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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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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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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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1979
The modern approach to geometry places emphasis on symmetry and transformations of the Euclidean plane. Traditional geometry consists of a few basic axioms and a series of theorems, each of which is proved by reference to those earlier in the series. In this chapter a formal statement is made of some important theorems, with examples to show how they ...
Joyce Perry, Owen Perry
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The modern approach to geometry places emphasis on symmetry and transformations of the Euclidean plane. Traditional geometry consists of a few basic axioms and a series of theorems, each of which is proved by reference to those earlier in the series. In this chapter a formal statement is made of some important theorems, with examples to show how they ...
Joyce Perry, Owen Perry
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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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Hyperbolic Plane Geometry [PDF]
, 1981 The properties in Chapter II belong to both absolute geometry and to Euclidean geometry, but the axioms there are sufficient to imply only a part of Euclidean geometry. For example, they do not imply that the angle sum of a triangle is 180°. To establish this, and many other facts of Euclidean geometry, some assumption equivalent to Euclid’s “parallell
Paul Kelly, Gordon Matthews
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Plane Geometry, Archimedean [PDF]
, 2010 context: no traces of ancient sources providing a context of similar problems, but: connection to non-trivial theorems/methodological devices with “potential” for future mathematical theories: (i) Diameters in configuration of tangent circles, theorem of Menelaus (→ points of similarity (projective geometry)) (ii) Arithmetical ...
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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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The geometry of lattice planes
Acta Crystallographica Section A, 1970The advantages are discussed of using a ball model to determine the arrangement of lattice points in a given lattice plane and for determining the stacking properties of such planes. It is shown that the ball model can be considered as a simple analogue computer for solving the Diophantine equations involved.
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1994
Let us divide a straight line p by a point O into two half-lines + p and − p (Fig. 5.1). Let us choose on p a unit of length. The coordinate x of a point M is defined to be the distance of the point M from the point O prefixed by a sign, plus or minus (the so-called directed distance) according as M belongs to + p or − p, respectively.
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Let us divide a straight line p by a point O into two half-lines + p and − p (Fig. 5.1). Let us choose on p a unit of length. The coordinate x of a point M is defined to be the distance of the point M from the point O prefixed by a sign, plus or minus (the so-called directed distance) according as M belongs to + p or − p, respectively.
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