Essays on Geometry

Abstract Most historians and mathematicians consider Archimedes of Syracuse as one of the greatest mathematicians of all time. His achievements in mathematics were outstanding. He contributed many theorems in geometry that have applications in other fields such as engineering, physics, and astronomy. One of which he is most famous for is his theorem that measures…

Conic Sections             When a plane (also called as cutting plane) intersects with the nappes (one or both) of a double cone, a non-degenerated curve can be made and these curves are called conic sections. A conic section may take either of the following forms: a circle or an ellipse, a hyperbola or parabola, and…

Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. Elliptic geometry, like hyperbolic geometry, violates Euclid’s parallel postulate, which asserts that there is exactly one line parallel to L passing through…

Sebastian Trigonometry and astronomy Trigonometry is used everywhere in our lives, since the beginning of development in our civilisations, people have been researching about the three lengths that have mystified for centuries. Trigonometry can almost be seen everywhere. First of all though we need to know its international definition, trigonometry is a study of triangles…

The problem Suppose you have a disk with more than 1024 cylinders. Suppose moreover thatyou have an operating system that uses the BIOS. Then you have a problem,because the usual INT13 BIOS interface to disk I/O uses a 10-bit field for thecylinder on which the I/O is done, so that cylinders 1024 and past areinaccessible….

Non-Euclidean geometry is any form of geometry that is based on axioms, or postulates, different from those of Euclidean geometry. These geometries were developed by mathematicians to find a way to prove Euclid’s fifth postulate as a theorem using his other four postulates. They were not accepted until around the nineteenth century. These geometries are…

Quick and Dirty Mohr’s Circle Solution for the Strain Gauge Rosette A 3 gauge rosette is attached to a simple tension bar. The three gauges of the rosette are at 45 degrees in relation to each other but the rosette is not aligned with the strap. The strap is 1. 00 inches wide and 0….

A parabola is a planar. mirror-symmetrical curve. which is about U-shaped when oriented as shown in the diagram. but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to specify curves of precisely the same form. One description of a parabola…

A hyperbola is a set of points in a plane the difference of whose distance from two fixed points, called foci is constant. A hyperbola is a type of smooth curie, lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces,…

A quadrilateral is a 2-dimensional closed shape with four straight sides. E.g. The shape ABCD shown here is a quadrilateral. A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. AC is a diagonal of quadrilateral ABCD, so is BD. TYPES & PROPERTIES OF…