The word ‘geometry’ comes form the Greek words ‘geo’, meaning the ‘earth’, and ‘metrein’, meaning ‘to measure’. Geometry appears to have originated from the need for measuring land. This branch of mathematics was studied in various forms in every ancient civilisation, be it in Egypt, Babylonia, China, India, Greece, the Incas, etc. The people of these civilisations faced several practical problems which required the development of geometry in various ways.
A pyramid is a solid figure, the base of which is a triangle, or square, or some other polygon, and its side faces are triangles converging to a point at the top.
The Greek mathematicians of Euclid's time thought of geometry as an abstract model of the world in which they lived.
A solid has shape, size, position, and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from another, and are said to have no thickness. The boundaries of the surfaces are curves or straight lines. These lines end in points.
Consider the three steps from solids to points (solids-surfaces-lines-points). In each step we lose one extension, also called a dimension.
Some of Euclid's axioms, not in his order, are given below :
Things which are equal to the same thing are equal to one another.
If equals are added to equals, the wholes are equal.
If equals are subtracted from equals, the remainders are equal.
Things which coincide with one another are equal to one another.
The whole is greater than the part.
Things which are double of the same things are equal to one another.
Things which are halves of the same things are equal to one another.
A system of axioms is called consistent, if it is impossible to deduce from these axioms a statement that contradicts any axiom or previously proved statement.
Euclid's fifth postulate is very significant in the history of mathematics. no intersection of lines will take place when the sum of the measures of the interior angles on the same side of the falling line is exactly 180°.
For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l’.
