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Lecturer(s)
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Peška Patrik, RNDr. Ph.D.
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Course content
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unspecified
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Activating (Simulations, Games, Dramatization)
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Learning outcomes
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The aim of the course is to introduce students to the mathematical principles of origami and their applications in solving geometric and algebraic problems. Emphasis is placed on algorithmic approaches and the connection between mathematics and practical construction. Students will: - understand the axiomatic foundations of origami (Huzita-Hatori axioms), - master the binary algorithm and its applications in paper folding, - learn how to construct rational ratios using origami, - understand solutions of classical Greek problems via paper folding, - study the solution of cubic equations using origami, - explore tessellations and fractal structures (fractigami), - gain insight into practical applications of origami in science and engineering.
After completing the course, the student: Knowledge: - understands the mathematical foundations and axiomatic system of origami, - knows algorithms for paper division and construction of ratios, - understands the connection between origami and algebraic problem solving (e.g. cubic equations), - is familiar with tessellations and fractal structures. Skills: - applies Huzita-Hatori axioms in constructions, - performs folding algorithms (binary, diagonal, Haga, etc.), - constructs geometric objects and ratios using origami, - solves selected geometric and algebraic problems via paper folding, - designs basic tessellations and fractal structures. Competences: - connects mathematical reasoning with hands-on construction, - develops algorithmic and constructive thinking, - uses origami as a didactic tool in mathematics education, - understands interdisciplinary applications of origami.
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Prerequisites
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Basic knowledge of Elementary Geometry, Algebra, and basic understanding of Algorithms are assumed. No prior experience with origami is required.
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Assessment methods and criteria
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Analysis of Activities ( Technical works), Systematic Observation of Student, Written exam
To successfully complete the course, the student must: - demonstrate understanding of the basic principles of Geometry in the context of origami, - understand the Huzita-Hatori axioms and their implications, - master basic folding algorithms (binary algorithm, diagonal methods, Haga, Fujimoto, etc.), - construct geometric objects and rational ratios using origami, - apply origami to classical geometric problems (e.g. Greek constructions), - understand the principle of solving cubic equations using origami, - create basic tessellations and fractal structures, - solve both practical and theoretical problems, - complete continuous assessment (practical tasks/projects), - pass the final assessment (course credit or exam).
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Recommended literature
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Sekanina M. (1986). Geometrie I. Praha.
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Hort D., Rachůnek, J. (2003). Algebra1. Olomouc.
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Jukl M. (2006). Lineární algebra. Olomouc.
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