Quoting yor_on:

So how did you get the idea Don?

It would be immensely cool if you were right of course

The seperation of polygonal numbers into those that

are of order greater than 2 and those that are not

is analogous to the seperation of natural numbers

into primes and composites.

Both the sequence of primes and the sequence of

polygonal numbers of order greater than 2 are

erratic, irregular, patternless, random and

utterly unpredictable, and I found it rather

amazing that mathematicians never developed

a counting function for polygonals of order

greater than 2, the way they had for the primes,

because polygonal numbers are among the most

studied numbers in the history of mathematics!

Thus it was quite natural for a curious person

such as myself to try and develop a counting

function for polygonal numbers of order > 2,

if only to see what such a function might look

like and what such a function might entail !

Now, when I began my research into this question,

the empirical data was hardly sufficient to even

hazard a guess as to what mathematical constructs

might be involved, so I developed several functions

based on what I considered to be reasonable assumptions,

employing a technique whereby

*one* constant is allowed

to emerge as a consequence of the "relative error".

I then asked several coders to provide me with more

empirical data, and as that data came in, it became

apparent that one of the constants in one of my functions

was either the fine structure constant, or some number

very close to it.

The emergence of the

**fine structure constant** in this

manner came as a complete and utter shock to me,

because I was expecting a

**mathematical** rather than

a

**physical** constant!

Quoting yor_on:

Then your idea should work equivalently well for other constants too,

if we were to assume that, don't you agree?

At this point, nobody knows.

It may turn out that the other physical constants

are

**related** to the

**fine structure constant** and the

**proton to electron mass ratio** in a way that will allow them

to be determined by some similar mathematical construct.

After all, the fine structure constant is already known

to involve many other constants, including the speed of

light and the reduced Planck constant.

Don.