Journal of Computational Mathematics and Applied Mathematics

Authors: Anwar A. Patel , Rukhsar K. Pathan

Abstract: Since we can calculate slope of two dimensional object and equation of Tangent and Normal of the any two dimensional curve. Slope (m) is change in Y-coordinates with respect to X-coordinate. But in three dimensional three axis should be considered. dx, dy, dz this changes in X, Y & Z are measured and slope can be calculated. Normal and Tangent equation in three dimensional has three points and three different distances. In two dimensional there is only one Tangent at one point to the curve but in three dimensional Cartesian three tangents at a point. One is parallel to X-axis, second is parallel to Y-axis and third one parallel tozaxis. radius of curvature or sphere can be easily calculated with the help of slope equation. The Cartesian plane is a two-dimensional mathematical graph. When graphing on it, a line may not start at zero as in the ski slope examples. In fact, a line goes on forever at both ends. The slope of a line, however, is exactly the same everywhere on the line. So, you can choose any starting and ending point on the line to help you find its slope. It is also possible that you might be given a line segment , which is a section of a line that has a beginning and an end. Or, you might be given two points and you are expected to draw (or imagine) the line segment between them. In all these situations, finding the slope works the same way. Just like with the ski slope, the goal is to find the change in height and the change in width. For the line segment in the image, you can simply count the squares on the grid. Three dimensional slope is useful to civil engineering in designing heavy structure of dam, bridge and constructive parts. Also this is helpful for mechanical industry and safety management. Radius of curvature is the radius of approximating sphere or elliptical shape elements. When engineers design train track, curve road they will need to ensure the curvature of track, bridge & tunnel to provide a comfortable ride for given speed of trains.