Geometry is a branch of mathematics concerned with spatial relations that arose from practical problems like land measurement. It derives from Greek words meaning "earth measurement". Ancient Egyptians developed surveying techniques to reestablish property values after floods, while Babylonians and Egyptians used geometry for tasks like construction and trade. Geometry studies two types of properties: local properties that depend on nearby points, and global properties that involve the entire geometric figure.

1. Introduction
By
Bed Prasad Dhakal
Lecturer, FOE

2. Geometry
 Babylonians- Extensive involvement in trade
 Egyptians- Practical considerations
(Regular flooding of the Nile River)
 derives from the Greek geo (earth) and metron (measure)
Geometry is
 branch of mathematics concerned with spatial relations
 Study of two properties (local and global)
 Study of five invariants - Felix Klein (1849-1925)
 An axiomatic System

3. Mathematics
The oldest branches of mathematics
Arisen in the concerns of everyday life
Quantity
Response to practical problems
Derived from Greek words
Meaning “Earth measurement.
Change
Egyptians inventing surveying in order to
reestablish property values after annual flood of Structure
the Nile
Excitement to know the volumes of solid figures Spatial
derived from the need to evaluate store oil and Relation
grain, and build dams and pyramids.

4. Study of two properties
Local Global
 Depend only upon points close  Involve the entire geometric
to a particular point figure
 Define in the neighborhood of a  Define as in whole
point
 Radius of curvature  One side-ness of Mobius strip

5. Local Property
Radius of curvature depends upon its neighborhoods.

6. Local Property
Radius of curvature depends upon its neighborhoods.

7. Global Property
One Sideness-Moebius Strip