Results 11 to 20 of about 2,846 (143)
Pythagorean Triples before and after Pythagoras
Computation, 2020 Following the corrected chronology of ancient Hindu scientists/mathematicians, in this article, a sincere effort is made to report the origin of Pythagorean triples.
Ravi P. Agarwal
doaj +3 more sources
Pythagorean Triples with Common Sides
Journal of Mathematics, 2019 There exist a finite number of Pythagorean triples that have a common leg. In this paper we derive the formulas that generate pairs of primitive Pythagorean triples with common legs and also show the process of how to determine all the primitive and ...
Raymond Calvin Ochieng +2 more
doaj +3 more sources
Transformations of Pythagorean triples generated by generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsWe present matrices that transform Pythagorean triples arising from generalized Fibonacci sequences into other such triples. We also show that entries in the powers of such matrices can be expressed in terms of generalized Fibonacci sequences.
Jathan Austin
doaj +1 more source
Alternative solutions to the Legendre's equation x²+ky²=z² [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we aim to provide alternative solutions of the Legendre's equation x²+ky²=z², where k is a square-free positive integer. The results also lead to solutions of the well-known Pythagorean triples and Eisenstein triples.
Kanwara Mukkhata, Sompong Chuysurichay
doaj +1 more source
Incremental and Transitive Discrete Rotations [PDF]
, 2006 A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation.
A. Amir +5 more
core +4 more sources
Efficient Certified Resolution Proof Checking [PDF]
, 2016 We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-
A Biere +29 more
core +3 more sources
Almost and Nearly Isosceles Pythagorean Triples
International Journal of Mathematics and Mathematical Sciences, 2016 This work is about extended pythagorean triples, called NPT, APT, and AI-PT. We generate infinitely many NPTs and APTs and then develop algorithms for infinitely many AI-PTs.
Eunmi Choi
doaj +1 more source
Generalized Pythagorean Triples and Pythagorean Triple Preserving Matrices
Missouri Journal of Mathematical Sciences, 2009 Traditionally, Pythagorean triples (PT) consist of three positive integers, $(x, y, z) \in \mathbb{Z}^3_+$, such that $x^2 + y^2 = z^2$, and Pythagorean triple preserving matrices (PTPM) $A$ are $3 \times 3$ matrices with entries in the real numbers $\R$, such that the product $(x, y, z)A$ is also a Pythagorean triple.
Tikoo, Mohan, Wang, Haohao
openaire +2 more sources
Clifford Algebras and Euclid's Parameterization of Pythagorean Triples
, 2012 We show that the space of Euclid's parameters for Pythagorean triples is endowed with a natural symplectic structure and that it emerges as a spinor space of the Clifford algebra $\mathbb{R}_{2,1}$, whose minimal version may be conceptualized as a 4 ...
Kocik, Jerzy
core +1 more source
Antieigenvalue analysis for continuum mechanics, economics, and number theory
Special Matrices, 2016 My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum ...
Gustafson Karl
doaj +1 more source