geometry introduction-a

Geometry

ByBed Prasad Dhakal

Lecturer, FOE

Introduction

GeometryBabylonians- Extensive involvement in tradeEgyptians- Practical considerations

(Regular flooding of the Nile River)derives from the Greek geo (earth) and metron (measure)

Geometry isbranch of mathematics concerned with spatial relationsStudy of two properties (local and global)Study of five invariants - Felix Klein (1849-1925)An axiomatic System

Spatial Relation

Structure

Change

Quantity

MathematicsThe oldest branches of mathematicsArisen in the concerns of everyday lifeResponse to practical problemsDerived from Greek wordsMeaning “Earth measurement.

Egyptians inventing surveying in order to reestablish property values after annual flood of the Nile

Excitement to know the volumes of solid figures derived from the need to evaluate store oil and

grain, and build dams and pyramids.

Study of two propertiesLocal Global

Depend only upon points close to a particular point

Define in the neighborhood of a point

Radius of curvature

Involve the entire geometric figure

Define as in whole

One side-ness of Mobius strip

Radius of curvature depends upon its neighborhoods.

Local Property

Radius of curvature depends upon its neighborhoods.

Local Property

One Sideness-Moebius Strip

Global Property