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Famous unsolvable problems.
Kesely, Michal ; Pražák, Dalibor (vedoucí práce) ; Pick, Luboš (oponent)
Title: Famous nnsolvable problems Author: Michal Kesely Department,: Deportment of Mathematical Analysis Supervisor: RNDr. Dalibor Prazak, Ph.D. Supervisor's e-mail address; prazak^karlin.inff.cuni.cz Abst.ra.ct: In the present work we study three famous problems of antiquity (the Delian problem, the trisect,ion of an angle and the squaring of a. cir- cle), which turned to be nnsolvable much later. In the first chapter we will formalize the concept of Euclidean construction, prove few theorems about algebraic numbers and show an interesting connection between con- structible numbers and algebraic numbers. In the next, two chapters we will prove the insolvability of the Delia.ii problem and the trisection of an an- gle using the properties of constructible numbers. Furthermore in (.he third chapter we will mention some incorrect solutions of the trisection problem, In the last, chapter we will prove the existence of transcendental numbers, build an appropriate apparatus and finally we will prove the transcendence of two famous const.nnts - c and TV. The insolvabilityof the squaring problem is a direct, consequence of the transcendence of T\. Keywords: unsolvable problem, constrnctible. transcendental
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MDS codes conjecture
Kesely, Michal ; Drápal, Aleš (vedoucí práce) ; Lisoněk, Petr (oponent)
V předloženej práci skúmame niektoré vlastnosti MDS kódov a venujeme sa najma domnienke o MDS kódoch. Najprv MDS kódy predstavíme, uvedieme ich príklady a základné vlastnosti, napríklad ich súvislosť s latinskými štvorcami alebo odlžnikmi. Neskor pristúpime k MDS domnienke a jej dokazovaniu v niektorých prípadoch. V tretej katipole uvedieme súvislosť medzi MDS kódmi a n-oblúkmi v propotívnych geometriách. Nakoniec ešte predstavíme preklad známych prípadov, pre ktoré je MDS domnienka dokázaná.
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Famous unsolvable problems.
Kesely, Michal ; Pick, Luboš (oponent) ; Pražák, Dalibor (vedoucí práce)
Title: Famous nnsolvable problems Author: Michal Kesely Department,: Deportment of Mathematical Analysis Supervisor: RNDr. Dalibor Prazak, Ph.D. Supervisor's e-mail address; prazak^karlin.inff.cuni.cz Abst.ra.ct: In the present work we study three famous problems of antiquity (the Delian problem, the trisect,ion of an angle and the squaring of a. cir- cle), which turned to be nnsolvable much later. In the first chapter we will formalize the concept of Euclidean construction, prove few theorems about algebraic numbers and show an interesting connection between con- structible numbers and algebraic numbers. In the next, two chapters we will prove the insolvability of the Delia.ii problem and the trisection of an an- gle using the properties of constructible numbers. Furthermore in (.he third chapter we will mention some incorrect solutions of the trisection problem, In the last, chapter we will prove the existence of transcendental numbers, build an appropriate apparatus and finally we will prove the transcendence of two famous const.nnts - c and TV. The insolvabilityof the squaring problem is a direct, consequence of the transcendence of T\. Keywords: unsolvable problem, constrnctible. transcendental
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