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1	Triângulos Heronianos Silva, Henri Flávio da January 2017 (has links) Orientador: Prof. Dr. Márcio Fabiano da Silva / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2017. / Neste trabalho,apresentamos um estudos obre os triângulos que possuem lados e área de medidas inteiras,doravante chamados de Triângulos Heronianos, muito estudados na teoria dos números a partir da fórmula de Heron,que relaciona a área de um triângulo aos seus três lados.Este tema traz o desafio de se encontrar triplas de inteiros que satisfaçam as condições da fórmula de Heron, problema este já resolvido desde o século VI pelo matemático indiano Brahmagupta por meio de parametrizações. Outro fator enriquecedor deste estudo é que esta classe de triângulos apresenta diversas propriedades que, apesar de não serem óbvias,podem ser demonstradas com conceitos de matemática básica,viabilizando o seu ensino nas aulas regulares de matemática. / In this work, we present a study on the triangles that have sides and area that are all integers, hance called Heronian Triangles, well studied in nnumber theory based on Heron¿s formula, which relates the area of a triangle to its three sides.This theme brings the challenge of finding triples of integers that satisfy the conditions of Heron¿s formula, a problem that has been solved since the sixth century by the Indian mathematician Brahmagupta by means of parametrizations. Another enriching factor of this study is that this class of triangles presents several properties that,although not obvious, can be demonstrated with concepts of basic mathematics,facilitating their teaching in regular math classes. FÓRMULA DE HERON TRIÂNGULOS HERONIANOS HERON FORMULA HERONIAN TRIANGLE
2	Trigonometry: Applications of Laws of Sines and Cosines Su, Yen-hao 02 July 2010 (has links) Chapter 1 presents the definitions and basic properties of trigonometric functions including: Sum Identities, Difference Identities, Product-Sum Identities and Sum-Product Identities. These formulas provide effective tools to solve the problems in trigonometry. Chapter 2 handles the most important two theorems in trigonometry: The laws of sines and cosines and show how they can be applied to derive many well known theorems including: Ptolemy¡¦s theorem, Euler Triangle Formula, Ceva¡¦s theorem, Menelaus¡¦s Theorem, Parallelogram Law, Stewart¡¦s theorem and Brahmagupta¡¦s Formula. Moreover, the formulas of computing a triangle area like Heron¡¦s formula and Pick¡¦s theorem are also discussed. Chapter 3 deals with the method of superposition, inverse trigonometric functions, polar forms and De Moivre¡¦s Theorem. Sum Identities Difference Identities Double-Angle Identities Product-Sum Identities Sum-Product Identities Ceva's Theorem Menelaus's Theorem Ptolemy's Theorem Law of Sines Law of Cosine Euler Triangle Formula Inverse Trigonometric Functions Euler's Formula De Moivre's Theorem Pick's Theorem Weitzenbock's Inequality Heron' Formula Polar Coordinates Angle Bisector Formula Brahmagupta's Formula Median Formula Stewart's Theorem Parallelogram Law

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Triângulos Heronianos

Trigonometry: Applications of Laws of Sines and Cosines