What is Geometry Used For

Introduction:
Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment- Euclidean geometry- set a standard for many centuries to follow. Here in this topic we are going to see what is geometry used for.

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Uses of geometry:


In home or a building geometry is useful in the improvement of projects. For example, to find the area of the floor, height of a building, to place tiles of particular dimension in a particular area, to place furniture in a required place, estimating the fabric needed, to paint the wall how much paint is needed. Geometry is also used to measure volumes. For example, amount of water needed in the fish tank, volume of the paint the wall by the surface area.

Geometry has many uses to find the size, shape, volume, or position of an object. As a school subject, it helps develop logical reasoning. Architects and engineers use geometry in planning buildings, bridges, and roads. Geometry is used by navigators to guide boats, planes, and even space ships. Military personnel use geometry to guide vessels and aim guns and missiles. Almost everything you do in your daily life involves geometry in some way.

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Some problems in geometry:


1) Find the volume paint used to paint the wall. The paint tin in the form of  a cylinder with radius 12 cm and height 19 cm

Given:                     radius r = 12 cm

                                height h = 19 cm  

Solution:

volume of paint = volume of the cylinder

         Volume of a cylinder  =  `pi` r^2 h

                                                =  3.14 (12)^2 19

                                                = 3.14 (144) 19

                                                = 8591.04 cm^3

Therefore the volume of the pait needed to paint the wall is 8591.04 cm^3.

2) A road roller is cylindrical in shape. The radius of the road roller is 35cm. Its length is 120cm. Find the surface area?

Solution

Given: r = 35cm, h = 120cm.

(i) The surface area = 2`pi` r (h +r)

                                = 2`pi` × 35 ( 120 + 35 )

                                = 34,100 cm2.

Geometry Terms Called Plane

Introduction to geometry terms called plane:

A surface which has thickness as zero and infinitely large in geometry terms is called as plane. The plane is imagined in both direction with infinite large length. In geometry, the plane term is two dimension surface and it does not have edges.This is created from analysis of point, line and space in geometry. Please express your views of this topic Define Parallel Lines by commenting on blog.


Explanation for plane in geometry terms


The terms plane is present in geometry:

In Euclidean geometry, the subspace are used for setting the plane and the plane is called in terms of whole space. The trigonometry, geometry terms are use the plane. The plane is consider the group of points and is called as undefined term.

In geometry the plane is considered as flat surface and the two vectors are used for span the surface. This terms are called linearly independent vectors. The planes are intersected and create the angle is called as dihedral angle.

The nonzero normal vector terms are used to derive the plane equation through the point,

n. ( x – x0 ) = 0 for n = ( a, b ,c ) and X0 = (x0 , y0, z0 )

where X = (x, y, z).This is derive the plane’s general equation as ax + by + cz + d = 0 where d = -ax0 – by0 – cz0.

The distance between the points are calculated as D =  `(d)/(sqrt(a^(2) + b^(2) + c^(2)))` .

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More about plane in geometry


Properties of plane terms in geometry:

In Euclidean space, the parallel planes are present or plane is parallel to the line. Rotation, translation, reflection ans glide reflections are followed in plane motions.

The plane terms in different branches:

A plane which one get the differential structure is called as differential geometry.
The complex analysis is rise the abstraction of complex plane.
If the spherical geometry is taken from a plane means that terms  are called as stereographic projection.

Three Different Types of Geometry

Introduction:

A non-Euclidean geometry is learning of figures and structure that do not chart straight to any n-dimensional Euclidean system, describe by a non-vanishing Riemann curve tensor. Examples of non-Euclidean geometries contain the hyperbolic and elliptic geometry, which are difference with a Euclidean geometry. The necessary difference among Euclidean and non-Euclidean geometry is the character of parallel lines.


Behavior of lines


Three different types of geometry method to explain the difference connecting these geometries is to think double directly lines indefinitely extensive in a two-dimensional level surface that are together vertical to a three line types:

In Euclidean geometry the position remain at a stable distance starting each other, and are well-known as parallels.
In hyperbolic geometry they "curve away" starting each other, rising in distance as one moves further from the position of intersection through the general perpendicular; these lines are frequently called ultra parallels.
In elliptic geometry the positions “curve toward" each extra and finally intersect.


Models of non-Euclidean geometry


Let us see about three different types of  geometry,

Elliptic geometry

The simplest type for elliptic geometry is a globe, anywhere lines are "great circles" (such as the equator or the meridians on a globe, and points reverse each other are recognized (considered to be the equal).In the elliptic type, for some certain line l and a point A, which is not on l, all position throughout A will intersect l.

Hyperbolic geometry

The pseudo globe has the suitable curve to model a section of hyperbolic space, and in a second document in the similar year, defined the Klein model, the Poincaré disk type, and the Poincaré half-plane type which type the total of hyperbolic space, and old this to explain three different types of geometry that Euclidean geometry and hyperbolic geometry be equip reliable, so that hyperbolic geometry was reasonably constant if and simply if Euclidean geometry.


Their Relationship to Each Other


Let us see about three different types of  geometry,

The different geometries are divided and connected to single another in different ways. The non-Euclidean geometries are closely similar to the geometry of Euclid, but that Euclid's postulate concerning analogous lines is replace and all theorems depending on this assume are changed therefore both Euclidean and non-Euclidean geometry are models of metric geometry, in which the length of line division and the volume of position may be careful and compared.