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Books on the topic 'Coordinate geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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1

Coordinate geometry. Mineola, N.Y: Dover Publications, 2005.

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2

M, Pang K., ed. Calculus and coordinate geometry. Hong Kong: Vision, 1992.

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3

Mark, June. Geography of the coordinate plane: Teaching guide. Portsmouth, NH: firsthand/Heinemann, 2014.

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4

Ross, Debra. Master math: Geometry : including everything from triangles, polygons, proofs, and deductive reasoning to circles, solids, similarity, and coordinate geometry. Clifton Park, NY: Thomson/Delmar Learning, 2005.

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5

Master math: Trigonometry : including everything from trigonometric functions, equations, triangle, and graphs to identities, coordinate systems, and complex numbers. Clifton Park, NY: Thomson/Delmar Learning, 2002.

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6

Ciarlet, Philippe G. An introduction to differential geometry with applications to elasticity. Dordrecht: Springer, 2010.

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7

Anderson, Moira. Grid coordinates by land, air, and sea. Mankato, Minn: Capstone Press, 2010.

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8

ill, Kenyon Tony, ed. Plotting points and position. Brookfield, Conn: Copper Beech Books, 1998.

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9

ill, Geehan Wayne, ed. Sir Cumference and the Viking's map. Watertown, MA: Charlesbridge, 2012.

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10

Coordinate-free multivariable statistics: An illustrated geometric progression from Halmos to Gauss and Bayes. Oxford: Clarendon Press, 1987.

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11

Thompson, Henry Dallas, and Henry Burchard Fine. Coordinate Geometry. Kessinger Publishing, LLC, 2007.

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12

Nicolaides, Anthony, and A. Nicolaides. Coordinate Geometry. Hyperion Books, 1994.

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13

Luther, Pfahler Eisenhart. Coordinate Geometry. Luther Press, 2007.

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14

Tripathi, Mukut Mani. Coordinate Geometry. Alpha Science International, Ltd, 2005.

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15

Pfahler, Eisenhart Luther. Coordinate Geometry. Dover Publications Inc., 2000.

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16

Thompson, Henry Dallas, and Henry Burchard Fine. Coordinate Geometry. Kessinger Publishing, LLC, 2007.

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17

Thompson, Henry Dallas, and Henry Burchard Fine. Coordinate Geometry - Illustrated. Merchant Books, 2006.

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18

Coordinate Geometry (Lifepac Math Grade 10-Geometry). Alpha Omega Publications (AZ), 2001.

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19

Loney, Sidney Luxton. The Elements Of Coordinate Geometry. 2nd ed. Merchant Books, 2007.

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20

Kishan, Hari. Coordinate Geometry of Two Dimensions. Atlantic Publishers & Distributors (P) Ltd., 2006.

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21

Loney, Sidney Luxton. The Elements of Coordinate Geometry. Historic Publishing, 2018.

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22

Mathers, Marci. Coordinate Graphing: Creating Geometry Quilts, Grades 4 & Up. Teacher Created Resources, 2010.

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23

Tewani, G. Mathematics For Joint Entrance Examination Jee Advanced: Coordinate Geometry. Cengage Publications, 2015.

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24

Gaskin, Thomas. The Solutions Of Geometrical Problems - Examples In Plane Coordinate Geometry. Merchant Books, 2007.

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25

Walton, William. Problems In Illustration Of The Principles Of Plane Coordinate Geometry. Kessinger Publishing, LLC, 2007.

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26

Series, Michigan Historical Reprint. Coordinate geometry, by Henry Burchard Fine and Henry Dallas Thompson. Scholarly Publishing Office, University of Michigan Library, 2005.

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27

Series, Michigan Historical Reprint. The elements of coordinate geometry, by S. L. Loney, M.A. Scholarly Publishing Office, University of Michigan Library, 2005.

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28

Volson, Wood De. The Elements of Coordinate Geometry : In Three Parts: 1. Cartesian Geometry; 2. Quaternions; 3. Modern Geometry, and an Appendix. Franklin Classics, 2018.

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29

1820-1884, Todhunter I., ed. Solutions to problems contained in A treatise on plane coordinate geometry. London: Macmillan, 1990.

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30

Wittman, David M. Spacetime Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199658633.003.0011.

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This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.
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31

Series, Michigan Historical Reprint. Problems in illustration of the principles of plane coordinate geometry. By William Walton. Scholarly Publishing Office, University of Michigan Library, 2005.

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32

Howe, George. Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus; with Answers to Problems,. Nabu Press, 2010.

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33

Takashi, Aoki, and Kyōto Daigaku. Sūri Kaiseki Kenkyūjo., eds. A fresh glimpse into the Stokes geometry of the Berk-Nevins-Roberts equation through a singular coordinate transformation. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2005.

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34

Deruelle, Nathalie, and Jean-Philippe Uzan. Cartesian coordinates. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0001.

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This chapter introduces Euclidean geometry, which provides the mathematical framework in which the laws of Newtonian physics are formulated. It first discusses how the concepts of ‘space’ and ‘relative, apparent, and common’ place are represented by a mathematical ensemble of points—the ‘absolute’ space ε‎3. A Cartesian frame of absolute space is materialized in ‘relative, apparent, and common’ space by a reference frame. Specifically, this reference frame is a solid trihedral—that is, an ensemble of physical objects whose relative distances are invariable in time and for which an orientation of the axes has been chosen. This chapter postulates that if the labeling of the points of ε‎3 is changed, the distance between two points remains unchanged. It then goes on to explain further the various associated formulas associated with Cartesian coordinates.
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35

Donal, Erwan, Seisyou Kou, and Partho Senguptadd. Left ventricle: cardiac mechanics and left ventricular performance. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780198726012.003.0019.

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The complexity of left ventricular (LV) function(s) assessment in heart failure patients is related to the complexity of heart anatomy, but also to the complexity of electromechanical interaction, and to the load dependency of all the parameters that could be applied in clinical practice. Three perpendicular axes orienting the global geometry of the LV define the local cardiac coordinate system: radial, circumferential, and longitudinal. Speckle tracking is the technique of choice for quantifying myocardial deformation (regional and global). Longitudinal LV deformation, which is predominantly governed by the subendocardial region, is the most vulnerable component of LV mechanics and therefore most sensitive to the presence of myocardial disease.
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36

Deruelle, Nathalie, and Jean-Philippe Uzan. The Einstein equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0044.

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This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if the gravitational field created by the matter can be neglected, the appropriate framework for describing the matter is that of special relativity. Einstein gravitational equations relate geometry and matter: specifically, they relate the Riemann tensor, or more precisely the Einstein tensor, to the geometrical object describing ‘inertia’, the energy content of the matter—that is, the energy–momentum tensor. These equations form a set of ten nonlinear partial differential equations. The coordinate system can be chosen arbitrarily.
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37

Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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38

Deruelle, Nathalie, and Jean-Philippe Uzan. Differential geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0004.

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This chapter presents some elements of differential geometry, the ‘vector’ version of Euclidean geometry in curvilinear coordinates. In doing so, it provides an intrinsic definition of the covariant derivative and establishes a relation between the moving frames attached to a trajectory introduced in Chapter 2 and the moving frames of Cartan associated with curvilinear coordinates. It illustrates a differential framework based on formulas drawn from Chapter 2, before discussing cotangent spaces and differential forms. The chapter then turns to the metric tensor, triads, and frame fields as well as vector fields, form fields, and tensor fields. Finally, it performs some vector calculus.
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39

Deruelle, Nathalie, and Jean-Philippe Uzan. Matter in curved spacetime. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0043.

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This chapter is concerned with the laws of motion of matter—particles, fluids, or fields—in the presence of an external gravitational field. In accordance with the equivalence principle, this motion will be ‘free’. That is, it is constrained only by the geometry of the spacetime whose curvature represents the gravitation. The concepts of energy, momentum, and angular momentum follow from the invariance of the solutions of the equations of motion under spatio-temporal translations or rotations. The chapter shows how the action is transformed, no longer under a modification of the field configuration, but instead under a displacement or, in the ‘passive’ version, under a translation of the coordinate grid in the opposite direction.
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40

Parallel Coordinates: Visual Multidimensional Geometry and Its Applications. Springer, 2008.

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41

Trilinear coordinates and other methods of modern analytical geometry of two dimensions: An elementary treatise. Cambridge: Deighton, Bell, and Co., 1991.

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42

Handbook of Normal Frames and Coordinates (Progress in Mathematical Physics). Birkhäuser Basel, 2006.

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43

Deruelle, Nathalie, and Jean-Philippe Uzan. Vector geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0002.

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This chapter defines the mathematical spaces to which the geometrical quantities discussed in the previous chapter—scalars, vectors, and the metric—belong. Its goal is to go from the concept of a vector as an object whose components transform as Tⁱ → 𝓡ⱼ ⁱTj under a change of frame to the ‘intrinsic’ concept of a vector, T. These concepts are also generalized to ‘tensors’. The chapter also briefly remarks on how to deal with non-Cartesian coordinates. The velocity vector v is defined as a ‘free’ vector belonging to the vector space ε‎3 which subtends ε‎3. As such, it is not bound to the point P at which it is evaluated. It is, however, possible to attach it to that point and to interpret it as the tangent to the trajectory at P.
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44

Farb, Benson, and Dan Margalit. Curves, Surfaces, and Hyperbolic Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0002.

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This chapter explains the basics of working with simple closed curves, focusing on the case of the closed surface Sɡ of genus g. When g is greater than or equal to 2, hyperbolic geometry enters as a useful tool since each homotopy class of simple closed curves has a unique geodesic representative. The chapter begins by recalling some basic results about surfaces and hyperbolic geometry, with particular emphasis on the boundary of the hyperbolic plane and hyperbolic surfaces. It then considers simple closed curves in a surface S, along with geodesics and intersection numbers. It also discusses the bigon criterion, homotopy versus isotopy for simple closed curves, and arcs. Finally, it describes the change of coordinates principle and three facts about homeomorphisms.
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45

Géométrie de direction: Application des coordonnées polyédriques. Propriété de dix points de l'ellipsoïde, de neuf points d'une courbe gauche du quatrième ordre, de huit points d'une cubique gauche. Paris: Gauthier-Villars, 1991.

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46

Rajeev, S. G. Geometric Integrators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0015.

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Generic methods for solving ordinary differential equations (ODEs, e.g., Runge-Kutta) can break the symmetries that a particular equation might have. Lie theory can be used to get Geometric Integrators that respect these symmetries. Extending thesemethods to Euler and Navier-Stokes is an outstanding research problem in fluid mechanics. Therefore, a short review of geometric integrators for ODEs is given in this last chapter. Exponential coordinates on a Lie group are explained; the formula for differentiating a matrix exponential is given and used to derive the first few terms of the Magnus expansion. Geometric integrators corresponding to the Euler and trapezoidal methods for ODEs are given.
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47

Chruściel, Piotr T. Geometry of Black Holes. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198855415.001.0001.

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There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.
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48

Ciarlet, Philippe G. An Introduction to Differential Geometry with Applications to Elasticity. Springer, 2006.

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49

Ciarlet, Philippe G. An Introduction to Differential Geometry with Applications to Elasticity. CreateSpace Independent Publishing Platform, 2016.

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50

Deruelle, Nathalie, and Jean-Philippe Uzan. The Schwarzschild black hole. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0047.

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This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.
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