There are three way to model the Earth’s shape: Plane (“Topographical plane”) Sphere (“Local Sphere”) Ellipsoid Geoid Plane Earth’s shape approximation: Topographical plane For very small earth’s shape modeling we can use a simple plan to represent it. The figure above illustrate the condition of two point A and B; the distance between A and ..
How to transform cartesian coordinates into polar coordinate, relate to a segment, also called Azimuth. Etymology (by Wikipedia) The word azimuth is in all European languages today. It originates from medieval Arabic al-sumūt, pronounced as-sumūt in Arabic, meaning “the directions” (plural of Arabic al-samt = “the direction”). Consider the figure In this post we talk ..
Coordinates rotation. If we indicate with the angle of rotation between the origin cartesian system to the new cartesian system, and if we indicate with the polar coordinates of point P in origin system, we can determine these relations (look the figure): There is another (but most used) kind of way to change the coordinates: ..
We consider a new origin of new two axes, called O’. Consider the cartesian coordinate of O’ in actual cartesian system. We have: We suppose that the new cartesian system is no rotated, and the new axes is parallels to the actuals. The coordinates of a point (called P) are: Topography notes: Table o..
From polar sytem to cartesian system We have for point P: Looking right triangle P”OP we can determine: . From cartesian system to polar system If we consider again the right triangle P”OP we have: Topography notes: Table o..
For determine all parameters of a quadrilateral is necessary to know five elements, two of those must be sides. The quadrilateral can be subdivided in many way: Two triangles Subtraction of two triangles One rectangle and three right triangles Topography notes: Table o..
Circumscribed circle (circumcircle) of a triangle The center of a circumcircle of a triangle is given by interception of the axes of sides. We have: If we don’t know any angles of the triangle we can use this: Incircle, inscribed circle The center of the inscribed ciricle of a triangle is also called incenter. The ..
For determine the area of a triangle we can use several way. we indicate the height of the triangle on side a: Consider semiperimeter: we have: Topography notes: Table o..
To solve a scalene triangle we need three element: one of wich must be a side. Now we explain all cases. Case a) knowing one side and adjacent angles of a triangle: To solve and determine all other paramether of the triangle we follow these steps: We know: , we looking for The sum of ..
Delambre law Similary to the Law of tangents, this law is a relation for the sides and the angles of a triangle. Briggs law The briggs law formulas give an angle of a triangle knowing the sides, it’s used for determine an angle with one single step. We call the semiperimeter of the triangle ..