Insights An Introduction to Theorema Primum

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Introduction
Whilst no doubt most frequenters of “Physics Forums” will be familiar with Nicolaus Copernicus as the scientist who advanced the (at the time) radical thesis that the Earth revolved around the sun rather than vice versa, a perhaps less well-known aspect of his work is the “nuts and bolts” geometry underlying his ground-breaking treatise: “De Revolutionibus Orbium Coelestium” (On the Revolutions of the Heavenly Spheres).  In this article (and perhaps others to follow), we analyse “Copernican geometry” in light of its stated intent:
Because the proofs which we shall use in almost the entire work deal with straight lines and arcs, with plane and spherical triangles, and because Euclid’s Elements, although they clear up much of this, do not have what is here most required, namely how to find the sides from the angles and the angles from the sides, since the angle does not measure the subtending straight line – just as the line does not measure the angle – but the arc does...

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Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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