Superfícies mínimas e bolhas de sabão no ensino médio
This work approaches the subject minimal surfaces in a very simple way, so that the material is accessible to teachers, students or any person who has curiosity about the subject. This way, all the mathematical concepts involved are presented in a clear and objective way. The reason for this name is...
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| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2016 |
| Country: | Brasil |
| Institution: | Universidade Federal do Ceará (UFC) |
| Repository: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/22156 |
| Online Access: | http://www.repositorio.ufc.br/handle/riufc/22156 |
| Access Level: | Open access |
| Keyword: | Superfícies mínimas Otimização Geometria diferencial |
| Summary: | This work approaches the subject minimal surfaces in a very simple way, so that the material is accessible to teachers, students or any person who has curiosity about the subject. This way, all the mathematical concepts involved are presented in a clear and objective way. The reason for this name is because, once a boundary is fixed, the minimum surface will be the one that has the smallest possible area for the given boundary. We can make an analogy between the minimal surfaces and soap bubbles. Due to surface tension, soap bubbles always make the smallest possible surface area, saving potential energy. Such a fact has been used in the research and optimization of many subjects and companies, from buildings and yogurt industries to the construction of efficient rockets or shoes. Besides the huge applicability of soap films studies, the created objects are so beautiful that it is impossible not to enchant anyone who observes them. The curiosity of why this happens occurs naturally, and from there, new concepts, which may be applied from basic school (i.e. questions about proportion and percentage) until an academic level course, even covering other subjects such as chemistry, physics, biology and economy, can be approached. Key-words: Minimal surfaces. Optimization. Differential Geometry. Soap Bubbles. Plateau’s |
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