相关论文: On Leonardo da Vinci's proof of the Theorem of Pyt…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
Pythagoras' theorem lies at the heart of physics as well as mathematics, yet its historical origins are obscure. We highlight a purely pictorial, gestalt-like proof that may have originated during the Zhou Dynasty. Generalizations of the…
We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing,…
We give a proof of Pythagoras' theorem which does not use neither squares nor similarity of triangles.
The classical Pythagoras theorem, binomial theorem, de Moivre's formula, and numerous other deductions are made using the uniqueness theorem for the initial value problems in linear ordinary differential equations.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
We present a new proof of a primality criterion first proved by Emmanuel Vantieghem.
There are two hypotheses on Leonardo's polyhedron based on the Pseudo-RCO and drawn for Luca Pacioli's book: Leonardo made an error, or: Leonardo draw it with intention, as it is. We give arguments, which support the Intention-hypothesis.
The Pythagorean Theorem is one of the oldest, more famous and more useful theorems of Mathematics, and possibly the one that has had the most impact in the evolution of this and other sciences. In this article, we look at it from different…
In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.
It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light $c$ is the unit of velocity allows to cast all…
We give a short proof of Szemer\'edi's regularity lemma, based on elementary Euclidean geometry. The general line of the proof is that of the standard proof (in fact, of Szemer\'edi's original proof), but most technicalities are swallowed…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak…
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
How was this proof overlooked for 181 years? We give a simple proof of Descartes's circle theorem using Cayley-Menger determinants.
Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number theorem.
We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.
We derive Pythagoras theorem. From the Pythagoras theorem, we also derive Mathieu's equation via modified Mathieu's equation. A spectral com- parison has been carried out between modified Mathieu's equation and Mathieu's equation. Apart…