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Geometry in Architecture of Santini-Aichl
Štíchová, Růžena ; Šarounová, Alena (advisor) ; Voráčová, Šárka (referee)
This text is meant for all people from general public with interest in mathematics and geometry. Primarily it is meant to be study material for teachers of mathematics and descriptive geometry at secondary schools. In the thesis there is included summary and properties of surfaces used in building constructions and their parametric and implicit expression. Thereinafter it deals with particular use of these rectilinear planes and also other ones in construction of arches, specifically in arches of some Santini's buildings. There is also mentioned a list of Santini's buildings and an in-depth analyse of geometry in plans of some of them. The text is supplemented with illustrative pictures made in Cabri Geometry II Plus (version 1.3.1), Maple 7, Rhino 3.0 and AutoCAD 2005, digital photographs and pictures from quoted literature.
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Graphs and graphical communication
Klemová, Hana ; Šarounová, Alena (advisor) ; Boček, Leo (referee)
This text is dedicated to the teachers of not only math and natural sciences. I wanted to show the readers a general view on the problems of graphical imagery and thematic cartography. In the beginning of the text I mentioned a brief historical prologue. In the next part I desribed reasons of using graphs and their significancy for today's society. To know the ropes in classification of graphs by their types is a headstone of understanding the graphical imagery. Thematic cartography is one of the parts of graphical communication, which is often forgotten, even though we come across it daily. In the end of my work I presented samples of graph utilisation in a non-mathematical subjects of high school tuition.
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Mathematical problems inspired by the nature
Králíková, Jana ; Šarounová, Alena (referee) ; Odvárko, Oldřich (advisor)
The diploma thesis consists of five exercises, which can be used within mathematical education at secondary schools. In these exercises students get involved with mathematical applications in ordinary life, which they can practically experience. A part of each exercise takes place outdoors, outside of the classroom. Objectives of the exercises are to display both mathematical and practical problems of the application. The topics of exercises are Tree height measuring, The measuring of unreachable distances, The altitude profile of a track, Cryptography and The Tower of Hanoi. I tried to make these exercises to solve real practical problems and to use the secondary school mathematics as much as possible at the same time. Students will use their knowledge in plane geometry, goniometry and trigonometry, functions and their graphs, sequences, series and proof by mathematical induction. Purposes of the exercises are to develop mathematical and logical thinking, to teach how to express the real situation in a mathematical way and to recognize mathematics in other fields of human activity.
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Golden Section
Chmelíková, Vlasta ; Bečvářová, Martina (referee) ; Šarounová, Alena (advisor)
Nazev prace: /laty fez Aulor: Vlasta Chmelikova Katedra: Didaktiky matemaliky Vedouci bakalafske prace: PhDr. Alcna Sarounova, CSc., Katedra didaktiky matematiky Matematieko-fyzikalni takulty Univerzity Karlovy v Praze. Sokolovska 83, Praha 8 e-mail vedoucihu: sarounov(o)karlin.mlT.euni.cz Abstrakt: Tenlo text je urcen vsem zajemcum z fad siroke vefejnosti, pfedevsfm vsak jako vzdelavaci material pro ucitcle matemaliky a dcskriptivni geometric na stfednich skolach. Prace zahrnuje postupy konstrukci zlateho fezu, vypocet zlateho cisla a jeho vlastnosti. Dale uka/uje souvislost zlateho cisla s Fibonacciho posloupnosti a pfiklady vyskytu zlateho fczu v rovinne geomelrii a v platonskych telesech. Text je doplnen nazornymi obrazky, vetsina z nich byla vytvofena v aplikaci DesignCAD. Vlastnosti zlateho cisla a rovinne konstrukce jsou uvcdcny vcetne podrobnych dukazu. Klicova slova: Zlaty fez, zlate cislo, platonska telesa, Fibonacciho posloupnost Title: The Golden Section Author: Vlasta Chmelikova Department: Didactics ofmathcmaties Supervisor: PhDr. Alena Sarounova, CSc., Katedra didaktiky matematiky Malematicko-fyzikalni fakulty UniverzityKarlovy v Praze. Sokolovska 83, Praha 8 Supervisor's e-mail adress: sarounov(S)karlin.mtT.euni.cz Abstract: This texl is especially intended as an educational material for...
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Surfaces Used in Architecture
Surynková, Petra ; Voráčová, Šárka (referee) ; Šarounová, Alena (advisor)
Nazev prace: Plochy stavcbni praxe Anfor: Pelra Surynkova Katedra (ustav): Katcdra didaktiky matematiky Yedouci diplomove prace: PhDr. Alena Sarounova, C'Sc. e-mail vcdouciho: Alena.Sarounovafajmff.cuni.cz Abstrakt: Bakalafska prace Plochy stavcbni praxe sc zabyva zakladnimi vlastnostmi ploch a jcjich vyuzitim v tcchnicke praxi. Specialne se venuje rozvinutelnym plocham. Prace je koncipovana jako ucebni text pro ucilele a studenty deskriptivni geometric a zajemcc o architekturu. Prace strucnc popisuje nektcre druhy ploch a ukazuje navrhy jejich vyuziti. Podrobnc pak studuje rozvinulelne plochy, jcjich vytvofcni, zakladni vlastnosti a uvadi i nekolik pfikladii rozvijeni rozvimitelnyeh ploch do roviny. Cast prace tcz pi'edklada inozna vyuziti ro/.vimitelnyeh ploch v praxi. K vctsine ploch jc pripojen take obrazek. K praci je pfidana obrazova pfiloha, ktera obsahuje fotografie staveb 7 eeleho svcta, na kteryeh sc /.minenc plochy vyskytuji. Soucasti bakalafske prace je rovnez pfilozcnc CD, na ncmz sc nachdzi dalsi obrazova pfiloha a bakalafska prace v clektronicke podobc. Kroine toho jsou na C'D zdrojove soubory vsech obrazku z bakalafske prace. Klicovci slova: plocha, rozvinutelna plocha, stfccha, klenba Title: Surfaces of Building Practice Author: Petra Surynkova Department: Department of Mathematics...
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Golden Section in Mathematics, Art and Nature
Jára, Václav ; Voráčová, Šárka (referee) ; Šarounová, Alena (advisor)
This graduation thesis discusses the occurrence and development of the golden section in ancient texts on mathematics. It is an introduction into the field of the golden section and it describes in an historical context the origin of the phenomenon and the processes that helped discover and make full use of its properties. It summarizes the main findings of Euclid's Elements, including later Supplement. It also mentions the contribution into the field by Arabian mathematicians. The work may serve either as a resource for seminars on the history of mathematics, or as a supplementary source for maths and geometry teachers willing to deepen their knowledge of the field. Texts contain pen drawings that correspond to original records. A CD is attached that contains the electronic form of the work.
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Geometry in Advertisements
Quittnerová, Lucia ; Ernestová, Martina (referee) ; Šarounová, Alena (advisor)
Nazov prace: Geomctria v reklamc - graficke zobrazovanie Autor: Lucia Quittnerova Katedra: Didaktika matematiky Veduci bakalarskej prace: PhDr. Alena Sarounova, CSc. Email veduceho: sarounov@karlin.mff.cuni.cz Abstrakt: Tymto textom by som chcela ukazat' rozne moznosti grafickeho zobrazovania. Na zaciatku tcxtu som uviedla strucny historicky uvod. V d'alsej casti som citatel'a zoznamila s popisnou statistikou, ktorii som v texte pouzfvala. Rozdelenie grafov podfa typu je najobsiahlejsou casl'ou tejlo prace. Dolezity jc i vyber grafu, ktory spravne vystihnc informacie, ktore chceme zobrazit', preto som sa venovala i tcjto problematike. V d'alsej casti textu som ukazala, ako spravne zobrazit' graf a na ktore parametre sa zamerat'. Prfklady roznych typov klamnych, alebo zavadzajucich grafov a obrazkov som prczentovala v zavcrecnej casti prace. Kl'ucova slova: graficke zobrazovanie, typy grafov, zneuzitie grafov Title: Geometry in advertisement - graphs Author: Lucia Quittnerova Department: Didactics mathematics Supervisor: PhDr. Alena Sarounova, CSc. Supervisor's e-mail address: sarounov@karlin.mff.cuni.cz Abstract: I would like to show various possibilities of displaying graphs. A short historical introduction opens the text. In its next part is the reader acquainted with the basic notions of descriptive...
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The trisection problem
Švecová, Michaela ; Šarounová, Alena (referee) ; Bečvář, Jindřich (advisor)
Na/ev prace: Trisekce uhlu. zajimave pfibli/.ne melody Autor: Michacla Sveeova Katedra (uslav): Katedra didaktiky matematiky Vedouei bakalafske prace: doc. RNDr. Jindfieh Becvaf, CSc. e-mail vedoueiho: beevano^karlin.mff.cuni.c/ Abslrakt: Tato pracc se zabyva problemein trisekce uhlu, coz je jedna z klasickych uloh fecke malematiky. Krome duka/u, /e tato uloha neni eukleidovsky fesitelna, jsou zde uvedeny ru/ne metody, k nimT: matematici beliem rady staleti dosli. Jednak to jsou postupy ,,pfesne", ktcre nejakym /pusobem porusuji pravidla cukleidovskyeh konstrukci. dale pak ..nepfesne" poslupy provadcne pouze za pomoci pravitka a kruzitka. Zde je mira nepresnosti odhadnuta vypoelem odchylky od occkavane tfetiny iihlu pro nektere specialni velikosti uhlu. Dale sc prace zabyva ruznymi nastroji - trisektory - pomocf nich/ l/e uhcl tfctinovc velikostijednoduse najit. Klicova slova: trisekce uhlu. eukleidovske konstrukcc, recka matematika Title: The Triseclion Problem Author: Michaela Sveeova Deparment: Department of Mathematics IZducation Supervisor: doc. RIM Dr. Jindfieh Becvar, CSc. Supervisor's e-mail adrcss: becvar(^karlin.mff.cuni.cx Abstract: This work deals with the problem of the angle triscclion which is one of the classical tasks of the Greek mathematics. Besides proving that this problem has no...
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