I. Convex Geometry
- Vincze Csaba: Convex Geometry, University of Debrecen, 2013, TÁMOP-4.1.2.A/1-11/1-2011-0025.
II. College Geometry
General computational skills. Numbers, polynomials, functions. Equations in one variable, quadratic equations, inequalities.
Elementary geometry. Right triangles, Pythagorean and related theorems. Trigonometry in right triangles. The extension of trigonometric expressions. General triangles, lines and circles in a triangle, sine and cosine rules. Quadrilaterals, sum of the interior angles, area. Special quadrilaterals. Polygons, decomposition into triangles, sum of the interior angles, area. Regular polygons. Circles, tangent and bitangent segments. The area of a circle, tangential and cyclic quadrilaterals. Geometrical transformations, isometries and similarity transformations.
Coordinate geometry. The analytic model of Euclidean geometry. Distance between points in the coordinate plane. Equation of lines (slope-intersect form) and circles. Parallelism and perpendicularity. Distance of a point from a line. Intersections (line-line, line-circle, circle-circle). Tangent lines to a circle from an external point. Conics (ellipse, hyperbole, parabole). Coordinate geometry on the sphere: longitudes and latitudes.