Pythagorean numbers and the calculation of the masses of the elementary particles

We attempt here to calculate the particle masses for all known elementary particles starting from the Rydberg equation and from the Sommerfeld fine structure constant. Remarkably, this is possible. Next, we try to explain why this is possible and what the meaning of the approach seems to be. Thereby, we find some interesting connections. In addition, we realize that there are two different kinds of mass-charge binding energies in an elementary particle: The internal mass-charge binding energy and the external mass-charge binding energy. These two kinds of mass-charge binding energies can explain the higher masses of the highly charged brother particles in some of the heavier particle triplets (such as the charmed sigma particles).

Connection Between A Right Triangle And An Equal Side Triangle

There is some evidence that a right triangle and an equilateral triangle are related. Information about Pythagorean numbers is given. The geometric meaning of the relationship between right triangles and equilateral triangles is shown. The geometric meaning of the relationship between an equilateral triangle and an equilateral triangle is shown.

Basic points resulting from mixed radius: النقاط الأساسية الناتجة من أنصاف أقطار مختلطة

Throughout this research, we present generating the correct points on the Pythagorean circle discussing the different cases of the radius that is defined by the following equation: Where: are different prime Pythagorean numbers. This research is going to create the fundamental points which generate the correct points in the circle. Besides, I am going to calculate the number of the correct points on the circumference of a circle in every different form of the equation (1) via the following: - Depending on the laws and theorems resulted from this research. - Depending on the computer program (C #) to yield fast and effective results. We conclude by saying: We should take into account that the aim of this study is to pinpoint the nature and the number of the correct points on the circumference of a Pythagorean circle. As a result, we can exploit these points to decipher the data when they are transferred between users via unsecured nets. The current applied mechanism is to use elliptic curves which are complex and difficult to use if compared to the use of central Pythagorean circles due to its features and characteristics.

An algorithm to search Pythagoreans numbers using functional programming

The article presents a possible solution to the search for numbers that are formed in Pythagorean triples by an implementation with functional programming under the technical and syntactical possibilities DrRacket Scheme language environment. The methodology is framed in educational research quantitative. The results of this algorithm and its use, show the possibility of finding simple solutions, from the functional point of view, to solve problems with some complexity and more meaningful learning and more sense in the field of computer programming by the students. The program presented is an example to find a more technological application instance and instrumental expression of mathematics.Keywords: Algorithm, functional programming, Pythagorean numbers, recursion.

Jeśmanowicz’ Conjecture with Congruence Relations. II

Let a, b, and c be primitive Pythagorean numbers such that a2 + b2 = c2 with b even. In this paper, we show that if b0 ≡ ∊(mod a) with ε ∊ {±1} for certain positive divisors b0 of b, then the Diophantine equation ax + by = cz has only the positive solution (x, y, z) = (2, 2, 2).

ON THE DIOPHANTINE EQUATION (8n)x+(15n)y=(17n)z

Let a,b,c be relatively prime positive integers such that a2+b2=c2. Half a century ago, Jeśmanowicz [‘Several remarks on Pythagorean numbers’, Wiadom. Mat.1 (1955/56), 196–202] conjectured that for any given positive integer n the only solution of (an)x+(bn)y=(cn)z in positive integers is (x,y,z)=(2,2,2). In this paper, we show that (8n)x+(15n)y=(17n)z has no solution in positive integers other than (x,y,z)=(2,2,2).