Reflections, Rotations, and Pythagorean Numbers

2008 ◽  
Vol 19 (1) ◽  
pp. 1-14 ◽  
Author(s):  
G. Aragón-González ◽  
J. L. Aragón ◽  
M. A. Rodríguez-Andrade ◽  
L. Verde-Star
Keyword(s):  
Pythagorean Numbers

Tenth wave, the Pythagorean numbers, and the etymology of “ten”

1858 ◽  
Vol s2-V (114) ◽  
pp. 194-197
Author(s):  
Andrew Steinmetz
Keyword(s):  
Pythagorean Numbers

Jeśmanowicz’ Conjecture with Congruence Relations. II

2014 ◽  
Vol 57 (3) ◽  
pp. 495-505 ◽  
Author(s):  
Yasutsugu Fujita ◽  
Takafumi Miyazaki
Keyword(s):  
Positive Solution ◽  
Diophantine Equation ◽  
Congruence Relations ◽  
Pythagorean Numbers

AbstractLet 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).

Pythagorean Numbers

1974 ◽  
Vol 67 (7) ◽  
pp. 667-669
Author(s):  
Israel Cohen
Keyword(s):  
Simple Method ◽  
Pythagorean Numbers

This article shows a simple method for finding the sets of integers that are the measures of sides of right triangles. It provides a method for the geometry teacher or students to generate right triangles.

The Pythagorean Numbers in Vector Problems

1964 ◽  
Vol 32 (11) ◽  
pp. 850-852 ◽  
Author(s):  
Leo Lavatelli
Keyword(s):  
Pythagorean Numbers

Pythagorean Numbers

1959 ◽  
Vol 59 (2) ◽  
pp. 99-100
Author(s):  
Earl G. Boyd
Keyword(s):  
Pythagorean Numbers

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

2021 ◽  
Vol 34 (3) ◽  
pp. 322-330
Author(s):  
Borros Arneth
Keyword(s):  
Elementary Particle ◽  
Fine Structure ◽  
Binding Energy ◽  
Structure Constant ◽  
Elementary Particles ◽  
Binding Energies ◽  
Fine Structure Constant ◽  
Internal Mass ◽  
Pythagorean Numbers ◽  
The Masses

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).

An algorithm to search Pythagoreans numbers using functional programming

2016 ◽  
Author(s):  
Omar Iván Trejos-Buriticá
Keyword(s):  
Educational Research ◽  
Functional Programming ◽  
Meaningful Learning ◽  
Point Of View ◽  
Technological Application ◽  
Pythagorean Triples ◽  
Pythagorean Numbers ◽  
Functional Point ◽  
Language Environment ◽  
Scheme Language

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.

Pythagorean numbers

1954 ◽  
Vol 47 (1) ◽  
pp. 16-21
Author(s):  
Philip J. Hart
Keyword(s):  
High School ◽  
Senior High School ◽  
Pythagorean Numbers

Pythagorean sets have interested mathematicians for over 2000 years. They may be of interest to some students in the mathematics classes of the senior high school and the college.

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