The Squaring Pi and the Floating point.
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages

You can see many of my works, in the following pages:

Email: ferman25@hotmail.com
Email: ferman30@yahoo.es

The Squaring Pi and the Floating point

The Squaring Pi, expressed as a Floating Point.

Friends, I understand that the squaring Pi has all the properties that the correct Pi must have, and therefore any critical mathematician "could" conclude that this is the correct Pi number.
* (All these properties can be seen on the web page corresponding to this work. (Pi: Direct Formula)).
Here we are going to see a characteristic that for me is very curious and mathematically interesting, and that simplified, it could be:
--- If we subject the Squaring Pi number to successive powers (Pi^n)......
--- And the solutions are expressed in the form of a Floating Point (FP = significand x base ^ exp.)......
--- We will have that for the exponent (exp=8), the significand will be ((2.Sqrt2) = Semi-square inscribed to the circumference of radius 1).
* For this solution, we will have subjected to sPi, to the power 17 (Pi^n = Pi^17)
------------------------
Therefore, and if we want to use this property to obtain the squaring Pi, it is enough to go through the formula in the opposite direction.
sPi = f(2) = [(2Sqrt2 x 10^8 )]^(1/17) = 3.14159144414199..........
-----------------------
Logically, this property of exponentiation of Pi is fulfilled by the Squaring Pi, but not by the current algorithmic Pi:
Squaring Pi -------- sPi^17 / 10^8 = 2.8284271247461....... = 2Sqrt2
Algorithmic Pi ----- aPi^17 / 10^8 = 2.82844563586533....NOT= 2Sqrt2
-----------------------
*** As complementary information, it must be said that exp=8, is the sum of the exponents (of radius 1) necessary to obtain the semi-square inscribed in the circumference by the Pythagorean theorem, theorem that is used as a principle and logical basis for obtaining (and explaining) the squaring Pi. (see drawing)

-----------------------

** Since Pi^2 is minor but close to 10^1, this case the exact relationship occurs when Pi(^2n+1) = b.10^n, and therefore for n=8 (sum of exponents by the Pythagorean theorem)

------------------------

Some qualities of the squaring Pi:

-- In the first place, a basic and very important quality for me is that of being obtained by the DIECT formula of all the constructive parameters of the circumference (Diameter, square circumscribed to the circumference, inscribed square) as well as the use of the Pythagorean theorem, of the Floating Point, (drawing) etc.
And it is important because it is the way to get the perimeters of all geometric figures (simple and regular geometric figures do not use approximation formulas to find their perimeter).
But it is that this property makes it a SPECIAL Pi number, since it is the only adjustment in the history of mathematics, that uses a direct formula, and not an approximation one as in the other methods.
In good logic, the approximation methods should not give us an exact result, since they do not have any construction parameter (reference parameter) of the circumference (r=1).

-- Another property of squaring Pi is that with formulas of its powers, we can obtain (to infinity) all the squares and circumscribed circles on a given one (ciscunscription theorem).