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1

Mukhopadhyay, Jayanta. Approximation of Euclidean Metric by Digital Distances. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9901-9.

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2

Li, Yuying. A Newton acceleration of the Weiszfeld algorithm for minimizing the sum of Euclidean distances. Cornell Theory Center, Cornell University, 1995.

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3

Liberti, Leo, and Carlile Lavor. Euclidean Distance Geometry. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60792-4.

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4

Ragnemalm, Ingemar. The Euclidean distance transform. Univ., 1993.

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5

Hanjoul, Pierre. Theoretical market areas under Euclidean distance. Institute of Mathematical Geography, 1988.

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6

Koolen, Jacobus Hendricus. Euclidean representations and substructures of distance-regular graphs. Technische Universiteit Eindhoven, 1996.

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7

Alfakih, Abdo Y. Euclidean Distance Matrices and Their Applications in Rigidity Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97846-8.

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8

Garibaldi, Julia. The Erdös distance problem. American Mathematical Society, 2010.

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9

Ibragimov, Zair. Topics in several complex variables: First USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, California. American Mathematical Society, 2016.

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10

Mukhopadhyay, Jayanta. Approximation of Euclidean Metric by Digital Distances. Springer Singapore Pte. Limited, 2020.

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11

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
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12

Lavor, Carlile, and Leo Liberti. Euclidean Distance Geometry: An Introduction. Springer, 2018.

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13

Lavor, Carlile, and Leo Liberti. Euclidean Distance Geometry: An Introduction. Springer, 2017.

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14

Dattorro, Jon. Convex Optimization & Euclidean Distance Geometry. Lulu.com, 2006.

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15

Convex optimization and euclidean distance geometry. Meboo Publishing, 2005.

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16

Alfakih, Abdo Y. Euclidean Distance Matrices and Their Applications in Rigidity Theory. Springer, 2018.

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17

Alfakih, Abdo Y. Euclidean Distance Matrices and Their Applications in Rigidity Theory. Springer, 2019.

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18

Squared Euclidean distance: A statistical test to evaluate plant community change. U.S. Dept. of Agriculture, Forest Service, Pacific Southwest Research Station, 1993.

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19

jrgeometry. Euclidean Geometry : With: 1)Applications to Algebra I, 2)Distance and Spherical Surfaces, 3)Four-Dimensional Spheres. Independently Published, 2018.

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20

jrgeometry. Euclidean Geometry : With: 1)Applications to Algebra I, 2)Distance and Spherical Surfaces, 3)Four-Dimensional Spheres. Independently Published, 2018.

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