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Geometriae Dedicata, 1982
Minkowski geometry in the plane is given by a closed, convex curve C and a point o~int conv C. If the ray ox intersects C at y, the norm of the vector ox in this geometry is I[ oxI[ = [ox[/[oy[ where ] [denotes the Euclidean norm. We do not assume that C is symmetric of center o. In general, II - v 1[ =p [[v [] for vectors in the plane. C is called the
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Minkowski geometry in the plane is given by a closed, convex curve C and a point o~int conv C. If the ray ox intersects C at y, the norm of the vector ox in this geometry is I[ oxI[ = [ox[/[oy[ where ] [denotes the Euclidean norm. We do not assume that C is symmetric of center o. In general, II - v 1[ =p [[v [] for vectors in the plane. C is called the
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1996
The authors deal with following model of plane geometry. The points are the points of the Euclidean plane \(\mathbb{R}^2\). There are four types of lines: a vertical Euclidean line; a horizontal Euclidean line; a translate of the hyperbola \(L= \{(x,y): x>0, y={1\over x}\}\); and a translate of the hyperbola \(L^*= \{(x,y): x0\) and \(g(x)= -{a\over x}\
Powers, R. C., Riedel, T., Sahoo, P. K.
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The authors deal with following model of plane geometry. The points are the points of the Euclidean plane \(\mathbb{R}^2\). There are four types of lines: a vertical Euclidean line; a horizontal Euclidean line; a translate of the hyperbola \(L= \{(x,y): x>0, y={1\over x}\}\); and a translate of the hyperbola \(L^*= \{(x,y): x0\) and \(g(x)= -{a\over x}\
Powers, R. C., Riedel, T., Sahoo, P. K.
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The Geometry of Vectors in the Plane
1983Many of the familiar theorems of plane geometry appear in a new light when we rephrase them in the language of vectors. This is particularly true for theorems which are usually expressed in the language of analytic or coordinate geometry, because vector notation enables us to use a single symbol to refer to a pair of numbers which gives the coordinates
Thomas Banchoff, John Wermer
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Geometry in the plane and in space [PDF]
, 2015 The chapter has two main goals. The first is to discuss the possibilities of representing objects in the plane and in three-dimensional space; in this sense we can think of this as an ideal continuation of Chap. 1. We shall introduce coordinate systems other than the Cartesian system, plus vectors and their elementary properties, and then the set ℂ of ...
Claudio Canuto, Anita Tabacco
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The geometry of lattice planes [PDF]
Acta Crystallographica Section A, 1969 A simple method is outlined for finding the arrangement of lattice points in a lattice plane of given Miller indices, and for determining the stacking properties of such planes.
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The Mathematics Teacher, 1951
Projects help the student to appreciate more fully the application of geometry to life situations, by the recognition of geometric form, the direct application of geometric principles and the use of geometric logic or methods in everyday reasoning.
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Projects help the student to appreciate more fully the application of geometry to life situations, by the recognition of geometric form, the direct application of geometric principles and the use of geometric logic or methods in everyday reasoning.
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Geometry of the Rational Plane
The College Mathematics Journal, 1986(1986). Geometry of the Rational Plane. The College Mathematics Journal: Vol. 17, No. 5, pp. 392-402.
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1981
In this chapter we will review the basic properties of Absolute Plane geometry, based on the Birkhoff axioms. All the theorems to be considered are also theorems of Euclidean geometry and hence, for the most part, will be familiar to the reader.
Gordon Matthews, Paul Kelly
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In this chapter we will review the basic properties of Absolute Plane geometry, based on the Birkhoff axioms. All the theorems to be considered are also theorems of Euclidean geometry and hence, for the most part, will be familiar to the reader.
Gordon Matthews, Paul Kelly
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