No, as I don't want or expect anyone here to take me seriously - I don't even!wtf wrote: ↑Wed Feb 12, 2020 1:56 amOk that's fine. But then do this. Say, "A standard polynomial is such and so. But for my purposes I want to define a nothing-polynomial as ..." then make your definition. In math you can make up any definition you want.

But when you change the definition of a standard term without first announcing that fact, you simply appear divorced from reality, claiming to have a polynomial with integer coefficients then presenting an expression that is nothing of the kind.

If you wish to communicate with others, then whenever you re-define standard terminology, announce that fact by clearly giving your own definition. Otherwise you can't be taken seriously. Doesn't that make sense?

3 is a real integer coefficient of 3π - the usage/definition is not uncommon.

Meaning devoid of grasping.

Such feedback is more appropriate via pm, not public - the sentiment is not altruistic otherwise.

There is a reason(s) for it, but not appropriate to talk about.

I am aware of Euler's but do not see e^(2πi)=1wtf wrote: ↑Wed Feb 12, 2020 1:56 amYou might find this helpful.

https://en.wikipedia.org/wiki/Euler%27s_formula

I don't myself care about "standard" anything - western science, including math, is rooted in much hubris and absurd assumptions. The same article you linked to already indicates the "geometric" implications:wtf wrote: ↑Wed Feb 12, 2020 1:56 amPlease define "geometric" in this context. Of course pi has many geometric relations. But in terms of standard math, with the standard definitions, do you understand that phi is algebraic, pi is transcendental, and that these are mutually exclusive classes of real numbers?

In deriving Φ by way of π the unit circle derived by way of Φ² = Φ + 1 is "geometrically" bound to the operation of π. This is broad spectrum and general, thus any desired base/power arrangement can be used for any purpose, and the relationship will be preserved because it is "geometrically" bound.This formula can be interpreted as saying that the function e^iφ is a unit complex number, i.e., it traces out the unit circle in the complex plane as φ ranges through the real numbers. Here φ is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counterclockwise and in radians.

...which is what makes it appear transcendental. It doesn't mean anything just "sitting" at a particular location:

it is like a pottery wheel: you can not shape pots without the wheel moving. Similarly, π is meaningless unless

in relation to some kind of motion if/when modelling anything at all in the real universe.

Each 2π is thus a "whole" rotational base. The relation is not different: it is the same.wtf wrote: ↑Wed Feb 12, 2020 1:56 amAll in all, as we wrap the real number line around the unit circle, it keeps cycling over the same points with a period of 2pi. That's the period of the sin and cosine functions, and also of the complex exponential. The point (1,0) in the plane, or the complex number 1, gets hit by rotating around the circle 0 radians, 2pi radians, 4pi radians, and in general every 2pi radians you come back to the same spot. This is true.

Your relation to phi is much less clear and I can't understand what you're doing.

All I am doing is showing that, if using (π + π√5) instead of (1 + √5) the '1' is derived naturally

as the unit circle, and intrinsically in relation to π (otherwise not the case if arbitrarily generating Φ with '1'):

every 2π concerns '1' and π√5 concerns a pentagram, with 2π being both a full circle and both symmetries of a pentagram.

I thought the implication would have been more obvious: the "marriage" of "line" and "curve" under a common base of '1'

concerning any possible Euclidean geometry.