Bhumiti was the term used to refer to geometry in ancient Hinduism. In ancient India, this branch was developed in connection with the performance of yajna (sacrifices). Information about this is found in Sulbasutra. It all started from preparing bricks proportionate in size to a triangle and quadrilateral. The layers of bricks were to be prepared as per the Shastra. Shulbasutra was the outcome of the need to prepare the yajna vedi (place where the yajna, or fire ritual, is performed).
Centimeter/inch is a small measure in modern bhumiti. In shulba,
angula was the measure. Anu was smaller than angula and was visible. Puru was
equal to 120 angulas. There were various measures in between these two, e.g.,
pradesha, pada, yuga, janu, bahu, prakrama, etc.
Shulbasutra explains the methods of construction by
equilateral triangle or quadrants. If two perpendicular lines are drawn on a
straight life, a rectangle can be constructed. It also explains th relationship
between a side and a diagonal of a quadrilateral. A number of constructions
were necessary for a vedi or yajna. Methods for constructing a long quadrilateral
from a given quadrilateral, triangle, circle, quadrant of a circle etc., are
given.
In modern geometry the Pythagorean theorem states, ‘the area
of a square on a diagonal of a right-angeled triangle is equal to the sum of
the areas of the squares on the remaining two sides.’ This was already used in
Sulbasutra and Brahmanapatha long before Pythagoras.
Aryabhata (5th century CE) wrote a book that covered
arithmetic, algebra, geometry and trigonometry. The topics of geometry like
triangle, circle, their areas, volumes, etc., were dealt with. The ratio of the
diameter to a perimeter of the circle was determined as 1:3.1416.
In his book Brahmasputasiddhanta, Brahmagupta has explained trigonometry
in one chapter. Bhaskaracharaya’s book named Lilavati cover the relation
between the areas of a triangle and quadrilateral drawn in a circle. It also
explains the relationship between diameter and area of a circle, the method of
calculating the length of each side of a regular polygon, octagon, hexagon,
etc. Further, it gives the method of calculating the volume of a pit; and the
ratio between the height and perimeter of a heap of grains.