Geometry (Ancient Greek: geo- “earth,” -metron “measuring”) is a discipline of mathematics concerned with the forms and sizes of things, as well as their relative positions and spatial qualities. Euclid, the Greek philosopher who is known as the “Father of Geometry,” developed a number of postulates and theorems. Let’s take a look at all of the major themes in Geometry.
Geometry
Geometry is a discipline of mathematics that connects distances, angles, patterns, areas, and volumes using mathematical concepts. Geometry is the umbrella term for all visually and spatially connected topics. Geometry is divided into three types: Euclidean, Hyperbolic, as well as Elliptical.
Euclidean Geometry
To grasp the principles of geometry, we learn Euclidean geometry. The science of flat and solid figures based on axioms (statements or propositions) and theorems is known as Euclidean Geometry. Points and Lines, Euclid’s Axioms including Postulates, Geometrical Proof, and Euclid’s Fifth Postulate are all essential notions in Euclidean geometry. Geometrical figures are defined by five basic postulates of Euclidean Geometry. From one point to another, a straight-line segment is drawn. Including both directions, a straight line can be stretched forever. Any point can be used as the centre of a circle, and the radius can be any length. Right angles are all the same. Any two straight lines that are equidistant from one other at two places are indefinitely parallel.
Non-Euclidean Geometry
The two non-Euclidean geometries are spherical and hyperbolic geometry. Non-Euclidean geometry varies from Euclidean geometry in its postulates about the nature of parallel lines and angles in flat space. The study of plane geometry on a sphere is known as spherical geometry. The shortest distance between two places that are along a line is defined as a line. The great circle is a line on a sphere that is an arc. The triangle’s angles add up to more than 180 degrees. A curved surface is referred to as hyperbolic geometry. The application of this geometry may be seen in topology. The total of the angles in a planar triangle is less than 180o, dependent on the interior curve of something like the curved surface.
Plane Geometry
The study of geometry in a plane is known as Euclidean geometry. The plane is a two-dimensional surface that extends endlessly in both directions. Every aspect of geometry as well as graph theory uses planes. Points, lines, & angles are equivalent to the basic components of planes in geometry. The no-dimensional fundamental unit of geometry is the point. A line is a one-dimensional unit that refers to a collection of points that extend in two opposing directions and is defined as the intersection of two planes. There are no ends on a line. It’s simple to tell the difference between a line, a line segment, and a ray. Lines can be perpendicular or parallel. Lines does or doesn’t cross.
Angles in Geometry
An angle is formed when two straight lines or rays cross at a location. Angles are commonly expressed in degrees. Acute, obtuse, right angle, straight angle, or obtuse angles are all possible. Angle pairs can be complimentary or supplemental. Geometry’s production of angles and lines is a complex process. The major step of trigonometry is the study of angles in a unit circle and a triangle. The fascinating features of parallel lines and associated theorems are established by transversals but also related angles.
Plane Shapes in Geometry
The features of flat forms aid in their identification and classification. Two-dimensional or flat geometric forms are called plane geometric shapes. Closed curves composed of much more than two lines are known as polygons. A triangle is a three-sided closed shape having three vertices. There are several theorems predicated on triangles that aid in our understanding of triangle characteristics. Heron’s formula, basic exterior angle theorem, and angle sum property, the fundamental proportionality theorem, the similarity and congruence in triangles, the Pythagoras Theorem, and others are some of the most important theorems based on triangles in geometry. These aid in the recognition of triangle angle-side connections. Quadrilaterals are four-sided polygons having four vertices. A circle has no edges or corners and is a closed shape. The collection of all points in a plane that are equidistant from a specific point termed the circle’s centre is known as the circumference. The formative chapters in geometry include a variety of topics such as symmetry, shape transformations, and shape building.
Solid Geometry
Geometric solid forms are three-dimensional in nature. The length, breadth, and height are the three dimensions that are taken into account. There are many various forms of solid shapes, such as a cylinder, cube, sphere, cone, cuboids, prisms, pyramids, and etc, which all take up space. They have vertices, faces, as well as edges that define them. In Euclidean space, the five platonic solids and polyhedrons exhibit intriguing features. The planar forms’ nets can be collapsed into solids.
