Results 301 to 310 of about 410,519 (339)
Some of the next articles are maybe not open access.
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
The Mathematical Gazette, 1929
It has been suggested that a sketch, limited to the real plane, of the theory of homogeneous coordinates and points at infinity which is developed for complex space in my Prolegomena to Analytical Geometry, would be of interest to teachers who without wanting to go deeply into the matter are humanly discontented with the crude treatment that makes of ...
openaire +2 more sources
It has been suggested that a sketch, limited to the real plane, of the theory of homogeneous coordinates and points at infinity which is developed for complex space in my Prolegomena to Analytical Geometry, would be of interest to teachers who without wanting to go deeply into the matter are humanly discontented with the crude treatment that makes of ...
openaire +2 more sources
1995
The axioms systems of Euclid and Hilbert were intended to provide everything needed for plane geometry without any prior development. The axioms of Hilbert include information about the lines in the plane that implies that each line can be identified with the structure commonly called the “real numbers” and denoted by ℝ.
Robert D. Richtmyer, Arlan Ramsay
openaire +2 more sources
The axioms systems of Euclid and Hilbert were intended to provide everything needed for plane geometry without any prior development. The axioms of Hilbert include information about the lines in the plane that implies that each line can be identified with the structure commonly called the “real numbers” and denoted by ℝ.
Robert D. Richtmyer, Arlan Ramsay
openaire +2 more sources
Analytic geometry of the plane
1975The main idea of analytic geometry is that geometric investigations can be carried out by means of algebraic calculations. This method has proved extraordinarily fruitful. The fusion of geometric and algebraic thinking, together with functional thinking, provides an important help to man’s understanding of the exploration and comprehension of objective
H. Küstner +4 more
openaire +2 more sources
2002
Crisp plane geometry starts with points, then lines and parallel lines, circles, triangles, rectangles, etc. In fuzzy plane geometry we will do the same. Our fuzzy points, lines, circles, etc. will all be fuzzy subsets of R × R. We assume the standard xy— rectangular coordinate system in the plane.
Esfandiar Eslami, James J. Buckley
openaire +2 more sources
Crisp plane geometry starts with points, then lines and parallel lines, circles, triangles, rectangles, etc. In fuzzy plane geometry we will do the same. Our fuzzy points, lines, circles, etc. will all be fuzzy subsets of R × R. We assume the standard xy— rectangular coordinate system in the plane.
Esfandiar Eslami, James J. Buckley
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
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
Science, 1896 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