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O modelo logístico de Verhulst sujeito a incertezas na condição inicial Verhulst logistic模型在初始条件下的不确定性
Revista Professor de Matemática On line Pub Date : 2016-12-09 DOI: 10.21711/2319023x2023/pmo1103
Everson Luiz Ricordi, Fabio Dorini
{"title":"O modelo logístico de Verhulst sujeito a incertezas na condição inicial","authors":"Everson Luiz Ricordi, Fabio Dorini","doi":"10.21711/2319023x2023/pmo1103","DOIUrl":"https://doi.org/10.21711/2319023x2023/pmo1103","url":null,"abstract":"Este trabalho analisa a equacao logistica sujeita a incertezas na condicao inicial. As funcoes de densidade de probabilidade da densidade populacional e do seu ponto de inflexao sao calculadas utilizando a funcao de distribuicao da populacao inicial, considerada/modelada neste trabalho como uma variavel aleatoria. Funcoes de densidade de probabilidade, momentos estatisticos e intervalos de confianca da densidade populacional e do seu ponto de inflexao sao obtidos analiticamente para o caso em que a populacao inicial e uniformemente distribuida. Por fim, sao realizados testes computacionais para ilustrar os principais resultados.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116769027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
O conceito de integrais nos cursos de Cálculo 微积分课程中的积分概念
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2019/pmo720
J. Magossi, A. Barros
{"title":"O conceito de integrais nos cursos de Cálculo","authors":"J. Magossi, A. Barros","doi":"10.21711/2319023x2019/pmo720","DOIUrl":"https://doi.org/10.21711/2319023x2019/pmo720","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121346270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Generalização do Mapa Logístico como estratégia de ensino de Sistemas Dinâmicos 逻辑图作为动态系统教学策略的推广
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2022/pmo1021
Cássio Kiechaloski Mello, Andre Fabiano Lisboa
{"title":"Generalização do Mapa Logístico como estratégia de ensino de Sistemas Dinâmicos","authors":"Cássio Kiechaloski Mello, Andre Fabiano Lisboa","doi":"10.21711/2319023x2022/pmo1021","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo1021","url":null,"abstract":"Neste trabalho apresentamos diferentes alternativas ao Logístico para o estudo de Sistemas Dinâmicos unidimensionais. Entre as alternativas estão o Mapa Logístico Generalizado, o Mapa Trigonométrico e o Mapa Tenda. Propomos a possibilidade de explorar os mapas utilizando ferramentas computacionais acessíveis e gratuitas e mostramos que este estudo pode ser introduzido com limitações para alunos do Ensino Médio como complemento ao estudo de progressões numéricas. Os exemplos abordados permitem identificar características comuns e diferenças no comportamento dos sistemas com relação à presença de caos. Abstract In this work, we present different alternatives to the Logistic Map to study one-dimensional Dynamic Systems. The other options are the Generalized Logistic Map, the Trigonometric Map, and the Tent Map. We propose the possibility of exploring maps using accessible and free computational tools and show that this study can be introduced with limitations for high school students as a complement to the study of numerical progressions. The examples discussed allow us to identify common characteristics and differences in the behavior of systems regarding the presence of chaos.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127316019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Contando quadrados coloridos com o Lema que não e de Burnside 用不属于伯恩赛德的引理数彩色方块
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2022/pmo1012
D. Diniz, Caio Gomes
{"title":"Contando quadrados coloridos com o Lema que não e de Burnside","authors":"D. Diniz, Caio Gomes","doi":"10.21711/2319023x2022/pmo1012","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo1012","url":null,"abstract":"Neste quadrados utilizando palitos de picol´e que tenham quadrados que podemos que palitos O processo de contagem dos quadrados coloridos envolve as rota¸c˜oes e reflex˜oes que preservam o quadrado, chamadas simetrias. No primeiro caso o conjunto de simetrias que consideramos consiste apenas das rota¸c˜oes que preservam o quadrado enquanto, no segundo caso, devemos considerar reflex˜oes. Em cada caso, com a composi¸c˜ao de fun¸c˜oes, o conjunto de simetrias que consideramos constitui uma estrutura alg´ebrica denominada grupo. No decorrer do artigo, apresentaremos o conceito de a¸c˜ao de grupo e um resultado relacionado que, entre v´arias denomina¸c˜oes, conhecido como o Lema que n˜ao ´e de Burnside. Abstract In this paper we count how many colored squares may be constructed with popsicle sticks painted, each one, with one of m colors. Two situations are considered, we paint one or both sides of each stick. We will see that in order to construct a square with sticks that have both sides painted, with the same color, we use more paint, however, the number of squares that may be constructed is smaller than using sticks with only one side painted. The method used to count the coloured squares involves rotations and reflections that preserve the square, called symmetries. In the first case the symmetries that we consider are the rotations that preserve the square while, in the second, case we also need to consider reflections. In each case, with the composition of functions, the set of symmetries considered forms an algebraic structure known as group. Throughout the paper we present the notion of group actions and a related result that, among many eponymous, became known also as The Lemma that is not Burnside’s.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127547417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Decomposição de números racionais positivos em frações egípcias: Os Teoremas de Fibonacci/Sylvester e Erdös/Stein e um correspondente Applet JavaScript 正有理数分解成埃及分数:斐波那契/西尔维斯特定理和erdos /Stein定理以及相应的JavaScript小程序
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2022/pmo1036
Humberto Bortolossi, C. Pereira
{"title":"A Decomposição de números racionais positivos em frações egípcias: Os Teoremas de Fibonacci/Sylvester e Erdös/Stein e um correspondente Applet JavaScript","authors":"Humberto Bortolossi, C. Pereira","doi":"10.21711/2319023x2022/pmo1036","DOIUrl":"https://doi.org/10.21711/2319023x2022/pmo1036","url":null,"abstract":"In this work, we present the Fibonacci/Sylvester and Erd¨os/Stein Theorems, their respective proofs, and a corresponding JavaScript applet related to the decomposition of positive rational numbers as the sum of distinct unit unity fractions.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126766852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Animações para o ensino de Matemática usando o Manim–Python 使用Manim - Python进行数学教学的动画
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2023/pmo1104
Eric Kishimoto, Vitor R. Coluci
{"title":"Animações para o ensino de Matemática usando o Manim–Python","authors":"Eric Kishimoto, Vitor R. Coluci","doi":"10.21711/2319023x2023/pmo1104","DOIUrl":"https://doi.org/10.21711/2319023x2023/pmo1104","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122944945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Um modelo matemático (discreto) de propagação de uma doença no Ensino Médio 高中疾病传播的(离散)数学模型
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2020/pmo835
Carlos Alberto de Assis
{"title":"Um modelo matemático (discreto) de propagação de uma doença no Ensino Médio","authors":"Carlos Alberto de Assis","doi":"10.21711/2319023x2020/pmo835","DOIUrl":"https://doi.org/10.21711/2319023x2020/pmo835","url":null,"abstract":"Epidemiological diseases are a major concern in our society. Thus, better understanding how the spread occurs, the places with the highest incidence, the disease’s lifetime, healing processes, and other related factors, are essential to control its spread. Therefore, this article will propose a simple (discrete) mathematical model, known by epidemiologists as the SIS (Susceptible-InfectedSusceptible) model, which can easily be worked on in high school in order to stimulate students’ curiosity. Hence, using the flu virus as a common disease, this article will show how the outbreak of this disease behaves in a population of children through this model.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121902694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ensino remoto de Matemática: possibilidades com a plataforma Desmos 远程数学教学:Desmos平台的可能性
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2020/pmo837
G. Antunes, Michel Cambrainha
{"title":"Ensino remoto de Matemática: possibilidades com a plataforma Desmos","authors":"G. Antunes, Michel Cambrainha","doi":"10.21711/2319023x2020/pmo837","DOIUrl":"https://doi.org/10.21711/2319023x2020/pmo837","url":null,"abstract":"In the period of the COVID-19 pandemic, many teachers, especially those working in Basic Education, had to adapt quickly to the new teaching reality imposed by the social distance measures. Distance learning is the new normal and the effort of the entire community of teachers to continue performing their work in the best possible way is being immense. The vast majority were forced to learn new tools for non-face-to-face teaching. In this context, grew our motivation to share our experience with Desmos, a platform which offers several activities on different mathematics topics in basic education, a totally free on-line graphing calculator and tools to create on-line activities that can be used with the class. In a scenario of still many uncertainties and with the possibility of a few more months without the possibility of face-to-face classes, we see Desmos as a versatile tool, capable of involving students and developing research skills in them.","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129097191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Girando sólidos platônicos ou como visualizar grupos finitos
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2023/pmo1107
G. Cruz
{"title":"Girando sólidos platônicos ou como visualizar grupos finitos","authors":"G. Cruz","doi":"10.21711/2319023x2023/pmo1107","DOIUrl":"https://doi.org/10.21711/2319023x2023/pmo1107","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124238310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inteiros Gaussianos
Revista Professor de Matemática On line Pub Date : 1900-01-01 DOI: 10.21711/2319023x2023/pmo1123
Lídia Alves, Renan Moura, Eleonesio Strey
{"title":"Inteiros Gaussianos","authors":"Lídia Alves, Renan Moura, Eleonesio Strey","doi":"10.21711/2319023x2023/pmo1123","DOIUrl":"https://doi.org/10.21711/2319023x2023/pmo1123","url":null,"abstract":"","PeriodicalId":274953,"journal":{"name":"Revista Professor de Matemática On line","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128040385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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