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Santos, Paula Daniele Borges dos. "Relação entre o máximo divisor comum, o mínimo múltiplo comum e o diagrama de Venn." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7119.
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Previous issue date: 2017-03-21<br>Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG<br>The present work intends to show an illustrative approach to calculate and understand Greater Common Divisor and Least Common Multiple, seeking a greater assimilation and concretization of the learning of this content. This methodology is presented in a chromological order following the evolution of mathematical concepts. Therefore, this text, aiming to produce a meaningful approach of the subject, seeks to expose in a simple way what comes to be the Prime Numbers according to Numbers Theory and Venn Diagram according to the Set Theory, in order to visualize and obtain the Relation between Greater Common Divisor, Least Common Multiple, and Venn Diagram.<br>O presente trabalho pretende mostrar uma abordagem ilustrativa para se calcular e entender Máximo Dividor Comum e Mínimo Múltiplo Comum, buscando uma maior assimilação e concretização da aprendizagem desse conteúdo. Esta metodologia é apresentada numa ordem cronológica seguindo a evolução dos conceitos matemáticos. Logo, este texto, visando produzir uma abordagem significativa do assunto, busca expor de forma simples o que vem a ser os Números Primos segundo a Teoria dos Números e Diagrama de Venn segundo a Teoria dos Conjuntos, para que assim se consiga visualizar e obter a Relação entre Máximo Divisor Comum, Mínimo Múltiplo Comum e o Diagrama de Venn.
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Hui, Wu. "Visualization of Bags." Thesis, Linnéuniversitetet, Institutionen för datavetenskap (DV), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-28398.
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The purpose of this thesis is to develop a toolkit to visualize bag calculations for teaching. We take full advantage of interaction techniques in Computer Science to achieve it, which could lead to a modern and impressive way for teaching. In this thesis, the developed toolkit is going to show the bag calculations and corresponding animations interactively and aesthetically which make new learners easier to acquire the concept of multiset.
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Ahmad, Sadaf. "Non-profit Organizations : Development of nonprofit organization’s sustainability reports." Thesis, Högskolan i Borås, Akademin för textil, teknik och ekonomi, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-26554.
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This study aims to analyze and evaluate three non-profit organizations regarding how their sustainability accounting reports have changed and developed between year 2017 and year 2019. The study analyzes how parameters in the sustainability index have been taken into consideration to perceive which parameters are the three non-profits organization’s focal points. In addition, the study will analyze how sustainability accounting reports meet the stakeholder's information needs. Given the prevailing issues and purpose of the study, a qualitative method is relevant to this study. The selection of organizations is based on organizations' availability of sustainability reports for the assessment period. In this study, non-probability selection was chosen, where the selection was made through a preliminary investigation. The study is based on a secondary data method which is a flexible and appropriate approach. This thesis consists of empirical studies that will help strengthen the quality of the study. The data collected in the empirical data have been analyzed on the basis of the theoretical frame of reference. Frame of reference in this thesis is based on sustainable development, sustainability accounting, Venn diagram of sustainable development, triple bottom line and stakeholder theory. The empirical data in this thesis consists of Red Cross Sweden, Save the Children Sweden and WWF. Based on the result of this thesis, the parameters under dimensions, environmental responsibility, social responsibility and financial responsibility in each organization have similarities. For example, the environmental requirements for purchasing and procurement are seen in both the Red Cross' and Save the Children's sustainability reports. Another example of similarity that can be seen in all three organizations' sustainability reports is gender equality and diversity. The organization's focus for different parameters in sustainability reports depends on the type of business they have. The development of each organization's sustainability reports in 2017 has been remarkable. Prior to 2017, Save the Children was a pioneer in presenting sustainability reports. While the Red Cross and WWF began to present sustainability reports in 2017. According to their stakeholder analysis, all three respective organizations have included all parameters that are important to their stakeholders. Through their dialogues with both internal and external stakeholders, the respective organizations meet the stakeholders' need for information.<br>Syfte: Denna studie syftar till att analysera och utvärdera tre ideella organisationer och hur deras hållbarhetsredovisning rapporter har förändrats och utvecklats mellan åren 2017 och2019. Studien analyserar hur parametrar i hållbarhetsredovisning rapporter har beaktats. Studien kommer också att analysera hur hållbarhetsredovisning rapporter möter intressenternas informationsbehov. Metod: Med hänsyn till uppsatsens syftet och frågeställningar har studien en kvalitativ ansats. Studien utgår ifrån en sekundärdata metod som är ett flexibelt och lämpligt tillvägagångssätt. Studien består också av empiriska studier som kommer att bidra till att stärka studiens kvalitet. Den insamlade datan i empirin har analyserats med underlag av den teoretiska referensramen. Teoretiska perspektiv: Den teoretiska referensram som uppsatsen bygger på är hållbarutveckling, hållbarhetsredovisning, triple bottom line och intressentteori. Empiri: De tre ideella organisationer som har undersökts i denna uppsats är Röda Korset, Rädda barnen och WWF. Resultat: Parametrarna under dimensioner, miljöansvar, socialt ansvar och ekonomiskt ansvar i respektive organisation har likheter. Till exempel ses miljökraven för inköp och upphandling i både Röda korsets och i Rädda barnens hållbarhetsrapporter. Ett annat exempel på likhet som kan ses i alla de tre organisationernas hållbarhetsrapporter är jämställdhet och mångfald. Organisationens fokus för olika parametrar i hållbarhetsrapporter beror på vilken typ av verksamhet de har. Utvecklingen av respektive organisations hållbarhetsrapporter under 2017har varit anmärkningsvärt. Före 2017 var Rädda barnen en pionjär när det gäller att presenterahållbarhetsrapporter. Medan Röda Korset och WWF började presentera hållbarhetsrapporter först år 2017. Alla de tre respektive organisationerna har enligt sin intressentanalys inkluderat alla parametrar som är viktiga för deras intressenter. De respektive organisationerna försöker genom sina dialoger med både interna och externa intressenter möter intressenternas behov av information.
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Загвойська, Л. Д., та О. Р. Пелюх. "Дослідження взаємодії стейкхолдерів з використанням діаграм Венна". Thesis, Ткачов О.О, 2016. http://essuir.sumdu.edu.ua/handle/123456789/47222.
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В умовах антропогену (Crutzen and Stoermer, 2000), коли людство на глобальному рівні виходить за межі безпечної операційної діяльності, особливо затребуваним стає адаптивний менеджмент (Holling, 1978; Walters, 1986; Lee, 1993). Його визначальними рисами є визнання обмеженості наукових знань про поведінку екосистем умовах наближення до порогових значень і необхідності коригування наступних управлінських рішень на основі вивчення реакції керованих систем на попередні рішення.
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Rein, Judith Ann. "Variables and Venn diagrams." Diss., The University of Arizona, 1997. http://hdl.handle.net/10150/289244.
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Venn diagrams were invented by John Venn in 1880 as an aid in logical reasoning. Since then, the diagrams have been used as an aid in understanding and organization for widely diverse audiences (e.g., elementary school children, business people) and widely diverse content areas (e.g., self-improvement courses, statistics). In this dissertation, Venn diagrams are used to illustrate and explain variable relationships. There are three main foci: (a) correlation and interaction, (b) variables and Venn diagrams, and (c) reliability and Venn diagrams. Confusion between correlation and interaction is explained, and the multicollinearity problem is illustrated using a Venn diagram composed of three circles and a horse-shoe shaped figure. Venn diagrams are presented for these variables: moderator; concrete and hypothetical intervening; component; traditional, negative, and reciprocal suppressor; covariate; disturbance; and confound. Venn diagrams are also used to differentiate among within-subjects, between-subjects, and reliability designs. Last, a detailed example, which assumes basic knowledge of classical test theory and generalizability theory, is presented to help illustrate, using Venn diagrams, the role of error variance in performance assessments. Evaluation based on comments of 13 American Educational Research Association, Division D, listserve members and 7 non-members was positive, and interest in the topic was shown by over 100 visits to the website where a portion of the dissertation was posted.
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Bultena, Albertha. "Venn diagrams with few intersections." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/MQ36611.pdf.
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Micallef, Luana. "Visualizing set relations and cardinalities using Venn and Euler diagrams." Thesis, University of Kent, 2013. https://kar.kent.ac.uk/47958/.
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In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses.
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Heberle, Henry. "Uma abordagem visual para análise comparativa de redes biomoleculares com apoio de diagramas de Venn." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-19032015-115427/.
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Sistemas biológicos podem ser representados por redes que armazenam não apenas informações de conectividade, mas também informações de características de seus nós. No contexto biomolecular, esses nós podem representar proteínas, metabólitos, entre outros tipos de moléculas. Cada molécula possui características anotadas e armazenadas em bases de dados como o Gene Ontology. A comparação visual dessas redes depende de ferramentas que permitam o usuário identificar diferenças e semelhanças entre as anotações feitas sobre as moléculas (atributos) e também sobre as interações conhecidas (conexões). Neste trabalho de mestrado, buscou-se desenvolver técnicas que facilitem a comparação desses atributos sobre as moléculas, tentando manter no processo a visualização das redes em que essas moléculas estão inseridas. Como resultado, obteve-se a ferramenta VisPipeline-MultiNetwork, que permite comparar até seis redes, utilizando operações de conjuntos sobre as redes e sobre seus atributos. Dessa forma, diferentemente da maioria das ferramentas conhecidas para a visualização de redes biológicas, o VisPipeline-MultiNetwork permite a criação de redes cujos atributos são derivados das redes originais por meio de operações de união, intersecção e valores exclusivos. A comparação visual das redes é feita pela visualização do resultado dessas operações de conjuntos sobre as redes, por meio de um método de comparação lado-a-lado. Já a comparação dos atributos armazenados nos nós das redes é feita por meio de diagramas de Venn. Para auxiliar este tipo de comparação, a técnica InteractiVenn foi desenvolvida, em que o usuário pode interagir com um diagrama de Venn efetuando operações de união entre conjuntos. Essas operações de união aplicadas sobre os conjuntos são também aplicadas sobre as respectivas formas no diagrama. Esta característica da técnica a diferencia das outras ferramentas de criação de diagramas de Venn. Integrando essas funcionalidades, o usuário é capaz de comparar redes sob diversas perspectivas. Para exemplificar a utilização do VisPipeline-MultiNetwork, dois casos no contexto biomolecular foram estudados. Adicionalmente, uma ferramenta web para a comparação de listas de cadeias de caracteres por meio de diagramas de Venn foi desenvolvida. Ela também implementa a técnica InteractiVenn e foi denominada InteractiVenn website.<br>Biological systems can be represented by networks that store not only connectivity information, but also node feature information. In the context of molecular biology, these nodes may represent proteins, metabolites, and other types of molecules. Each molecule has features annotated and stored in databases such as Gene Ontology. A visual comparison of networks requires tools that allow the user to identify differences and similarities between nodes attributes as well as known interactions between nodes (connections). In this dissertation, we sought to develop a technique that would facilitate the comparison of these biological networks, striving to maintain in the process the visualization of the network connectivities. As a result, we have developed the VisPipeline-MultiNetwork tool, which allows comparison of up to six networks, using sets of operations on networks and on their attributes. Unlike most known tools for visualizing biological networks, VisPipeline-MultiNetwork allows the creation of networks whose attributes are derived from the original networks through operations of union, intersection and unique values. A visual comparison of the networks is achieved by visualizing the outcome of such joint operations through a all-in-one comparison method. The comparison of nodes attributes is performed using Venn diagrams. To assist this type of comparison, the InteractiVenn technique was developed, in which the user can interact with a Venn diagram, performing union operations between sets and their corresponding diagrams. This diagram union feature differs from other tools available for creating Venn diagrams. With these tools, users manage to compare networks from different perspectives. To exemplify the use of VisPipeline-MultiNetwork, two case studies were carried out in the biomolecular context. Additionally, a web tool for comparing lists of strings by means of Venn diagrams was made available. It also implements the InteractiVenn technique and its site has been named InteractiVenn.
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Hingston, Phillip Anthony, and Hingston@bigpond com. "Animated proportional Venn diagrams: a study into their description, construction and business application." RMIT University. Economics, Finance and Marketing, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080213.111255.
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Anecdotal observation of the way in which data visualisation techniques are utilised to present relationships in data to audiences informed the author's view that data visualisation had not evolved to utilise the capabilities of ubiquitous business computer equipment. In an information rich but attention poor business environment, a search for a new tool was undertaken to supplement those techniques available to help audiences understand statistical relationships in presentation data. This search resulted in the development of a practical software tool based on animated Venn diagrams (Dvenn) that attempted to exploit the inherent human ability to perceive quantities visually, a faculty described herein as visual numeracy. The exploitation of this faculty is considered here to be a valuable aid for group understanding of business presentation data. The development of the tool was an essential part of the research that was undertaken and the resulting software forms a significant portion of this practise based research. The aim of the software development was to develop a readily accessible tool that could be utilised in a non-specialist business environment to better facilitate an honest shared meaning of numerical data between a presenter and their audience. The development of the tool progressed through a number of iterations and the software that accompanies this work is an important component that needs to be viewed in conjunction with the text. The test of the final version was undertaken with undergraduate University students in an attempt to validate the efficacy of the data visualisation technique. The test of the Dvenn software was made against the mature yardstick of scatter-plots. Interestingly, the correlations presented by scatter-plot were not as readily identified as would have been assumed, however, the results for the Dvenn tests were not supportive of the technique for widespread adoption. Nevertheless, further research into the best method of harnessing visual numeracy would seem to be justified.
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Ayaz, Razmjooei. "Investigation of SomeCognitive Difficulties inSet Theory." Thesis, Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-91976.
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A previous study on students approach to problems of Set Theory in Iran brought me somehypotheses. These encouraged me to test the hypotheses in this supplementary study. Mypurpose of this study was to consider some students' cognitive difficulties in Set Theory. Iinvestigated students’ conceptual understanding of two major concepts of Set Theory – theconcepts of inclusion and belonging. I also studied the ways students use Venn diagram tofigure out problems in Set Theory. I wanted to examine how students figure out the differentmeanings of words in the natural and formal language. To do so, I analyzed six experiments. Icompared three experiments with the experiments of my previous study in Iran. My researchquestions suggested using a qualitative research method. My theoretical framework built aroundtheories of semiotic activities, which were used in the analysis.The results indicated that students can make unfortunate use of Euler–Venn diagrams. A set ofsets was a difficult concept for students. Some words in natural language, even the word "set" inboth natural and formal language, caused confusion for students when introduced in Settheoretic contexts. Students failed sometimes to distinguish between sets and elements. Theexperiments showed that students’ cultural context had affect on students' cognition regardingmathematical objects.
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Nilsson, Jonas. "Differences in staurolite mode due to changes in bulk composition as an effect of mass transfer by fluids during metamorphism." Thesis, Stockholms universitet, Institutionen för geologiska vetenskaper, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-100141.
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Results from petrographic analyses, chemical analyses and mineral phase diagram calculations show that staurolite minerals grew in selvages adjacent to quartz veins. Previous studies show the same relationships between quartz veins and garnet, as well as kyanite growth. The selvages are formed as metamorphic fluids flow through cracks, altering the bulk composition by mass transfer and triggers the nucleation and growth of new minerals. A pseudosection for a staurolite absent sample has been calculated using THERMOCALC. No stability field correlates to visually observed mineralogy. This indicates that a reaction forming staurolite never was triggered since no fluids was present during metamorphism.
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Bultena, Bette. "Face-balanced, Venn and polyVenn diagrams." Thesis, 2013. http://hdl.handle.net/1828/4873.
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A \emph{simple} $n$-\emph{Venn diagram} is a collection of $n$ simple intersecting closed curves in the plane where exactly two curves meet at any intersection point;
the curves divide the plane into $2^n$ distinct open regions, each defined by its intersection of the interior or exterior of each of the curves.
A Venn diagram is \emph{reducible} if there is a curve that, when removed, leaves a Venn diagram with one less curve and \emph{irreducible} if no such curve exists.
A Venn diagram is \emph{extendible} if another curve can be added, producing a Venn diagram with one more curve.
Currently it is not known whether every simple Venn diagram is extendible by the addition of another curve.
We show that all simple Venn diagrams with $5$ curves or less are extendible to another simple Venn diagram.
We also show that for certain Venn diagrams, a new extending curve is relatively easy to produce.
We define a new type of diagram of simple closed curves where each curve divides the plane into an equal number of regions;
we call such a diagram a \emph{face-balanced} diagram.
We generate and exhibit all face-balanced diagrams up to and including those with $32$ regions;
these include all the Venn diagrams.
Venn diagrams exist where the curves are the perimeters of polyominoes drawn on the integer lattice.
When each of the $2^n$ intersection regions is a single unit square, we call these \emph{minimum area polyomino Venn diagrams}, or \emph{polyVenns}.
We show that polyVenns can be constructed and confined in bounding rectangles of size $2^r \times 2^c$ whenever $r, c \ge 2$ and $n=r+c$.
We show this using two constructive proofs that extend existing diagrams.
Finally, for even $n$, we construct polyVenns with $n$ polyominoes in $(2^{n/2} - 1) \times (2^{n/2} + 1)$ bounding rectangles in which the empty set is not represented as a unit square.<br>Graduate<br>0405<br>0984<br>bbultena@uvic.ca
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Návarová, Daniela. "Vlastnosti textu jako faktor řešení slovních úloh s využitím Vennových diagramů." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-312869.
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Title: Text properties as a factor in solving word problems with the use of Venn diagrams Author: Bc. Daniela Návarová Department: Department of Mathematics and Mathematical Education Supervisor: doc. RNDr. Jarmila Novotná, CSc. Supervisor's e-mail address: Jarmila.Novotna@pedf.cuni.cz This diploma thesis deals with the word problems where Venn diagrams can be used. The word problems are studied as texts and their specific text properties are scrutinised in the first, theoretical, part of the thesis. The second part describes an experiment that focuses on the importance of text properties of word problems for the problem solvers. The main aims of this diploma thesis are to show the possibility of textual examination of the chosen texts and to unfold some connections between the mathematical and linguistic views on the area of word problems. Keywords: text, word problem, Venn diagram
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Lai, Qun-Yu, and 賴群宇. "Applying the Venn Diagram Based Text-Mining and Eye-Tracking Technology to Advertising Recommendation." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/30730996875982814103.
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碩士<br>國立暨南國際大學<br>資訊管理學系<br>104<br>While online advertising usually incorporates eye-catching images or pop-ups to attract user attention, it is less likely to mine data generated by user interaction with the system when browsing. This study attempts to utilize natural human reading behavior and determine which contents user attention is focused on to investigate users’ underlying preferences and recommend targeted advertising for said users. The experiment utilizes eye tracking technology combined with Venn diagram concepts to propose a data mining method. Using Venn diagram concepts, words in different sets are assigned weighted values and are transformed into units that can be used for calculation. This study first verified the effectiveness of the method of categorization, and then analyzed its predictive ability via experimentation. Results show that, in terms of advertising recommendation predictivity, the system exceeds the value of the threshold for non-random probability.
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Vojířová, Barbora. "Vennovy diagramy - výuka na střední škole metodou CLIL." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-394108.
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This thesis focuses on the teaching of mathematics using the CLIL method. The topic is Venn diagrams and learning how to solve problems using these diagrams. The language chosen for the CLIL method is English. First, the CLIL method is described, and later I introduce sets and Venn diagrams. The aim of the thesis is to prepare and implement two lessons using the CLIL method in English, and two lessons in Czech, followed by preparing a test in both languages for a third lesson. The thesis was realized by conducting a teaching experiment, which took place in two classes of multi- year grammar school (in the Quintas - the first year of secondary school). I have compiled and tested four worksheets - two with Czech tasks, two with English tasks, a presentation for the lesson using the CLIL method, and tests for both language versions. Both the tasks and solutions are part of the thesis. Before the preparation of the thesis, the following two research questions were identified: 1. What needs to be taken into consideration when preparing for the Venn diagrams lesson using the CLIL method, and what needs to be added to this lesson compared to the Czech lesson? 2. At what success rate will pupils learn using the CLIL method in English and pupils using Czech, with regard to equation building and answers to...
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Ahmadi, Mamakani Abdolkhalegh. "Searching for Simple Symmetric Venn Diagrams." Thesis, 2013. http://hdl.handle.net/1828/4709.
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An n-Venn diagram is defined as a collection of n finitely intersecting closed curves dividing the plane into 2^n distinct regions, where each region is in the interior of a unique subset of the curves. A Venn diagram is simple if at most two curves intersect at any point, and it is monotone if it has some embedding on the plane in which all curves are convex. An n-Venn diagram has n-fold rotational symmetry if a rotation of 180 degrees about a centre point in the plane leaves the diagram unchanged, up to a relabeling of the curves. It has been known that rotationally symmetric Venn diagrams could exist only if the number of curves is prime. Moreover, non-simple Venn diagrams with rotational symmetry have been proven to exist for any prime number of curves. However, the largest prime for which a simple rotationally symmetric Venn diagram was known prior to this, was 7. In this thesis, we are concerned with generating simple monotone Venn diagrams, especially those that have some type(s) of symmetry. Several representations of these diagrams are introduced and different backtracking search algorithms are provided based on these representations. Using these algorithms we show that there are 39,020 non-isomorphic simple monotone 6-Venn diagrams in total. In the case of drawing Venn diagrams on a sphere, we prove that there exists a simple symmetric n-Venn diagram, for any n >= 6, with the following set(s) of isometries : (a) a 4-fold rotational symmetry about the polar axis, together with an additional involutional symmetry about an axis through the equator, or (b) an involutional symmetry about the polar axis together with two reflectional
symmetries about orthogonal planes that intersect at the polar axis. Finally, we introduce a new type of symmetry of Venn diagrams which leads us to the discovery of the first simple rotationally symmetric Venn diagrams of 11 and 13 curves.<br>Graduate<br>0984<br>Khalegh@GMail.com
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Weston, Mark Richard Nicholas. "Symmetries of Venn diagrams on the sphere." Thesis, 2009. http://hdl.handle.net/1828/1348.
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A diagram on a surface is a collection of coloured simple closed curves which generally intersect only at points, and a Venn diagram of n curves has the additional property that there are exactly 2^n faces in the diagram, each corresponding to a unique intersection of the interiors of a subset of the curves. A diagram has rotational symmetry if it can be constructed by rotating a single closed curve in the plane n times, each time by 2 \pi /n, and changing the colour of the curve for each rotation; equivalently, the diagram can be constructed from a region forming a "pie-slice" of the diagram and containing a
section of each curve, and then copying and rotating this region n times, recolouring the sections of curves in the region appropriately. This and reflective symmetries are the only non-trivial ways a finite plane diagram can have some kind of symmetry.
In this thesis, we extend the notion of planar symmetries for diagrams onto the sphere by constructing and projecting diagrams onto the sphere and examining the much richer symmetry groups that result. Restricting our attention to Venn diagrams gives a rich combinatorial structure to the
diagrams that we examine and exploit. We derive several constructions of Venn diagrams with interesting symmetries on the sphere by modifying the landmark work of Griggs, Killian and Savage from 2004 which provided
some important answers to questions about planar symmetric diagrams. We examine a class of diagrams that exhibit a rotary reflection symmetry (a rotation of the sphere followed by a reflection), in which we make
some initial steps towards a general construction for n-Venn diagrams realizing a very rich symmetry group of order 2n, for n prime or a power of two. We also provide a many-dimensional construction of very simple Venn diagrams which realize any subgroup of an important type of symmetry group that use only reflection symmetries. In summary, we exhibit and examine at least one Venn diagram realizing each of the 14 possible different classes of finite symmetry groups on the
sphere, many of these diagrams with different types of colour symmetry. All of these investigations are coupled with a theoretical and practical framework for further investigation of symmetries of diagrams and discrete combinatorial objects on spheres and higher-dimensional surfaces.
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Chow, Stirling Christopher. "Generating and drawing area-proportional Euler and Venn diagrams." Thesis, 2007. http://hdl.handle.net/1828/128.
Full textAbstract:
An Euler diagram C = {c_1, c_2,..., c_n}
is a collection of n simple closed curves (i.e., Jordan curves) that partition the plane into connected subsets, called regions, each of which is enclosed by a unique combination of curves. Typically, Euler diagrams are used to visualize the distribution of discrete characteristics across a sample population; in this case, each curve represents a characteristic and each region represents the sub-population possessing exactly the combination of containing curves' properties. Venn diagrams are a subclass of Euler diagrams in which there are 2^n regions representing all possible combinations of curves (e.g., two partially overlapping circles).
In this dissertation, we study the Euler Diagram Generation Problem (EDGP), which involves constructing an Euler diagram with a prescribed set of regions. We describe a graph-theoretic model of an Euler diagram's structure and use this model to develop necessary-and-sufficient existence conditions. We also use the graph-theoretic model to prove that the EDGP is NP-complete. In addition, we study the related Area-Proportional Euler Diagram Generation Problem (w-EDGP), which involves constructing an Euler diagram with a prescribed set of regions, each of which has a prescribed area. We develop algorithms for constructing area-proportional Euler diagrams composed of up to three circles and rectangles, as well as diagrams with an unbounded number of curves and a region of common intersection. Finally, we present implementations of our algorithms that allow the dynamic manipulation and real-time construction of area-proportional Euler diagrams.
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Moremedi, Kobamelo. "Towards a comparative evaluation of text-based specification formalisms and diagrammatic notations." Diss., 2015. http://hdl.handle.net/10500/21938.
Full textAbstract:
Specification plays a vital role in software engineering to facilitate the development of highly dependable software. The importance of specification in software development is to serve, amongst others, as a communication tool for stakeholders in the software project. The specification also adds to the understanding of operations, and describes the properties of a system. Various techniques may be used for specification work.
Z is a formal specification language that is based on a strongly-typed fragment of Zermelo-Fraenkel set theory and first-order logic to provide for precise and unambiguous specifications. Z uses mathematical notation to build abstract data, which is necessary for a specification. The role of abstraction is to describe what the system does without prescribing how it should be done.
Diagrams, on the other hand, have also been used in various areas, and in software engineering they could be used to add a visual component to software specifications. It is plausible that diagrams may also be used to reason in a semi-formal way about the properties of a specification. Many diagrammatic languages are based on contours and set theory. Examples of these languages are Euler-, Spider-, Venn- and Pierce diagrams. Euler diagrams form the foundation of most diagrams that are based on closed curves.
Diagrams, on the other hand, have also been used in various areas, and in software engineering they could be used to add a visual component to software specifications. It is plausible that diagrams may also be used to reason in a semi-formal way about the properties of a specification. Many diagrammatic languages are based on contours and set theory. Examples of these languages are Euler-, Spider-, Venn- and Pierce diagrams. Euler diagrams form the foundation of most diagrams that are based on closed curves.
The purpose of this research is to demonstrate the extent to which diagrams can be used to represent a Z specification. A case study is used to transform the specification modelled with Z language into a diagrammatic specification. Euler, spider, Venn and Pierce diagrams are combined for this purpose, to form one diagrammatic notation that is used to transform a Z specification<br>School of Computing<br>M. Sc. (Information Systems)
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Pereira, Joyce Liliana Calvinho. "Desenvolvimento do pensamento estatístico em crianças de três anos." Master's thesis, 2020. http://hdl.handle.net/10400.1/14634.
Full textAbstract:
A matemática assume um papel fundamental na estruturação do pensamento do ser humano assim como desempenha uma importante função para a vida do dia a dia. Dada a sua importância, desde cedo, é relevante estimular competências matemáticas para a criança ser, futuramente, um cidadão matematicamente literato. Neste sentido, trabalhar com as crianças a organização e tratamento de dados (OTD), no domínio da matemática, constitui uma forma de desenvolver uma cidadania informada nas crianças desde o pré-escolar.
A organização e tratamento de dados, concretamente, o pensamento estatístico, pressupõe a formulação de questões e conceção do plano, a recolha de dados, a representação e análise de dados e a interpretação dos dados e formulação de conclusões. Nesta perspetiva, os objetivos e questões de pesquisa enquadram-se na recolha de dados, como meio de estimular o reconhecimento individual e coletivo de uma população, e na construção, análise e interpretação de representações tabelares e gráficas no contexto da realidade das crianças.
Esta investigação decorreu no contexto de educação pré-escolar, numa Instituição Particular de Solidariedade Social (IPSS), no sotavento algarvio. Realizou-se com um grupo de vinte e uma crianças de três anos, de ambos os sexos, e visou o desenvolvimento do pensamento estatístico, entendido como uma forma de estruturar a realidade. Neste estudo, a intervenção educativa consubstanciou-se em três tarefas matemáticas, relacionadas com alimentação, que exploram os diagramas de Venn e de Carroll e um gráfico de barras manipulativo e visual, em 3D.
Os dados apontam para a capacidade de as crianças de três anos construírem os diagramas referidos atendendo a categorias simples, disjuntas e complementares. Na construção do gráfico de barras, as crianças manifestaram igualmente alguma capacidade para associar as suas escolhas individuais à construção de uma representação coletiva, neste caso dos frutos preferidos. Os dados apontam igualmente para dificuldades de análise das representações com especial incidência no diagrama de Carroll por ser uma tabela com dupla entrada, ao invés das restantes representações lineares.<br>Mathematics plays a key role in structuring human thinking as well as playing an important role in everyday life. Given its importance, from an early age, it is relevant to stimulate mathematical skills for the child to be a mathematically literate citizen in the future. In this sense, working with children on data handling in the field of mathematics is a way of developing informed citizenship in children from preschool.
Data handling, namely statistical thinking, presupposes the formulation of questions and design of the plan, data collection, data representation and analysis, and interpretation of data and formulation of conclusions. From this perspective, the research objectives and questions are framed in data collection as a means of stimulating individual and collective recognition of a population, and in the construction, analysis and interpretation of tabular and graphic representations in the context of children's reality.
This research took place in the context of pre-school education in a Social Solidarity Institution (IPSS) in the eastern Algarve. It was carried out with a group of twenty-one three-year-olds of both genders and aimed at the development of statistical thinking, understood as a way of structuring reality. In this study, the educational intervention consisted of three food-related mathematical tasks that explore the Venn and Carroll diagrams and a manipulative and visual 3D bar graph.
The data point to the ability of children from three years to build the diagrams serving simple, disjoint and complementary categories. In constructing the bar graph, the children also expressed some ability to associate their individual choices with the construction of a collective representation, in this case of the preferred fruits. The data also point to difficulties in the analysis of the representations with special incidence in the Carroll diagram because it is a double entry table, instead of the other linear representations.
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Friendrich, Wernher Rudolph. "Towards the elicitation of hidden domain factors from clients and users during the design of software systems." Diss., 2008. http://hdl.handle.net/10500/2629.
Full textAbstract:
This dissertation focuses on how requirements for a new software development system are elicited and what pitfalls could cause a software development project to fail if the said requirements are not captured correctly. A number of existing requirements elicitation methods, namely: JAD (Joint Application Design), RAD (Rapid Application Development), a Formal Specifications Language (Z), Natural Language, UML (Unified Modelling Language) and Prototyping are covered. The aforementioned techniques are then integrated into existing software development life cycle models, such as the Waterfall model, Rapid Prototyping model, Build and Fix model, Spiral model, Incremental model and the V-Process model. Differences in the domains (knowledge and experience of an environment) of a client and that of the software development team are highlighted and this is done diagrammatically using the language of Venn diagrams. The dissertation also refers to a case study highlighting a number of problems during the requirements elicitation process, amongst other the problem of tacit knowledge not surfacing during elicitation.
Two new requirements elicitation methodologies are proposed namely: the SRE (Solitary Requirements Elicitation) and the DDI (Developer Domain Interaction) methodology. These two methods could potentially be more time consuming than other existing requirements elicitation methods, but the benefits could outweigh the cost of their implementation, since the new proposed methods have the potential to further facilitate the successful completion of a software development project. Following the introduction of the new requirements elicitation methods, they are then applied to the aforementioned case study and highlight just how the hidden domain of the client may become more visible, because the software development team has gained a deeper understanding of the client’s working environment. They have therefore increased their understanding of how the final product needs to function in order to fulfil the set out requirements correctly.
Towards the end of the dissertation a summary and a conclusion as well as future work that could be undertaken in this area are provided.<br>Computer Science<br>M. Sc. (Computer Science)
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Ramaniuk, Volha. "Růst Mycobacterium smegmatis na agarovém médiu a agarovém médiu pokrytém celofánovou folií - morfologická a proteomová studie." Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-305796.
Full textAbstract:
Biofilm formation is one of the most common bacterial survival strategies. Majority of bacterial species are able to form these three-dimensional structures, including pathogens like Mycobacterium tuberculosis. Representatives of Mycobacterium genus widely occur in the nature, although they can cause serious problems when they appear in medical equipment and artificial replacements of the human body. Non-pathogenic Mycobacterium smegmatis mc2 155 was used as a model organism in our experiments. We investigated morphology of the three- and six-day-old colonies (in fact biofilms) on agar and agar covered with cellophane using Stereo microscope and Scanning Electron Microscope. We found that a type of surface as well as a carbon source has a great influence on the morphology of the M. smegmatis colonies. We isolated proteomes from the agar and cellophane cultures and from planktonic culture. Two-dimensional electrophoresis was used as the main proteomic method. Proteomic data were analyzed using PDQuest software. Then the sets of proteins detected by qualitative and quantitative analyses were compared using Venn diagrams. As a result, we recognized 7 unique proteins that might be specific for recognition and adhesion of bacteria to the cellophane, no unique protein in agar proteome and 46 unique...