Mathematics › Geometry and Topology

Mathematics and Applications

Works Count: 102848

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This cluster of papers covers a wide range of topics in geometric mathematics, including hyperbolic geometry, loops, billiards in ellipses, Poncelet's theorem, Moufang loops, trigonometry, algebraic structures, and their applications in relativity and inversive geometry.

Keywords

Geometry; Hyperbolic; Loops; Billiards; Poncelet; Moufang; Trigonometry; Algebraic; Relativity; Inversive

A Combinatorial Problem in Geometry

2009-01-01

P. Erdős , G. Szckeres

Our present problem has been suggested by Miss Esther Klein in connection with the following proposition. From 5 points of the plane of which no three lie on the same … Our present problem has been suggested by Miss Esther Klein in connection with the following proposition. From 5 points of the plane of which no three lie on the same straight line it is always possible to select 4 points determining a convex quadrilateral.

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Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints

1972-01-01

K. S. Kölbig , F. Schäff

On p. 263, in formula 6.6.6 the coefficient of Ix(a, b) should read a + b -ax, in place of a + b -ab.Corresponding to this correction, on p. 944 … On p. 263, in formula 6.6.6 the coefficient of Ix(a, b) should read a + b -ax, in place of a + b -ab.Corresponding to this correction, on p. 944 the right side of formula 26.5.12 should read --l--{blz(a, b + 1) + a(l -x)Ix(a + 1, b -1)}.a(\ -x) + b On p. 541, in formula 14.5.12 the coefficient of t?" 16/3 should read .0008453619 999, instead of .0002534684 115, as first noted by Isacson [1].

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Algebraic geometry: a first course

1993-05-01

Joe Harris

1: Affine and Projective Varieties. 2: Regular Functions and Maps. 3: Cones, Projections, and More About Products. 4: Families and Parameter Spaces. 5: Ideals of Varieties, Irreducible Decomposition. 6: Grassmannians … 1: Affine and Projective Varieties. 2: Regular Functions and Maps. 3: Cones, Projections, and More About Products. 4: Families and Parameter Spaces. 5: Ideals of Varieties, Irreducible Decomposition. 6: Grassmannians and Related Varieties. 7: Rational Functions and Rational Maps. 8: More Examples. 9: Determinantal Varieties. 10: Algebraic Groups. 11: Definitions of Dimension and Elementary Examples. 12: More Dimension Computations. 13: Hilbert Functions and Polynomials. 14: Smoothness and Tangent Spaces. 15: Gauss Maps, Tangential and Dual Varieties. 16: Tangent Spaces to Grassmannians. 17: Further Topics Involving Smoothness and Tangent Spaces. 18: Degree. 19: Further Examples and Applications of Degree. 20: Singular Points and Tangent Cones. 21: Parameter Spaces and Moduli Spaces. 22: Quadrics.

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Geometry of Discrete Groups

2006-11-27

Alan F. Beardon

Geometric Measure Theory

1988-01-01

Herbert Fédérer

Geometric Integration Theory

1957-12-31

Hassler Whitney

A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be … A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

An Introduction to the Geometry of Numbers

1959-01-01

J. W. S. Cassels

Linear Algebraic Groups

1975-01-01

James E. Humphreys

Differential and Integral Inequalities

2019-01-01

Dorin Andrica , Themistocles M. Rassias

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Positivity in Algebraic Geometry I

2004-01-01

Robert Lazarsfeld

Theory of Functions of a Complex Variable

1966-06-01

A. I. Markushevich , Richard A. Silverman , J. Gillis

Volume I, Part 1: Basic Concepts: I.1 Introduction I.2 Complex numbers I.3 Sets and functions. Limits and continuity I.4 Connectedness. Curves and domains I.5. Infinity and stereographic projection I.6 Homeomorphisms … Volume I, Part 1: Basic Concepts: I.1 Introduction I.2 Complex numbers I.3 Sets and functions. Limits and continuity I.4 Connectedness. Curves and domains I.5. Infinity and stereographic projection I.6 Homeomorphisms Part 2: Differentiation. Elementary Functions: I.7 Differentiation and the Cauchy-Riemann equations I.8 Geometric interpretation of the derivative. Conformal mapping I.9 Elementary entire functions I.10 Elementary meromorphic functions I.11 Elementary multiple-valued functions Part 3: Integration. Power Series: I.12 Rectifiable curves. Complex integrals I.13 Cauchy's integral theorem I.14 Cauchy's integral and related topics I.15 Uniform convergence. Infinite products I.16 Power series: rudiments I.17 Power series: ramifications I.18 Methods for expanding functions in Taylor series Volume II, Part 1: Laurent Series. Calculus of Residues: II.1 Laurent's series. Isolated singular points II.2 The calculus of residues and its applications II.3 Inverse and implicit functions II.4 Univalent functions Part 2: Harmonic and Subharmonic Functions: II.5 Basic properties of harmonic functions II.6 Applications to fluid dynamics II.7 Subharmonic functions II.8 The Poisson-Jensen formula and related topics Part 3: Entire and Meromorphic Functions: II.9 Basic properties of entire functions II.10 Infinite product and partial fraction expansions Volume III, Part 1: Conformal Mapping. Approximation Theory: III.1 Conformal mapping: rudiments III.2 Conformal mapping: ramifications III.3 Approximation by rational functions and polynomials Part 2: Periodic and Elliptic Functions: III.4 Periodic meromorphic functions III.5 Elliptic functions: Weierstrass' theory III.6 Elliptic functions: Jacobi's theory Part 3: Riemann Surfaces. Analytic Continuation: III.7 Riemann surfaces III.8 Analytic continuation III.9 The symmetry principle and its applications Bibliography Index.

Classical and new inequalities in analysis

1993-12-01

D. S. Mitrinović , J. E. Pečarić , A. M. Fink

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Basic Algebraic Geometry 2

1994-01-01

Igor R. Shafarevich

Lectures on Classical Differential Geometry.

1952-02-01

Claude Springer , D. J. Struik

RELATIONS BETWEEN TWO SETS OF VARIATES

1936-12-01

Harold Hotelling

Journal Article RELATIONS BETWEEN TWO SETS OF VARIATES Get access HAROLD HOTELLING HAROLD HOTELLING Columbia University Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume … Journal Article RELATIONS BETWEEN TWO SETS OF VARIATES Get access HAROLD HOTELLING HAROLD HOTELLING Columbia University Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 28, Issue 3-4, December 1936, Pages 321–377, https://doi.org/10.1093/biomet/28.3-4.321 Published: 01 December 1936

Generators and Relations for Discrete Groups

1972-01-01

H. S. M. Coxeter , W. O. J. Moser

Two-dimensional gravity and intersection theory on moduli space

1990-01-01

Edward Witten

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A Hilbert Space Problem Book

1982-01-01

Paul R. Halmos

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Smithsonian Miscellaneous Collections

1924-07-01

A cONTRIBUTION , Toward An , Robert E. Snodgrass

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Metric Spaces of Non-Positive Curvature

1999-01-01

Martin R. Bridson , André Haefliger

Handbook of Discrete and Computational Geometry, Second Edition

2004-04-13

Jacob E. Goodman , Joseph OʼRourke

COMBINATORIAL AND DISCRETE GEOMETRY Finite Point Configurations, J. Pach Packing and Covering, G. Fejes Toth Tilings, D. Schattschneider and M. Senechal Helly-Type Theorems and Geometric Transversals, R. Wenger Pseudoline Arrangements, … COMBINATORIAL AND DISCRETE GEOMETRY Finite Point Configurations, J. Pach Packing and Covering, G. Fejes Toth Tilings, D. Schattschneider and M. Senechal Helly-Type Theorems and Geometric Transversals, R. Wenger Pseudoline Arrangements, J.E. Goodman Oriented Matroids, J. Richter-Gebert and G.M. Ziegler Lattice Points and Lattice Polytopes, A. Barvinok New! Low-Distortion Embeddings of Finite Metric Spaces, P. Indyk and J. Matousek New! Geometry and Topology of Polygonal Linkages, R. Connelly and E.D. Demaine New! Geometric Graph Theory, J. Pach Euclidean Ramsey Theory, R.L. Graham Discrete Aspects of Stochastic Geometry, R. Schneider Geometric Discrepancy Theory and Uniform Distribution, J.R. Alexander, J. Beck, and W.W.L. Chen Topological Methods, R.T. Zivaljevic Polyominoes, S.W. Golomb and D.A. Klarner POLYTOPES AND POLYHEDRA Basic Properties of Convex Polytopes, M. Henk, J. Richter-Gebert, and G.M. Ziegler Subdivisions and Triangulations of Polytopes, C.W. Lee Face Numbers of Polytopes and Complexes, L.J. Billera and A. Bjoerner Symmetry of Polytopes and Polyhedra, E. Schulte Polytope Skeletons and Paths, G. Kalai Polyhedral Maps, U. Brehm and E. Schulte ALGORITHMS AND COMPLEXITY OF FUNDAMENTAL GEOMETRIC OBJECTS Convex Hull Computations, R. Seidel Voronoi Diagrams and Delaunay Triangulations, S. Fortune Arrangements, D. Halperin Triangulations and Mesh Generation, M. Bern Polygons, J. O'Rourke and S. Suri Shortest Paths and Networks, J.S.B. Mitchell Visibility, J. O'Rourke Geometric Reconstruction Problems, S.S. Skiena New! Curve and Surface Reconstruction, T.K. Dey Computational Convexity, P. Gritzmann and V. Klee Computational Topology, G. Vegter Computational Real Algebraic Geometry, B. Mishra GEOMETRIC DATA STRUCTURES AND SEARCHING Point Location, J. Snoeyink New! Collision and Proximity Queries, M.C. Lin and D. Manocha Range Searching, P.K. Agarwal Ray Shooting and Lines in Space, M. Pellegrini Geometric Intersection, D.M. Mount New! Nearest Neighbors in High-Dimensional Spaces, P. Indyk COMPUTATIONAL TECHNIQUES Randomization and Derandomization, O. Cheong, K. Mulmuley, and E. Ramos Robust Geometric Computation, C.K. Yap Parallel Algorithms in Geometry, M.T. Goodrich Parametric Search, J.S. Salowe New! The Discrepancy Method in Computational Geometry, B. Chazelle APPLICATIONS OF DISCRETE AND COMPUTATIONAL GEOMETRY Linear Programming, M. Dyer, N. Megiddo, and E. Welzl Mathematical Programming, M.H. Todd Algorithmic Motion Planning, M. Sharir Robotics, D. Halperin, L.E. Kavraki, and J.-C. Latombe Computer Graphics, D. Dobkin and S. Teller New! Modeling Motion, L.J. Guibas Pattern Recognition, J. O'Rourke and G.T. Toussaint Graph Drawing, R. Tamassia and G. Liotta Splines and Geometric Modeling, C.L. Bajaj New! Surface Simplification and 3D Geometry Compression, J. Rossignac Manufacturing Processes, R. Janardan and T.C. Woo Solid Modeling, C.M. Hoffmann New! Computation of Robust Statistics: Depth, Median, and Related Measures, P.J. Rousseeuw and A. Struyf New! Geographic Information Systems, M. van Kreveld Geometric Application of the Grassmann-Cayley Algebra, N.L. White Rigidity and Scene Analysis, W. Whiteley Sphere Packing and Coding Theory, G.A. Kabatiansky and J.A. Rush Crystals and Quasicrystals, M. Senechal New! Biological Applications of Computational Topology, H. Edelsbrunner New! GEOMETRIC SOFTWARE Software, J. Joswig Two Computation Geometry Libraries: LEDA and CGAL, L. Kettner and S. Naher Index of Defined Terms New! Index of Cited Authors

AREAS, VOLUMES, PACKING, AND PROTEIN STRUCTURE

1977-06-01

Frederic M. Richards

Many bacterial clustered regularly interspaced short palindromic repeats (CRISPR)–CRISPR-associated (Cas) systems employ the dual RNA–guided DNA endonuclease Cas9 to defend against invading phages and conjugative plasmids by introducing site-specific ...Read … Many bacterial clustered regularly interspaced short palindromic repeats (CRISPR)–CRISPR-associated (Cas) systems employ the dual RNA–guided DNA endonuclease Cas9 to defend against invading phages and conjugative plasmids by introducing site-specific ...Read More

LIII. On lines and planes of closest fit to systems of points in space

1901-11-01

Karl Pearson

(1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 2, No. 11, … (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 2, No. 11, pp. 559-572.

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ELEMENTS OF ALGEBRAIC TOPOLOGY

1972-01-01

Kazimierz Kuratowski

Principles of Algebraic Geometry

1994-08-02

Phillip Griffiths , Joseph Harris

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SEMI-RIEMANNIAN GEOMETRY With Applications to Relativity

1984-05-01

M. A. H. MacCallum

By Barrett O'neill: pp. 468. £29.80. (Academic Press, 1983.) By Barrett O'neill: pp. 468. £29.80. (Academic Press, 1983.)

Tables of Integrals

1962-06-01

J Crank

A deservedly popular work of reference, first published almost thirty years ago, this book now appears in a fourth edition, re-designed and reset. The section on definite integrals has been … A deservedly popular work of reference, first published almost thirty years ago, this book now appears in a fourth edition, re-designed and reset. The section on definite integrals has been considerably enlarged and a section added on integrals essentially of elliptic type.

The Linear Complementarity Problem.

1993-01-01

M. E. B. Brigden , Richard W. Cottle , Jong‐Shi Pang +1 more

4. The Linear Complementarity Problem. By R. W. Cottle, J.‐S. Pang and R. E. Stone. ISBN 0 12 192350 9. Academic Press, San Diego, 1992. 762 pp. $59.95. 4. The Linear Complementarity Problem. By R. W. Cottle, J.‐S. Pang and R. E. Stone. ISBN 0 12 192350 9. Academic Press, San Diego, 1992. 762 pp. $59.95.

On the method of bounded differences

1989-08-03

Colin McDiarmid

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On the foundations of differential geometry

1964-01-01

Ramón G. Rubio

Cuba) (Recibido 14 de augusto de 1962) 1. ESTRUCTURAS Y MORFISMOS 1.1.Este es un trabajo de caracter metodologico.Definiremos de manera semiformal la notion de especie de estructura y de estructura … Cuba) (Recibido 14 de augusto de 1962) 1. ESTRUCTURAS Y MORFISMOS 1.1.Este es un trabajo de caracter metodologico.Definiremos de manera semiformal la notion de especie de estructura y de estructura de una especie dada sobre un conjunto de base E. La definition de estructuras sobre varios conjuntos de base, no difiere esentialmente de la anterior, como el lector puede corroborar en [3j.Ademas ?la definition a la manera de Ehresmann [4], (Definiciones 6 y 7) contiene como caso particular la de Bourbaki para uno o mas conjuntos de base.Sea E un conjunto que designaremos como " conjunto base" y A l9 ...,A n varios conjuntos que designaremos como "conjuntos auxiliares".Una construccion escalonada sobre E, de n -f 1 terminos, es una sucesion C i9 ..., C k de conjuntos que cumple las siguientes conditiones: a J Cj = E, C2 = -Ai,..., C" + i = A n .b) Para cada C i9 2 ^ i " fc, o bien: l) existen dos indices i 0 , i x < i tales que d = C io x C h (i 0 e i t pueden ssr iguales), o bien: 2) existe algun i 0 < i tal que C t = 1 ) Podemos pues hablar de ,,el axióma" de una estructura.

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Elements of Homotopy Theory

1978-01-01

George W. Whitehead

Differential Topology

1976-01-01

Morris W. Hirsch

Princeton Mathematical Series

1948-12-01

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content. An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Commutative Algebra

1995-01-01

David Eisenbud

Geometric Measure Theory

1996-01-01

Herbert Fédérer

The Geometry of Discrete Groups

1983-01-01

Alan F. Beardon

A Decision Method for Elementary Algebra and Geometry

1951-12-31

Alfred Tarski , J. C. C. McKinsey

Stochastic Geometry and Its Applications.

1988-06-01

David Aldous , D. Stoyan , W. S. Kendall +1 more

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Real Algebraic Geometry

1998-01-01

Frédéric Mangolte , Jean-Philippe Rolin , Kurdyka Krzysztof +2 more

Differential and Integral Inequalities

1970-01-01

Wolfgang Walter

NOW IS NOT THE TIME FOR NEO-CLASSICISM: THE CASE FOR NEO-CLASSICISM

2025-06-25

Matthew Shlomowitz | Tempo

Abstract Neoclassicism is now largely eschewed within New Music. While there seems space in our pluralistic scene for modernist, postmodernist, minimalist, performative and conceptual music, the compositional values of neoclassicism … Abstract Neoclassicism is now largely eschewed within New Music. While there seems space in our pluralistic scene for modernist, postmodernist, minimalist, performative and conceptual music, the compositional values of neoclassicism seem out of step and anachronistic. This article advocates that classical principles should be put back on the table, arguing not for a return to a historical neoclassicism but rather for idiosyncratic forms of neoclassicism that emphasise characteristics such as entertainment, playfulness, clarity, forms of tonality and engagement with received form.

Derivatives of Real Functions

2025-06-25

Nicolas A. Pereyra | CRC Press eBooks

Review of Trigonometric Functions

2025-06-25

Nicolas A. Pereyra | CRC Press eBooks

Additional Properties of Derivatives

2025-06-25

Nicolas A. Pereyra | CRC Press eBooks

Some basic facts about monodromy groups

2025-06-24

| Princeton University Press eBooks

None

2025-06-24

Didier Henrion , Jean B. Lasserre | Comptes Rendus Mathématique

We introduce a minor variant of the approximate D-optimal design of experiments with a more general information matrix that takes into account the representation of the design space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math>. … We introduce a minor variant of the approximate D-optimal design of experiments with a more general information matrix that takes into account the representation of the design space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math>. The main motivation (and result) is that if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>⊂</mml:mo><mml:msup><mml:mi>ℝ</mml:mi> <mml:mi>d</mml:mi> </mml:msup></mml:mrow></mml:math> is the unit ball, the unit box or the canonical simplex, then remarkably, for every dimension <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math> and every degree <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>, one obtains an optimal solution in closed form, namely the equilibrium measure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math> (in pluripotential theory). Equivalently, for each degree <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>, the unique optimal solution is the vector of moments (up to degree <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:math>) of the equilibrium measure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math>. Hence finding an optimal design reduces to finding a cubature for the equilibrium measure, with atoms in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math>, positive weights, and exact up to degree <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:math>. In addition, any resulting sequence of atomic D-optimal measures converges to the equilibrium measure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math> for the weak-star topology, as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> increases. Links with Fekete sets of points are also discussed. More general compact basic semi-algebraic sets are also considered, and a previously developed two-step design algorithm is easily adapted to this new variant of D-optimal design problem.

A Review on Kobers Trigonometric and Hyperbolic Inequalities in Optimization and Control Application

2025-06-24

D. P. Wagh | International Journal for Research in Applied Science and Engineering Technology

Kober’s trigonometric and hyperbolic inequalities form a significant class of functional inequalities that provide sharp bounds for nonlinear expressions involving sine, cosine, hyperbolic sine, and hyperbolic cosine functions. These inequalities, … Kober’s trigonometric and hyperbolic inequalities form a significant class of functional inequalities that provide sharp bounds for nonlinear expressions involving sine, cosine, hyperbolic sine, and hyperbolic cosine functions. These inequalities, originally established to refine classical analytic results, have found widespread application in modern optimization and control theory. In control system analysis, such inequalities are instrumental in deriving stability conditions, particularly in Lyapunovbased methods and the analysis of time-delay and nonlinear systems. Moreover, they serve as essential tools in the design of robust and adaptive controllers, where bounding nonlinearities is crucial for ensuring system performance and convergence. In optimization problems involving trigonometric constraints or cost functions, Kober-type inequalities aid in the convexification and approximation of non-convex terms, thereby enabling tractable solutions. This work presents an overview of Kober’s inequalities involving trigonometric and hyperbolic functions and explores their theoretical foundations, refinements, and applications in control system design and constrained optimization

Coupling Special Pair of Rectangles with Woodall and Euclid Primes

2025-06-22

G. Janaki | INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT

This study aims to systematically identify pairs of rectangles wherein the sum of their respective areas corresponds precisely to either a Woodall prime or a Euclid prime. For each such … This study aims to systematically identify pairs of rectangles wherein the sum of their respective areas corresponds precisely to either a Woodall prime or a Euclid prime. For each such prime encountered, the investigation further delineates the total number of contributing rectangle pairs, with a clear distinction drawn between primitive configurations—those with co-prime side lengths—and non-primitive ones, which may share common factors. Key Words: Pair of rectangles, Woodall prime, Euclid Prime, Primitive, Non-primitive, Area.

109.24 On a couple of simple quadratic inequalities

2025-06-20

Mehdi Hassani | The Mathematical Gazette

109.26 A simple self-improvement of the Cauchy-Schwarz inequality

2025-06-20

Reza Farhadian , Vadim Ponomarenko | The Mathematical Gazette

109.20 Less than equable triangles on the Eisenstein lattice

2025-06-20

Christian Aebi , Grant Cairns | The Mathematical Gazette

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109.27 A weighted Hölder’s inequality

2025-06-20

Kambiz Razminia | The Mathematical Gazette

109.29 Reverse of the Weitzenböck inequality

2025-06-20

Wei-Dong Jiang | The Mathematical Gazette

Questions arising from a duality between the median triangle theorem and a theorem of Pompeiu

2025-06-20

Mowaffaq Hajja , Panagiotis T. Krasopoulos | The Mathematical Gazette

This Article is motivated by the observation that the median triangle theorem can be thought of as a dual to a theorem of Pompeiu. It treats questions that arise from … This Article is motivated by the observation that the median triangle theorem can be thought of as a dual to a theorem of Pompeiu. It treats questions that arise from the pursual of this duality, and especially of certain imperfections in this duality.

Visualising alternating geometric series

2025-06-20

Michael R. Waters , Ritam Sinha | The Mathematical Gazette

When first learning about geometric series, students often wonder why these series are termed 'geometric'. The geometry of some geometric series is readily apparent for some common series such as … When first learning about geometric series, students often wonder why these series are termed 'geometric'. The geometry of some geometric series is readily apparent for some common series such as $$\sum\limits_{n = 1}^\infty {\left( {\frac{1}{2}} \right)}^n = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...{\text{ }}.$$

109.17 Covering a Hex Number with Octagonal Numbers

2025-06-20

Günhan Çağlayan | The Mathematical Gazette

Variations of the Vecten configurations

2025-06-20

Hans Humenberger , Michael de Villiers | The Mathematical Gazette

We present some less known variations of the the Vecten configuration and give purely geometric proofs for them. It is unlikely that these variations (and even proofs?) are new, probably … We present some less known variations of the the Vecten configuration and give purely geometric proofs for them. It is unlikely that these variations (and even proofs?) are new, probably just well-hidden in the literature. If a reader happens to know references for the variations discussed (or other geometric proofs), please let the authors know. At [1] the reader can find a dynamic webpage on our topic.

109.23 The derivative of the integral, redux

2025-06-20

George Stoica | The Mathematical Gazette

On conformal anomaly and pair production

2025-06-20

M. N. Chernodub | International Journal of Modern Physics A

The Schouten-Nijenhuis bracket, co-differential of products and generalized interior products of p-forms

2025-06-20

E. Huguet , J. Queva , Jacques Renaud | International Journal of Geometric Methods in Modern Physics

Odd run sums and fractions

2025-06-20

Ron Knott | The Mathematical Gazette

A series of consecutive odd numbers has interesting properties useful for classroom investigation [1]. This Article was inspired by the series of fractions for ${{1}\over{2}}$ using only sums of consecutive … A series of consecutive odd numbers has interesting properties useful for classroom investigation [1]. This Article was inspired by the series of fractions for ${{1}\over{2}}$ using only sums of consecutive odd numbers $$\frac{1}{3} = \frac{{1 + 3}}{{5 + 7}} = \frac{{1 + 3 + 5}}{{7 + 9 + 11}} = {\text{ }} \ldots {\text{ }} = \frac{{1 + 3 + {\text{ }} \ldots {\text{ }} + (2n - 3) + (2n - 1)}}{{(2n + 1) + (2n + 3) + {\text{ }} \ldots {\text{ }} + (2n + (2n - 1))}}.$$

Hunt for solutions to a problem of Euler

2025-06-20

Kapil Joshi | The Mathematical Gazette

A couple of years ago, a non-mathematician friend of mine who takes an interest in mathematics mainly as puzzles mentioned a problem of Euler. A couple of years ago, a non-mathematician friend of mine who takes an interest in mathematics mainly as puzzles mentioned a problem of Euler.

Measures of unequilaterality and refinements of inequalities

2025-06-20

Martin Lukarevski , Dan Ștefan Marinescu | The Mathematical Gazette

Let ABC be a triangle with sides a, b, c, semiperimeter s , circumradius R, inradius r and area Δ. We introduce $$Q\, = \,{(a - b)^2}\, + \,{(b - … Let ABC be a triangle with sides a, b, c, semiperimeter s , circumradius R, inradius r and area Δ. We introduce $$Q\, = \,{(a - b)^2}\, + \,{(b - c)^2}\, + \,{(c - a)^2}$$ and $$M\, = \,{(\left| {a - b} \right|\, + \left| {b - c} \right|\, + \,\left| {c - a} \right|)^2}.$$

PURE LINEAR ORDERINGS OF MORLEY O-RANK 1

2025-06-19

Viktor Verbovskiy , Aisha Yershigeshova | International Journal of Mathematics and Physics

The study of pure linear orderings—sets equipped solely with a linear (total) order—has deep historical roots in mathematical logic and order theory. Initial investigations trace back to Cantor’s work on … The study of pure linear orderings—sets equipped solely with a linear (total) order—has deep historical roots in mathematical logic and order theory. Initial investigations trace back to Cantor’s work on ordinal numbers, which laid the foundation for understanding different sizes of ordered sets. Early 20th-century research by Hausdorff and others explored order types and their classification. Later, developments in model theory and set theory refined the structural properties of pure linear orderings, including their rigidity, embeddability, and definability in various logical frameworks. So, pure linear ordering and its classification are one of the classical mathematical questions. Descriptions of o-minimal and weakly o-minimal pure linear orderings are known, as well as we know that any pure linear ordering has an o-superstable elementary theory. The aim of this paper is to start investigation of pure linear ordering that have o-ω-stable elementary theory. So, we give the complete description of pure linear ordering of Morley o-rank 1. Key words: Pure linear ordering, o-minimal structure, o-stable theory, Dedekind’s cut, ordered structure, Morley o-rank.

From Linear to Circular Model

2025-06-19

Francesco Poggi | Routledge eBooks

Mukai Lifting of Self-Dual Points in ℙ 6

2025-06-18

Barbara Betti , Leonie Kayser | Experimental Mathematics

Differential Geometry

2025-06-17

Mehdi Ghayoumi | Chapman and Hall/CRC eBooks

Symmetry and invariance

2025-06-17

| Cambridge University Press eBooks

Orbitalization ellipse via singular value decomposition

2025-06-16

Sushil Pokharel , Olga Korotkova | Optics Letters

On multipolynomial extensions of Kahae-Salem-Zygmund inequality and applications

2025-06-14

N. Albuquerque , Lindinês Coleta , T. Velanga | Topological Methods in Nonlinear Analysis

Some classical and recent Kahane-Salem-Zygmund inequalities developed into several contexts are extended to multipolynomials. The study compares such extensions to each other to comprehend which of them yields the smallest … Some classical and recent Kahane-Salem-Zygmund inequalities developed into several contexts are extended to multipolynomials. The study compares such extensions to each other to comprehend which of them yields the smallest norm for the associated function. Applications to the multilinear and polynomial scenarios are provided. For instance, a polynomial version of \cite[Corollary 1.2]{pelrap} is given, in which the constants are asymptotically bounded by $1$.

A geometric incompatibility by any other name

2025-06-13

David Abergel | Nature Physics

Schubert defects in Lagrangian Grassmannians

2025-06-13

Wei Gu , Leonardo C. Mihalcea , Eric Sharpe +3 more | Journal of High Energy Physics

A bstract In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. … A bstract In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory.

Beauty in/of mathematics: tessellations and their formulas

2025-06-13

Heinrich Begehr , Duo Wang | Applicable Analysis

Metric Geometry

2025-06-10

N. Vittorio | CRC Press eBooks