In the following 18 Episodes of this Continuation Course all the basic concepts dealt with in the Introductory Course get deepened with hopefully engrossing tutorials for those who like this way of practicing Geometry.
Again the Course is divided into 3 Parts and every Episode has the same number as the previous lecture in the Introductory Course: so Ep. 1 of the CC follows Ep. 1 of the IC and broadens your knowledge of this topic and so on until Ep. 18.
Part 1, Basic Geometry, consisting of Episodes 1 to 5, continues to deal with locus lines. We will start, however, with bodies like cuboid, prism and pyramid, look at their surfaces, draw their nets and see that their boundary figures again consist of rectangles, special triangles and polygons. Then we will perform basic tasks with rectangles, study relations between angles and use the properties of Symmetry to formulate proofs of different statements or theorems.
Part 2, Intermediate Geometry, Episodes 6 to 11, explores Thales’ Theorem, all sorts of triangles, their special lines and points as well as the sum of the inner angles, their congruence and construction given 3 sides or angles. Then we will deal with the family of quadrilaterals looking for the formulae of their area – and we achieve this goal by converting them to our known rectangle -, show how to construct some of them. Finally we answer the question how double reflections could be proceeded depending on the situation of the 2 axes – while
Part 3, Advanced Geometry, Episodes 12 to 18, studies the so called similarity of figures – combining the Congruence with the Dilation leads to this mapping – we will find new captivating applications, then we will provide a convincing proof of Pythagoras’ theorem including some applications. Circles with their parts as well and round solids (cylinders, cones, spheres) will be the focus next which means we will get to know the famous number Pi and the basic formulae for area, perimeter, volume and surface. Eventually we will take further steps into the field of Trigonometry, where we will extend our knowledge in new situations; to do this we will apply, of course, the sine, cosine and tangent functions we already studied in the Introductory Course.