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Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry
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Solid Geometry
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Lezioni di Geometria Proiettiva
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Notes On Stereotomy
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An Elementary Treatise on Plane Trigonometry
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Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance
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Elements of Geometry and Plane Trigonometry. With an Appendix, and Copious Notes and Illustrations
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Scientific Romances
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Junior High School Mathematics
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Geometrical Amusements
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Solution of Triangles
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New Analytic Geometry
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Key to Milne’s Plane and Solid Geometry
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The Illustrated Architectural, Engineering, & Mechanical Drawing-book
Notes On Roulettes and Glissettes
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A Treatise On the Analytical Geometry of the Point, Line, Circle, and Conic Sections
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Elements of Geometry, and Plane and Spherical Trigonometry
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The Mathematical Questions Proposed in the Ladies' Diary, and Their Original Answers
A Treatise On Mensuration
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The Illustrated Architectural, Engineering, & Mechanical Drawing-book
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Plane Trigonometry, Part 1
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Introductory Modern Geometry of Point, Rsy, and Circle
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The Elements of Euclid
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A Treatise on Conic Sections and the Application of Algebra to Geometry
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Elements of Plane and Spherical Trigonometry, With its Applications to the Principles of Navigation and Nautical Astronomy; With the Logarithmic and Trigonometrical Tables
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Elements of Geometry, After Legendre
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The Elements of Euclid
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Plane Trigonometry, Part 1
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The Secret of the Circle and the Circle Squared
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Euclide's Elements
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Geometric Algebra
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Radix Mission
The book is in 3 chapters, the first looks at mathematical series and shows how we can get the sum of arithmetic and geometric series and how the theorem of series can be applied towards the solution of convergence and divergence. In the second chapter we look at the Newton expansion and how it can be used to accurately and quickly evaluate pi to high precision. We are introduced to the opensource GMP arbitrary precision package that massively quickens our calculations and we show how pi can be calculated to phenomenal accuracy very quickly on a modest pc. In the third chapter we look at regular convex polyhedra and we show why there are only 5 of such. we show how we can construct them from their base regular polygons. We show their visualisation in 3D design software.
Euclide’s Elements
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How Many Zeroes?
This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein's theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein's original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students.
Certificates of Positivity for Real Polynomials
This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positivity for a real polynomial is an algebraic identity that gives an immediate proof of a positivity condition for the polynomial. Certificates of positivity have their roots in fundamental work of David Hilbert from the late 19th century on positive polynomials and sums of squares. Because of the numerous applications of certificates of positivity in mathematics, applied mathematics, engineering, and other fields, it is desirable to have methods for finding, describing, and characterizing them. For many of the topics covered in this book, appropriate algorithms, computational methods, and applications are discussed. This volume contains a comprehensive, accessible, up-to-date treatment of certificates of positivity, written by an expert in the field. It provides an overview of both the theory and computational aspects of the subject, and includes many of the recent and exciting developments in the area. Background information is given so that beginning graduate students and researchers who are not specialists can learn about this fascinating subject. Furthermore, researchers who work on certificates of positivity or use them in applications will find this a useful reference for their work.
Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity
This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled "Einstein Equations: Physical and Mathematical Aspects of General Relativity". Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like: Quantum ergosphereGeneral relativistic Poynting-Robertson effect modellingNumerical relativityLength-contraction in curved spacetimeClassicality from an inhomogeneous universeEinstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.
