Geometry And The World

Geometry And The World

Did you notice that geometry is all around us? Anything and everything that has shape and size, that moves or does not move, that is a living thing or a non-living thing has an element of geometry in it. It is amazing to find the uses of geometry too, in our daily lives as well as our professions.

Let us take a glimpse at Geometry.

What is Geometry?

Geometry is that branch of mathematics that deals with shapes, sizes, positions and properties of space. It is one of the oldest mathematical sciences,

Geometry has originated as a practical science which dealt with measurements, areas, volumes etc. that benefited the then common people in their daily lives.

Roots of geometry

The earliest recorded use of geometry can be traced back to the ancient Mesopotamia, Indus valley and Egypt. Early geometry was a collection of certain principles formed by the men out of their own observations and experiences that would meet their practical needs. Some of the earliest texts in geometry are the Egyptian Rhind Papyrus, the Babylonian clay tablets the Indian Shulba Sutras. Euclid, the Father of Geometry, was a Greek mathematician whose Elements (c. 300 BCE) was one of the most important early texts on Geometry. His ideas on geometry came to be known as Euclidean geometry.

In the 19th century the development of non- Euclidean geometry has brought about a phenomenal change in the way of studying geometry today. Lobachevsky, Bolyai and Gauss are credit with the development of non- Euclidean geometry.

Use of Formulas in geometry

Formulas are one of the most important portion of geometry. It is so because students can identify and make functional use of geometry with the help of formulas.

For example, one can find the area of a circle by using the formula, where (pi) is a constant = 3.14(approx.), and is the radius of the circle.

A word about pi

Pi is a mathematical constant, written as . It is an irrational number, i.e., a number that does not end. Pi is given by the ratio of the circumference of a circle and its diameter = that is also equal to the ratio of the area of a circle and the square of its radius = = 3.14159

Symbols

Given below is a list of a few symbols used in geometry:

 Symbols Meaning Examples ∆ Triangle ∆ABC is an equilateral triangle. Angle is an acute angle ∟ Right angle ∟= 90° ‖ Parallel lines AB ‖ CD Perpendicular lines AB CD ° Degree 180°is called a straight angle. Similar ∆ABC ∆PQR Congruent ∆PQR ∆DEF Therefore M = N

Classification of geometry

Geometry may be classified as:

(a) Analytical geometry

The creation of analytical geometry by Ren Descartes(1596 – 1650) and Pierre de Fermat (1601 – 1665) was the most important event in the world of geometry in the 17th century. This is the kind of geometry that is taught in schools. It deals with coordinates, equations etc.

(b) Descriptive geometry

- It is the art of drawing plane figures, representing solid figures, and solving problems of size and space etc.
Descriptive geometry is used by those like engineers, architects who work with shapes and sizes of objects.

(c) Non 3 –D geometry

This geometry is concerned about there being more than three dimensions, i.e., length (y) , width (x), thickness (the radius of the sphere) and source (z). It is based on the thought that the universe is made up of infinite spheres.

Applications of Geometry

• Geometry is used in constructing structures like buildings, cars, ships, aircrafts etc.
• Computer graphics is based on geometry since it is about the transformation of images when viewed differently.
• Representation of shapes in computers to create images based on which structures are made mechanically or manually.
• In medicines, the reconstruction of the shape of a tumor needs geometry, besides other medical measurements.
• In nature also we find geometrical shapes all around us
• For example, the planets, satellites , the moon are spheres.