Im trying to prove that the intervals size has to shrink by somewhat close to a factor of 12 every cycle, but its tricky and its late.

The geometric mean is less well-known but works similarly to the arithmetic mean.

If all of the numbers in a sequence are identical, then its arithmetic mean, geometric mean and median will be identical, since they would all be equal to the common value of the terms of the sequence.

However, if the sequence is not constant, then the arithmetic mean will be greater than the geometric mean, and the median may be different than either of those means.

Cmd Gm Dn Series Of Values

Being a series of values, Randall suggests that this is ideally suited to being itself subjected to the comparative averaging method.

Not just once, but as many times as it takes to narrow down to a sequence of three values that are very close to one another.

Each row in this table shows the set Fn(.) composed of the average, geomean and median computed on the previous row, with the sequence 1,1,2,3,5 as the initial F0.

While GMDN is not differentiable, due to the median, this can be interpreted as somewhat similar to a heat equation which approaches equilibrium through averaging.

Interestingly, the maximum value alternates between the average and the median (highlighted in bold in the table), while the minimum value alternates between the geomean and the median.

This holds for many inputs thus providing the basis for a possible proof-by-induction of convergence on the range (see discussions).

It is a method without any danger of divergence of values, since all three averaging methods stay within the interval covering the input values (and two of them will stay strictly within that interval).

Randall suggests that the (non-Pythagorean) median, which does not have such good mathematical properties with relation to convergence, is, in fact, the secret sauce in his definition.

Suppose the bank will exchange US Dollars to Euros at a rate of 5 for 6 (about 0.83333 or 1.20000).

Suppose the bank will exchange Euros to US Dollars at a rate of 7 for 6 (about 0.85714 or 1.16667).

This creates two new exchange rates which are closer than the orginal rates, but the new rates are still different for each other.

Megan and Cueball can then iterate this process and the rates will converge to the geometric mean of the original rates, namely.

In some ways its also philosophically similar to the truncated mean (extremities of the value range, e.g.

Winsorized mean (instead of ignored, the values are readjusted to be the chosen floorceiling values that they lie beyond, to still effectively be counted as edge conditions), only with a strange dilution-and-compromise method rather than one where quantities can be culled or neutered just for being unexpectedly different from most of the other data.

This may have been selected because the Fibonacci sequence also has a convergent property: the ratio of two adjacent numbers in the sequence approaches the golden ratio as the length of the sequence approaches infinity.

Geothmetic means art of Geothming based on the etymology of Arithmetic (from Ancient Greek () (arithmtik (tkhn), (art of) counting).

This is an exciting new terminology that is eminently suitable for modern cosmology high energy physics - particularly when doing math on the multiverse.

However, it is unlikely this etymology is related to the term geothmetic meandian as coined by Randall, as it can be more simply explained as a portmanteau of the three averages in its construction: geo metric mean, ari thmetic mean, and me dian.

Cmd Gm Dn How To Explain It

But how to explain it Gonna have to think about that.

Theres a definite risk that mine might, as written.) 141.101.99.229 03:45, 11 March 2021 (UTC).