One of the classical disciplines of mathematics, Geometry is derived from the Greek which means Earth and Metron, upon translating it roughly means “Earth Measurement” because on the whole it is concerned with the properties of space and figures. It is primarily studied to be a practical guide for measuring lengths, areas, and volumes, and is still studied further in various important projects. Euclid considered to be the Father of Geometry turned this field of study into an axiomatic form at around 3rd century BC, and these axioms are still useful. An important evolution for the science of geometry was created when Rene Descartes was able to create the concept of analytical geometry (geometry using coordinates). Because of it, plane figures can now be represented analytically and is one of the driving forces for the development of calculus. For an elementary or middle school student, it is all about different basic shapes including their naming, properties, and formulas related to their areas and volumes. In addition, the rise of different perspectives in this field of study has given rise to projective geometry. But modern geometry is a little more advanced and has strong ties with physics and is an integral part of new physical concepts such as relativity and strong theories, diverging the study of geometry much more from these basic concepts. But none of these has changed their existence and applications of geometry in daily life and it still reflects in our everyday experience. Let us look at some of the uses of Geometry in Daily Life.
The most basic forms of geometry are called Euclidean geometry which comprises of lengths, areas, and volumes are dealt here. Circumferences, radii, and areas are few of the concepts concerning length and area. Also, the volume of 3-dimensional objects such as cubes, cylinders, pyramids, and spheres can be computed using geometry. It used to be all about shapes and measurements, but numbers have also started making its way to geometry. Considering the Pythagoreans, numbers are introduced in geometry in the form of numerical values of lengths and areas. Numbers are further utilized when Descartes was able to formulate the concept of coordinates.
Hence the sub-fields of Contemporary Geometry are:
- Euclidean geometry includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles and analytic geometry. Euclidean geometry has applications practical applications in computer science, crystallography, and various branches of modern mathematics
- Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics, including in general relativity
- Topology is the field of study concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, it actually deals with large-scale properties of spaces, such as connectedness and compactness
- Convex geometry investigates convex shapes in the Euclidean space and it’s more abstract analogs, it uses real analysis techniques. It is closely connected to convex analysis, optimization and functional analysis and has important applications in number theory
- Algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in many areas, including cryptography and string theory
- Discrete geometry is concerned mainly with questions of the relative position of simple geometric objects, such as points, lines, and circles. It shares many methods and principles with combinatorics
Applications of Geometry in Daily Life
Geometry briefly is used in various daily life applications such as surveying, astronomy, navigation and building and much more. Some of such applications of Geometry in daily life in different fields are described below-
Mathematics and art are related in a variety of ways. For instance, the theory of perspective (a graphical representation of on a flat surface of an image as seen by eyes) showed that there is more to geometry than just the metric properties of figures: and this perspective is the basis of the origin of projective geometry.
The concept of geometry is also applied in the fields of robotics, computer, and video games. Geometry provides handy concepts both for computer and video game programmers. The way & the design of the characters that move through their virtual worlds requires geometric computations to create paths around the obstacles concentrating around the virtual world. Video game engines typically put to use raycasting, which is a technique that simulates a 3-D world using a 2-D map. Using this form of geometry helps speed up processing because calculations are only done for the vertical lines on the screen.
Just like other forms of arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building i.e. to create the design of the building its shape, height, structure basically the construction blueprint. Apart from this the Pythagoreans of the sixth century BC onwards used geometry to create forms considered harmonious, and thus to lay outbuildings and their surroundings according to mathematical, aesthetic and sometimes religious principles and also to decorate buildings with mathematical objects such as tessellations, and even mitigate the hazard arising from wind speeds around the bases of tall buildings.
Also, one of the best examples of the application of geometry in daily life will be the stairs which are built in homes in consideration to angles of geometry constructed at 90 degrees.
Geometry concepts are also applied in CAD (Computer Aided Design) where it helps the software to render visual images on the screen.
Astronomy & Physics
Here, geometry is used in the field of astronomy, helping to map the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies.
In the field of Physics, there is a deep link between pseudo-Riemannian geometry and general relativity
Geographic Information Systems
Geometry concepts are used in satellites in GPS systems, it calculates the position of the satellite and location of GPS gauged by the latitudes and longitudes.