Related papers: The Pythagoras' Theorem

A formal theory of experimentation will be presented. Such a theory presents the necessary & sufficient conditions a world must satisfy in order to admit the use of the scientific method.

We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

A detailed and rigorous analysis of G\"odel's proof of his first incompleteness theorem is presented. The purpose of this analysis is two-fold. The first is to reveal what G\"odel actually proved to provide a clear and solid foundation upon…

After a review of the results in arXiv:1203.3184 [math-ph] about Pythagorean inequalities for products of spectral triples, I will present some new results and discuss classes of spectral triples and states for which equality holds.

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.

The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…

We provide an alternative unified approach for proving the Pythagorean theorem (in dimension $2$ and higher), the law of sines and the law of cosines, based on the concept of shape derivative. The idea behind the proofs is very simple: we…

The story on the early days of the Quantum Ergodic Theorem. Alternative proof, underlying heuristics, physical analogies and interpretations.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…

We give an elementary proof to Hasse theorem.

Parikh's theorem is a fundamental result of the formal language's theory. There had been published many proofs and many papers claimed to provide a simplified proof, but most of them are long and still complicated. We provide the proof that…

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.

We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and…

We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…

In the early part of the paper, various geometrical formulas are derived. Then, at some point in the paper, the concept of a Pythagorean rational is introduced. A Pythagorean rational is a rational number which is the ratio of two integers…

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…