“The True Nature and the Transcendental Approach

of the Universal Constant š – known as Archimedes’ Number”


As viewed by a Mechanical Engineer of the National Technical University of Athens (NTUA)

Mr. Moschos Ath. Karagounis


The New Transcendental Theory Reveals and Proves the following:


1. The problem of Number š (as well as the dependent problem of the squaring of the circle) was never a “closed problem”

The circle closes conclusively and perfectly only with the absolute value of š = 3,1416 exactly, which in conjunction with the equally Constant m = 4k  = 0,8584, constitute the two real and unequal roots of the Algebraic Equation of the circle, under the formula:


x2 - (š + m)x + š m = x2 - 4x + 2,69674944 = 0


2. We did not know neither what the wanted was, nor its nature. The New Transcendental Theory reveals both, by proving that it is the common ratio of:

with the corresponding

so that:


3. The number m = 0,8584 = 0,81 + 0,0484 = 0,92 + 0,222, as the sum of two squares, leads us to the construction, by means of Ruler and Compass, of the chord (BnC) = R.

The same holds true for the number š = 4 –  = 22 – (0,92 + 0,222), as the difference of two squares, which makes possible the construction

of the chord (ABn) = R.

This results to the squaring of the circle, only by means of Ruler and Compass.


Moschos Ath. Karagounis

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