Euclid’s time thought of geometry as an abstract model of the world in which they lived.
1. A solid has shape, size, position, and can be moved from one place to another. Its boundaries are called surfaces.
2. The boundaries of the surfaces are curves or straight lines. These lines end in points.
There are three steps from the conversion of solids to points.
Step 1: solids - surfaces
Step 2: surfaces - lines
Step 3: lines - points
In each step of this conversion, we lose one extension. Such extension is also called as a dimension.
Dimensions of shapes:
1. Solid - Three dimension
2. Surface - Two dimension
3. Line - One dimension
4. Point - No dimension
The study of flat shapes or two-dimensional spaces is called Euclidean geometry.
Example: Straight line, angle and point
The surfaces that deal with apart from Euclidean geometry are called as Non-Euclidean geometry. That is three-dimensional objects.
Example: Curved shapes or spherical shapes
In geometry, some concepts can't be defined.
For example, a point, a line and a plane (two-dimensional figure) are undefined terms.
Euclid assumed some properties, which were not to be proved. These assumptions are known as the ‘universal truths’. Euclid divided these properties into two types: axioms and postulates.
National Council of Educational Research and Training (2006). Mathematics. Chapter-5 Introduction to Euclid's Geometry(pp. 78-88). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.