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The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate. 1929 Craster parabolic =Putniņš P4: Pseudocylindrical Equal-area John Craster Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect. 1949
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m, a common perpendicular would have slope −1/m and we can take the line with equation y = −x/m as a common perpendicular ...
Because the lines are parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance.
Equirectangular projection of the world; the standard parallel is the equator (plate carrée projection). Equirectangular projection with Tissot's indicatrix of deformation and with the standard parallels lying on the equator True-colour satellite image of Earth in equirectangular projection Height map of planet Earth at 2km per pixel, including oceanic bathymetry information, normalized as 8 ...
For example, a set of points on a line in n-space transforms to a set of polylines in parallel coordinates all intersecting at n − 1 points. For n = 2 this yields a point-line duality pointing out why the mathematical foundations of parallel coordinates are developed in the projective rather than euclidean space. A pair of lines intersects at ...
The Clifford parallels through points on the surface all lie in the surface. A Clifford surface is thus a ruled surface since every point is on two lines, each contained in the surface. Given two square roots of minus one in the quaternions , written r and s , the Clifford surface through them is given by [ 1 ] [ 3 ]
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting" [1] [2]) the metric notions of distance and angle.. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines.
Let r and s be two ultraparallel lines.. From any two distinct points A and C on s draw AB and CB' perpendicular to r with B and B' on r.. If it happens that AB = CB', then the desired common perpendicular joins the midpoints of AC and BB' (by the symmetry of the Saccheri quadrilateral ACB'B).