Introduction to Geometry

Mathematics is neither created nor discovered. It was created from the discovery of the universe.

Geometry is the name given to the mathematical method used to solve real life problems. It is the word related to the earth and its measurements. To know about the each and every beautiful structure and shape of this universe, geometry helps us a lot.  

It was used in the processes like building houses, making structures and many other things which involved with shapes. So they started to improve it from their ancient time. 
It was later improved due to the geometrical needs that faced by humans in their life. 
To overcome every problem he was supposed to use geometry. So he is able to solve many physical problems easily.

To learn geometry, we defined many definitions. To explain big things we started from the small things. 
We learned lower levels to the higher levels.

When you focused on the objects around us, you can notice that most of the objects are not in perfect shapes like rectilinear or circular. They will be in different and different shapes. They will not fit with each other. By using the curved shape stones we can’t make a good house without holes because if you used curved shapes it will not fit correctly. 
For that reason we don’t want to handle natural objects that has imperfect shapes. 
They know that they must alter the stones into some perfect shapes to use it in our real life. 
You can see it on bee house. Great example for closed and well altered shape is bee house. Perfect polygons are used by bees naturally.     

For all these reasons, we tried to alter the stones in perfect shapes. Also in perfect shapes, we are using the special shapes like square, rectangle, and polygon. Only then we can find the properties like areas, volumes easily.  

I will tell you another problem which involved in curved shapes and non-special perfect shapes. That is, if the shapes are not special means the process of making the parts that used in fitting of the building will become tough. If the first shape is not uniform and if we want to make the next shape then that second shape must be in the shape that can be perfectly fit with the first shape. So, if this process goes on continuously you can’t make the third plate until placing the first two plates. The process will take more time. So we must try to make the process simple. Simple means the plates must be produced easily like the technique used in the factories.   

We are trying to find a common shape which is easy to build much kind of houses and also the process of making the shapes must be fast. So which is the most common and easy to enclose completely?

You can see that most of the answers are squares, rectangles, rhombus, parallelogram, hexagon and many other polygons. Here the shape means it must also define the sizes ( length, breadth, area, volume).

 Lengths are the main thing used. When we tried to fit the stone shapes it must satisfy the condition that it must be in same length which is suitable for fitting. The shapes should satisfy the lengths for good fitting. You can’t make a big stone shape for a small hole. In the same way areas and volumes are also used. 

Take any solid figures.  To make it simple, blast it into smaller parts. Comparing to the curved 3 dimensional shape, straight line 3D shape will be better. And if it is in the 2 dimensional shape or plane surface shape there 2D lines will be better. Now if you go more deep it will split into smaller parts like small dust. Here we got a shape. We can assume that it is the basic shape for all shapes.

It is called point……… The definitions goes on.

To define it mathematically we must go one by one.

Various kinds of geometries are there.

To a little deep in geometry we will first go to the Euclidean Geometry. You can study the Euclid's elements books by clicking the link. The full book is given here.

Euclid's elements books (this site will take little time to show)