio, ϕ:
πϕ = 5.0832
However, 138 turns out to be the best integer denominator to approximate πϕ:
700/138 = 5.0725 ≈ πϕ
This is what I’ve dubbed the Bitcoin Golden Pi Bottom Ratio.
In the spirit of numerology I must mention that 137 does have some things going for it: it’s a prime number and is very famously almost exactly the reciprocal of the fine structure constant (α is within 0.03% of 1/137).
Now why 350 and 700 and not say 360 and 720? After all, 360 is obviously much more numerologically significant than 350, which is proven by the fact that 360 has its own wikipedia page, and 350 does not! Using 360/115 and 720/142, which are also approximations of π and πϕ respectively, this also calls cycle tops and bottoms.
There are infinitely many such ratios that could work to approximate π and πϕ (although there are a finite number whose daily moving averages are defined). Further analysis is needed to find the range(s) of numerators (the numerator determines the denominator when maintaining the ratio) that correctly produce bottom and top signals.
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