Catching Proteus: the collaborations of Wallis and Brounker. II. Number problems

2000 ◽  
Vol 54 (3) ◽  
pp. 317-331 ◽  
Author(s):  
Jacqueline A. Stedall
Keyword(s):  
Number Theory ◽  
Continued Fractions

Following the discussion of Brouncker's work on quadrature, rectification and continued fractions in Part I of this paper, Part II analyses the disputes between Brouncker and Wallis in England and Fermat in France over problems in what would now be called number theory. Contemporary and later observers regarded Brouncker and Wallis as equally responsible for the English contribution, but it was Brouncker who took the greater interest in Fermat's challenges and who produced the more sophisticated solutions. The paper ends with an assessment of Brouncker's contribution to mathematics and argues that his contemporary reputation was well deserved and his mathematics of lasting value.

scholarly journals Про Эйлера и Чебышёва, основателей российской математики

2021 ◽  
pp. 42-63
Author(s):  
A. Papadopoulos
Keyword(s):  
Number Theory ◽  
Continued Fractions ◽  
Applied Science ◽  
Pure Mathematics ◽  
Mathematics Integration

On the occasion of Chebyshev’s twohundredth anniversary, I review part of his work, showing that in several respects he was the heir of Euler. In doing this, I consider the works of Euler and Chebyshev on three topics in applied science: industrial machines, ballistics and geography, and then on three topics in pure mathematics: integration, continued fractions and number theory, showing that in each filed the two mathematicians were interested in the same kind of questions. По случаю двухсотлетнего юбилея Чебышёва я изучил часть его работ и пришел к выводу, что в целом ряде моментов он продолжает научные традиции Эйлера. Я рассматривал работы Эйлера и Чебышёва по трем прикладным темам: промышленное оборудование, баллистика и география, а также по трем разделам чистой математики: интегральное исчисление, непрерывные дроби и теория чисел. Показано, что во всех случаях оба математика изучали один и тот же круг вопросов.

scholarly journals QUANTUM BOUND STATES FOR A DERIVATIVE NONLINEAR SCHRÖDINGER MODEL AND NUMBER THEORY

2004 ◽  
Vol 19 (36) ◽  
pp. 2697-2706 ◽  
Author(s):  
B. BASU-MALLICK ◽  
TANAYA BHATTACHARYYA ◽  
DIPTIMAN SEN
Keyword(s):  
Number Theory ◽  
Binding Energy ◽  
Continued Fractions ◽  
Bound States ◽  
Coupling Constant ◽  
Nonlinear Schrödinger ◽  
Farey Sequences ◽  
Negative Binding Energy

A derivative nonlinear Schrödinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant η. The ranges of η within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N≥3, the N-body bound states can have both positive and negative momenta. For η>0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.

The Plaid Model

2019 ◽  
Author(s):  
Richard Evan Schwartz
Keyword(s):  
Dynamical System ◽  
Number Theory ◽  
Continued Fractions ◽  
Planetary Motion ◽  
Elementary Number Theory ◽  
Convex Shape ◽  
Tile System ◽  
Outer Billiards ◽  
Combinatorial Model ◽  
Self Similar

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. This book provides a combinatorial model for orbits of outer billiards on kites. The book relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid model,” has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.

Multiplicative Number Theory I

2006 ◽  
Author(s):  
Hugh L. Montgomery ◽  
Robert C. Vaughan
Keyword(s):  
Number Theory
Sign in / Sign up

Export Citation Format

Share Document