A Casinha da Matemática

A Álgebra é generosa; ela frequentemente dá mais do que aquilo que lhe é pedido. (D'Alembert)

Project MATHEMATICS!

Criado e dirigido por Tom M. Apostol e James F. Blinn, ambos do do Instituto de Tecnologia da Califórnia

by · Published · Updated

Project MATHEMATICS! consiste num conjunto de vídeos educativos e livros de acompanhamento para professores que exploram tópicos básicos da matemática do ensino secundário de maneiras que não podem ser feitas no quadro-negro ou num livro-texto. Os vídeos usam ação ao vivo, música, efeitos especiais e animações imaginativas. Estes vídeos foram distribuídos sem fins lucrativos.

Foi objetivo do projeto atrair jovens para a matemática através de módulos educativos de alta qualidade que mostram que a matemática é compreensível, excitante e eminentemente valiosa. Cada módulo consiste num vídeo, juntamente com um caderno de acompanhamento, e explora um tópico básico em matemática que pode ser facilmente integrado em qualquer currículo do ensino secundário. Os módulos estão criados no sentido de incentivar a interação entre alunos e professores.

A série foi desenvolvida por Tom M. Apostol e James F. Blinn, ambos do Instituto de Tecnologia da Califórnia, em Pasadena, CA. Apostol liderou a produção da série, enquanto Blinn forneceu a animação por computador usada para descrever as ideias discutidas. Blinn mencionou que parte de sua inspiração foi a série de filmes científicos da Bell dos anos 50.

Vencedores de vários prémios internacionais, The Theorem of Pythagoras, The Story of Pi, Similarity, Polynomials, The Tunnel of Samos, Sines and Cosines (Part I, II and III) e Early History of Mathematics estão também disponíveis em português numa versão da responsabilidade científica do Centro de Matemática e Aplicações Fundamentais da Universidade de Lisboa. Estas versões portuguesas, O Teorema de Pitágoras, A História do Pi, Semelhanças e Polinómios, O Túnel de Samos, Senos e Cosenos (Partes I, II e III) e Os Primórdios da História da Matemática são uma excelente ajuda audiovisual que complementada com os cadernos de trabalho representa um instrumento utilíssimo para a didática da matemática.

Em 2017, toda a série de vídeos foi disponibilizada no YouTube.

 

 

Project MATHEMATICS!

Episode 1: Similarity - Project MATHEMATICS!
Episode 1. Similarity: Scaling multiplies lengths by the same factor and produces a similar figure. It preserves angles and ratios of lengths of corresponding line segments. Animation shows what happens to perimeters, areas, and volumes under scaling, with various applications from real life. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1990 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 2: The Story Of Pi - Project MATHEMATICS!
Episode 2. The Story of Pi: Although pi is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles. Animated sequences dissect a circular disk and transform it to a rectangle with the same area as the disk. Animation shows how Archimedes estimated pi using perimeters of approximating polygons. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1989 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 3: The Theorem Of Pythagoras - Project MATHEMATICS!
Episode 3. The Theorem of Pythagoras: Several engaging animated proofs of the Pythagorean theorem are presented, with applications to real-life problems and to Pythagorean triples. The theorem is extended to 3-space, but does not hold for spherical triangles. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1988 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 4: Sines And Cosines Part I - Project MATHEMATICS!
Episode 4. Sines and Cosines, Part I: (Waves) Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related to vibrating motion, and as ratios of sides of right triangles. They are related by reflection or translation of their graphs. Animation demonstrates the Gibbs phenomenon of Fourier series. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1992 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 5: Sines And Cosines Part II - Project MATHEMATICS!
Episode 5. Sines and Cosines, Part II: (Trigonometry) This video focuses on trigonometry, with special emphasis on the law of conies and the law of sines, together with applications to The Great Survey of India. The history of surveying instruments is outlined, from Hero’s dioptra to modern orbiting satellites. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1993 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 6: Sines And Cosines Part III - Project MATHEMATICS!
Episode 6. Sines and Cosines, Part III: (Addition formulas) Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy’s Almagest. This leads to elegant derivations of addition formulas, with applications to simple harmonic motion. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1994 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 7: Polynomials - Project MATHEMATICS!
Episode 7. Polynomials: Animation shows how the Cartesian equation changes if the graph of a polynomial is translated or subjected to a vertical change of scale. Zeros, local extrema, and points of inflection are discussed. Real-life examples include parabolic trajectories and the use of cubic splines in designing sailboats and computer-generated teapots. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1991 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 8: The Tunnel of Samos - Project MATHEMATICS!
Episode 8. The Tunnel of Samos: This video describes a remarkable engineering work of ancient times: excavating a one-kilometer tunnel straight through the heart of a mountain, using separate crews that dug from the two ends and met in the middle. How did they determine the direction for excavation? The program gives Hero's explanation (ca. 60 A.D.), using similar triangles, as well as alternative methods proposed in modern times. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©1995 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Episode 9: Early History - Project MATHEMATICS!
Episode 9. Early History of Mathematics: This video traces some of the landmark developments in the early history of mathematics, from Babylonian calendars on clay tablets produced 5000 years ago, to the introduction of calculus in the seventeenth century. A Program Guide and Workbook is available for each episode, except episodes 6 and 9, and is available in PDF and TIFF formats for download: https://caltech.box.com/s/magxt15ygyrz40u32dse5sqry011gpt5 ©2000 California Institute of Technology
Autor: caltech
Publicado: 03-03-2017
Trailer 1: Siggraph 1988 - Project MATHEMATICS!
A short demonstration video of the computer animations for "Project MATHEMATICS!" produced by Jim Blinn for the 1988 Special Interest Group on Graphics (Siggraph) of the Association for Computing Machinery conference. Visit http://JimBlinn.com for more details.
Autor: caltech
Publicado: 03-03-2017
Trailer 2: Siggraph 1990 - Project MATHEMATICS!
A short demonstration video of the computer animations for "Project MATHEMATICS!" produced by Jim Blinn for the 1990 Special Interest Group on Graphics (Siggraph) of the Association for Computing Machinery conference. Visit http://JimBlinn.com for more details.
Autor: caltech
Publicado: 03-03-2017
Trailer 3: Siggraph 1993 - Project MATHEMATICS!
A short demonstration video of the computer animations for "Project MATHEMATICS!" produced by Jim Blinn for the 1993 Special Interest Group on Graphics (Siggraph) of the Association for Computing Machinery conference. Visit http://JimBlinn.com for more details.
Autor: caltech
Publicado: 03-03-2017
Teachers Workshop - Project MATHEMATICS!
©1991 California Institute of Technology
Autor: caltech
Publicado: 08-03-2019
Contest - Project MATHEMATICS!
©1995 California Institute of Technology
Autor: caltech
Publicado: 08-03-2019

 

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