Geometry

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

none

Course Contents

Explanation of axiom and theorem concepts, explanation methods of direct and indirect mathematical proof. Axiom and theorems about symbolic logic, applications on symbolic logic. Universal and existence quantitatives, explanation of set concept, operations on set concepts. Cartesian product of sets and drawing graph, Relation concept and properties, varieties of relation, ordered and equivalence relations and their properties. Construction of numbers assisted equivalence relation. Function concept, inverse function, kinds of function, composite function, operations with functions. Power concept in mathematics, finite and infinite sets.

Weekly Schedule

1) Definition of geometry, its’ struction and using in real life. Axiom, non-defining concept, explanation of theorem. Euclid and non-euclide geometries. Basic axioms of euclid geometry. Relations between point in space, line and plane.
2) Angle concept, kinds of angle, equation of angles and equality axioms, bisector, theorems related angles and applications on angles
3) Definition of trianngle concept, kinds of triangles, basic and aide-components of triangle. Equality axiom and theorems about triangles, applications about equality on triangles.
4) Basic theorems and applcations related isosceles triangle, equilateral triangle, right-angled triangle
5) Similar triangles, similarity theorems, applications about similarity on triangles, metric relations on right-angled triangle
6) I., II. Thales Theorems, bisector theorem, Menelaus Theorem, Ceva Theorem.
7) Definition of poligon concept, proof of related theorems as on quadrangle, parallelogram, equilateral quadrangle, rectangle, square, deltoid, trapezoid, isosceles trapezoid, applications related quadrangles
8) Midterm examination/Assessment
9) Concepts of circle and disk, angle, arc, chord, tangent, theorems and proofs related length on circle and disk, applications related angle and length on circle and disk.
10) Inscribed quadrilateral, calculation on length of circle and arc, tangent quadrangle, common tangent of two circle, power of point according to circle.
11) Concept of geometrical place, basic drawings ( as drawing triangle given some elements…)
12) Areas of polygonal regions, areas of polygons, areas of regular polygons, calculations on disk, properties of matters in space, solid matter, prisms, right and oblique prisms
13) Areas and volumes of prisms, pyramids, areas and volumes of pyramids, applications related prisms and pyramids
14) Conic, area and volume of conic, cutting pyramids, area and volumes of cutting pyramids, applications related conic and cutting pyramids
15) Sphere, slice of sphere, concept of sphere cover, their area and volumes, applications related sphere.
16) Final examination

Recommended or Required Reading

1- Demir,H., Hilbert Aksiyomlarıyla Euclides Geometrisi, ODTÜ Vakfı, (1987)
2- S. Hızarcı, A. Kaplan, A.S. İpekçi, C. Işık, Euclides Geometrisi ve Öğretimi, Aktif Yayınevi, (2003)
3- Demir,H., Hilbert Aksiyomlarıyla Euclides Geometrisi, ODTÜ Vakfı, (1987)
4- S. Hızarcı, A. Kaplan, A.S. İpekçi, C. Işık, Euclides Geometrisi ve Öğretimi, Aktif Yayınevi, (2003)
5- Doneddu, A., Düzlem Euclides Geometrisi, Milli eğitim Basımevi, (1976)

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	30%
Contribution of Final Examination to Course Grade	70%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required