Results 301 to 310 of about 1,036,417 (320)
Some of the next articles are maybe not open access.
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
openaire +2 more sources
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
openaire +2 more sources
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 ...
openaire +1 more source
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.
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire +2 more sources
Journal of Mathematical Sciences, 2009
The “true form” of plane trees, i.e., the geometry of sets p−1[0, 1], where p is a Chebyshev polynomial, is considered. Empiric data about the true form are studied and systematized.
openaire +2 more sources
The “true form” of plane trees, i.e., the geometry of sets p−1[0, 1], where p is a Chebyshev polynomial, is considered. Empiric data about the true form are studied and systematized.
openaire +2 more sources
Analytic Geometry in the Plane
1984We pointed out in §5 that if we construct a system of Cartesian coordinates in a plane P and if \(F\left( {x,y} \right)\) is a function of the two independent variables x and y, then the equation $$F(x,y) = 0$$ (1) defines a curve in the plane, namely, all of the points \(z = (x,y)\) whose coordinates satisfy the equation (1).
openaire +2 more sources
Euclidean Geometry in the Plane
2003In this chapter, there are plane isometries, triangles and angles at the circumference, similarities, inversions and even pencils of circles. But there is also, and we are forced to begin with this, a discussion of what an angle is and how to measure it.
openaire +2 more sources
2009
Minkowski’s spacetime diagrams are extracted directly from Einstein’s 1905 postulates, using only some very elementary plane geometry. I have spent a significant part of my career looking at familiar results from unfamiliar perspectives. This has been partly because I very much enjoy teaching courses about aspects of physics to nonscientists, for whom ...
openaire +2 more sources
Minkowski’s spacetime diagrams are extracted directly from Einstein’s 1905 postulates, using only some very elementary plane geometry. I have spent a significant part of my career looking at familiar results from unfamiliar perspectives. This has been partly because I very much enjoy teaching courses about aspects of physics to nonscientists, for whom ...
openaire +2 more sources