Secant Lines In Geography

For tangent cylindrical and conic projections or secant planar projections resulting in one standard line, place the standard line in the middle of the map extent. When using cylindrical and conic secant projections, place the pair of standard lines one-third 13 from each map edge. Figure 18.

For example, the conic and cylindrical projections shown in the illustration cut through the ellipsoid. The map is projected both inward and outward onto it and there is no distortion on the two lines of exact scale, standard lines. They are created along the small circles where the cone and the cylinder intersect the ellipsoid.

A tangent line just touches a curve at a point, matching the curve's slope there. From the Latin tangens quottouchingquot, like in the word quottangiblequot. A secant line intersects two or more points on a curve. From the Latin secare quotcut or severquot They are lines, so extend in both directions infinitely.. Circle. On a circle they look like this Theorems. There are three theorems of interest here

A cone is placed over a globe. The cone and globe meet along a latitude line. This is the standard parallel. The cone is cut along the line of longitude that is opposite the central meridian and flattened into a plane. Conic secant A cone is placed over a globe but cuts through the surface. The cone and globe meet along two latitude lines.

For the Conical and Cylindrical classes, the paper touches along a line. In the secant case, the paper passes through the globe obviously this must be a mathematical form of projection. The result is that azimuthal maps will have a circle of contact and cones and cylinders will have two lines of contact see below. Example of Distortion

Generally, the developable surfaces will touch the ellipsoid in either two places which creates two secant lines, or at a single location and creates a single tangent line. In the illustration shown the tangent line is touching the ellipsoid of the South Pole which should give us a polar view of the earth.

These examples show tangent and secant conic map projections. As you move farther away from the tangent or secant lines, distortion increases. As you move farther away from the tangent or the secants in either a northerly or southerly direction, distortion increases. For a tangent map projection, this places the center of the map on a line that

Common lines and line segments on a circle, including a secant. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line.A chord is the line segment that joins two distinct points of a circle. A chord is therefore contained in a unique secant line and each

A secant line is a straight line and therefore can be written as a linear equation. The first step to finding the equation of a secant line is to find its slope.. How to Find Slope of a Secant Line

A secant line is useful to calculate the slope of a line. A secant line is the equivalent of the average rate of change or the slope between two points. Once you have calculated the slope of a line we can find the equation of the line through the two points. The two points of a secant line are denoted by x 1, y 1 and x 2, y 2 Slope of a