What is geometry?

Recorded growth of geometry spans more than two millennia. It is hardly astonishing that perceptions of what constituted geometry evolved throughout the ages. The geometric paradigms offered below should be viewed as 'Pictures at an exhibition' of a sort: they do not weaken the subject of geometry but rather reflect some of its defining themes.
Practical geometry:
There is small doubt that geometry originated as a practical science, concerned with surveying, measurements, areas, and volumes. Among the distinguished accomplishments one finds formulas for lengths, areas and volumes, such as Pythagorean theorem, circumference and area of a circle, area of a triangle, volume of a cylinder, sphere, and a pyramid. Development of astronomy led to appearance of trigonometry and spherical trigonometry, together with the attendant computational techniques.