COURSE OUTLINE FOR PLANE AND ANALYTIC GEOMETRY, SMA105

DAMIAN M MAINGI

1. COURSE DESCRIPTION DURATION:45 hours LECTURER: Dr Damian Maingi Office: Exam Centre G06-Chiromo Campus Email: [email protected]

Indicative Content: Coordinates, coordinate systems, lines, circles, conics - Ellipses, Parabolae and Hypberbolae, trigonometry. Prerequisite: SMA101 Background: Geometry etymologically means measurement of earth thanks to the Greeks. It is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. It began to see ele- ments of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treat- ment?Euclidean geometry?set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as Ren Descartes and Pierre de Fermat. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience. Contemporary geometry has the following subfields:

Euclidean geometry is geometry in its classical sense. One studies points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, and analytic geometry in their mandatory educational curriculum. Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics, including in general relativity. Topology is the field dealing with the properties of geometry that are unchanged by con- tinuous functions. In practice, this means that it deals with large-scale properties of a spaces such as connectedness and compactness. 1 2 DAMIAN M MAINGI

Algebraic geometry studies geometry through the use of polynomials and other algebraic techniques. OUTLINE: 1: Coordinates (1) Coordinate systems

(2) Position of a point in the xy-plane

(3) Distance between 2 points

(4) Parallel and perpendicular lines 2: The straight line (1) The equation of a line

(2) Slope and intercepts

(3) Concurency

(4) Angle biscetors 3: The Circle (1) Concept

(2) The general form

4: Conics (1) The Ellipse

(2) The Parabola

(3) The hyperbola

(4) Transformation of Coordinates 5: Trigonometry (1) Basic notions

(2) Angles

(3) Trigonometric functions COURSE OUTLINE FOR PLANE AND ANALYTIC GEOMETRY, SMA105 3

References [1] Atherton S:Essentials of Plane and Analytic Geometry

[2] Robert Yates:Analytic Geometry Springer undergraduate Mathematics series

School of Mathematics, College of Biological and Physical Sciences, Chiromo Campus, off Riverside Drive, University of Nairobi, P.O Box 30197, 00100 Nairobi, Kenya E-mail address: [email protected]