| Course title | Elementar Geometry |
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| Course code | KAG/KELG |
| Organizational form of instruction | Seminary |
| Level of course | Master |
| Year of study | not specified |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | unspecified |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Plane geometry: Nomenclature and notation. Conception of solving constructional problems. Solvability of geometric problems. Method of construction based on algebraic expression, dividing ratio. Sets of points. The Apollon circle. Apollon's and Pappos' problems. Conic section - definition, construction and focal characteristics of ellipse, hyperbola and parabola. Construction of conic sectioncs Power point to circle, chordal, potency centre. Bonds of circles, application. Congruences in a plane - definition, classification, their characteristics, assembling and application. Similarity and homothety in a plane, characteristics and application. Euler's straight line and Feuerbach's circle. Circular inversion - mapping of points, straight lines, circles, characteristics. Application. Hilbert's axiomatic system. 2. Stereometry. Positional and metric characteristics of fundamental geometric formations, mutual position, parallelism, distance, angle deviation, perpendicularity - definition, property criterions. Elementary surfaces and solids. Convex solids and Platon's solids. Parallel projection - basic characteristic and invariant parallel projection, special characteristics of rectangular projection. Axial affinity in space and plane, characteristics, picture circle in axial affinity. Collineation - conception, basic characteristic. Volitional parallel projection - basic characteristic, mapping of square and round solids. Cut of solids with plane, points of intersection straight line with solid, solving cubic constructional exercise. The Monge projection - basic concepts, mapping of points, straight lines and planes. Positional and metric exercises. Mapping of simple elements use fundamental positional and metric exercises.
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| Learning activities and teaching methods |
| Lecture, Work with Text (with Book, Textbook) |
| Learning outcomes |
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Deepen knowledges in sets of points laid characteristic and basic mappings in plane. Determine properties of geometric shapes with basic characteristics of geometric formations and the basic characteristics of some parallel projections.
1. Knowledge Students describe geometric constructions and mappings in plane and space. |
| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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Student performance, Analysis of Activities ( Technical works)
Credit: developing examples - see the website http://www.kag.upol.cz/homepage_chodorova/elementarni-geometrie-kelg1/ http://www.kag.upol.cz/homepage_chodorova/prace/ Exam: the student has to understand the subject and be able to solve assigned problems. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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