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Print: $8.95 Download: $2.50 For children from age 8 to 14.
“Drawings from Angola” present an introduction to an African story telling tradition. The tales are illustrated with marvelous drawings made in the sand.
The book conveys the stories of the stork and the leopard, the hunter and the dog, the rooster and the fox, and others. It explains how to execute the drawings. The reader is invited to draw tortoises, antelopes, lions, and other animals. The activities proposed throughout the book invite the reader to experiment and to explore the ‘rhythm’ and symmetry of the illustrations. Surprising results will be playfully obtained, such as in arithmetic, a way to calculate quickly the sum of a sequence of odd numbers. Children will live the beautiful mathematics of the Angolan sanddrawings.
Answers to the activities are provided.
The book can be used both in classrooms and at home. (72 pp.)
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Print: $23.08 Download: $7.00 Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike. They may be explored individually or in clubs, either during leisure time or at school.
The book presents hundreds of puzzles, which you can solve using some, or all, of the fourteen ‘biLLies’, the pieces of the game. “Warming-up exercises” pave the way for the rest of the book. In the second part of the book you are invited to build sequences of rather similar patterns. In the third part you will discover an interesting secret that will allow you to understand why some puzzles are so difficult. You will also be asked to make certain symmetrical patterns. Each chapter presents activities and puzzles, followed by one or more rounds of questions, answers and solutions. The Appendix explains how the ‘biLLies’ were conceived. (252 pp.)
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Print: $11.95 Download: $5.00 Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike, and may be explored individually or in clubs, either in leisure time, or at school.
This book "More puzzle fun with biLLies" presents one hundred puzzles, which you can solve using all fourteen 'biLLies', the pieces of the game. For instance, you can make the happy puppet on the front cover using the fourteen 'biLLies'.
You will be asked to make certain symmetrical patterns.
Have fun with the intriguing and tantalizing 'biLLies'! (76 pp.)
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Print: $11.95 Download: $5.00 Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike, and may be explored individually or in clubs, either in leisure time, or at school.
This book "More puzzle fun with biLLies" presents one hundred puzzles, which you can solve using all fourteen 'biLLies', the pieces of the game. For instance, you can make the happy puppet on the front cover using the fourteen 'biLLies'. You will be asked to make certain symmetrical patterns.
Have fun with the intriguing and tantalizing 'biLLies'! (76 pp.)
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Print: $8.88 Download: $2.94 Who does not like a pastime that can divert and educate at the same time?
More than 50 puzzles will be presented in this booklet. To solve the puzzles one needs some or all nine pieces of the game. We will call the pieces bisos.
The puzzles involve making figures that display certain properties.
For example, with the nine bisos one can form a hexagon (see the front cover).
The bisos puzzles and games could be an individual pastime, but can also be used by teachers as activities in clubs or to deepen various concepts of the school curriculum like those of polygons and symmetries.
The bisos puzzles and games are accessible to children and adults from six to one hundred years of age.
Amuse yourself! (72 pp.)
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Print: $11.96 Download: FREE "Introducing Paulus Gerdes' Ethnomathematics Books: A Collection of Prefaces, Forewords, Afterwords, and Afterthoughts" contains texts by Ubiratan D’Ambrosio, Bruno D’Amore, Maurice Bazin, Jaime Carvalho, Marcos Cherinda, Joan Conolly, Donald Crowe, Peter Damerow, Hippolyte Fofack, Mohamed Hassan, Márcio Imenes, Abdulcarimo Ismael, Mateus Katupha, Aderemi Kuku, Sarifa Magide, Dubner Medina, Alcido Nguenha, Gaston N’Guérékata, Emília Nhalivilo, Giovanni Nicosia, Jan Persens, Arthur Powell, Harald Scheid, Erhard Scholz, Gert Schubring, Greet Van Keymeulen, and the late Dirk Struik.
This black-and-white edition (134 pp.) contains only the texts. The colour edition (156 pp.)contains also a reproduction of the covers of the ethnomathematics books. Both editions are available in print and as free download.
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Print: $51.00 Download: FREE "Introducing Paulus Gerdes' Ethnomathematics Books: A Collection of Prefaces, Forewords, Afterwords, and Afterthoughts" contains texts by Ubiratan D’Ambrosio, Bruno D’Amore, Maurice Bazin, Jaime Carvalho, Marcos Cherinda, Joan Conolly, Donald Crowe, Peter Damerow, Hippolyte Fofack, Mohamed Hassan, Márcio Imenes, Abdulcarimo Ismael, Mateus Katupha, Aderemi Kuku, Sarifa Magide, Dubner Medina, Alcido Nguenha, Gaston N’Guérékata, Emília Nhalivilo, Giovanni Nicosia, Jan Persens, Arthur Powell, Harald Scheid, Erhard Scholz, Gert Schubring, Greet Van Keymeulen, and the late Dirk Struik.
The colour edition (160 pp.) contains also a reproduction of the covers of the ethnomathematics books.
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Print: $15.95 Download: $4.00 “Geometry and Basketry of the Bora in the Peruvian Amazon” presents geometric aspects of the making and decoration of baskets in the Bora culture (Colombian, Brazilian and Peruvian Amazon).
After a brief presentation of the Bora people, various aspects of the decoration of circular trays and cylindrical baskets is analysed, from their design and manufacture to the composition and colouring of finite and plane patterns. Some suggestions for the incorporation of geometrical features of Bora basketry into mathematics education are presented.
This book contributes to an appreciation of the Bora scientific and cultural experience.
Dubner Medina Tuesta, coordinator of the Bilingual Teacher Education Programme, wrote the Preface. The book has 170 pp. Also available from Lulu is a Supplement with images in colours (36 pp.)
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Print: $15.95 Download: $3.75 The supplement contains images in colour of the black-and-white photographs included in the books "Geometry and Basketry of the Bora in the Peruvian Amazon" (Lulu, 2009, 170 pp.) and "Geometria e Cestaria dos Bora na Amazonia Peruana" (Lulu, 2007, 170 pp.)
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Print: $29.96 Download: $5.95 Gitonga speaking basket weavers, mostly women, from Inhambane in the Southeast of Mozambique make colourful 'sipatsi' purses, and handbags. They are very creative in inventing new decorative designs and patterns. This book, resulting from thirty years of enquiring, collecting and observing, is unique. It presents a series of 'snapshots', which collectively constitute a short film that records an unfolding exploration of personal and collective memory, of symmetry, of combinations of colour and pattern, and of variations of order and logic to create new designs. The book includes a catalogue of over 700 different decorative patterns.
In several chapters, activities and problems for exploration in mathematics (teacher) education have been presented, underscoring the scientific and educational wealth of the 'sipatsi' as a mathematical construct. (422 pp.)
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Print: $27.95 Download: $4.95 The supplement (56 pp.) of the book "Sipatsi: Basketry and Geometry in the Tonga Culture of Inhambane (Mozambique, Africa)" (Lulu, 2009, 422 pp.) contains the original colour images of the black-and-white photographs photographs included in the aforementioned book.
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Print: $19.95 Download: $5.00 From the Preface:
“Over the years, Paulus Gerdes has established himself as the pre-eminent expert on patterns in African weaving and basketry, and the broader implications of these patterns. …
This new book is a broad gallery of plaited African designs. These range over much of the continent while concentrating on those parts of Africa that are closest to his Mozambique center, including Kongo, Mbole and Mangbetu from Congo, Cokwe and Lunda from Angola, Digo from Kenya, Soga from Uganda, Zulu from South Africa, and Makhuwa in Mozambique itself, but including such distant peoples as Bamileke in Cameroon.
In Gerdes’ gallery we are shown the love of patterns and symmetries that are the result of centuries of exultant exploration.
Enjoy!”
Donald W. Crowe
Professor of Mathematics, Emeritus
University of Wisconsin (220 pp.)
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Print: $30.50 Download: $6.00 This volume constitutes an updated version of the bibliography published in 2004 by the African Mathematical Union.
The African Studies Association attributed the original edition a ‘special mention’ in the 2006 Conover-Porter Award competition.
The book contains over 1600 bibliographic entries.
The appendices contain additional bibliographic information on (1) mathematicians of the Diaspora, (2) publications by Africans on the history of mathematics outside Africa, (3) time-reckoning and astronomy in African cultures, (4) string figures in Africa, (5) examples of books published by African mathematicians, (6) board games in Africa, (7) research inspired by geometric aspects of the ‘sona’ tradition. The book concludes with several indices (subject, country, region, author, ethnographic and linguistic, journal, mathematicians).
Professor Jan Persens of the University of the Western Cape (South Africa) and president of the African Mathematical Union (2000-2004) wrote the preface. (430 pp.)
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Print: $29.95 Download: $7.95 This volume presents a catalogue of over 2000 doctoral theses by Africans in all fields of mathematics, including applied mathematics, mathematics education and history of mathematics. The introduction contains information about distribution by country, institutions, period, and by gender, about mathematical density, and mobility of mathematicians. Several appendices are included (female doctorate holders, doctorates in mathematics education, doctorates awarded by African universities to non-Africans, doctoral theses by non-Africans about mathematics in Africa, activities of African mathematicians at the service of their communities). Paulus Gerdes compiled the information in his capacity of Chairman of the African Mathematical Union Commission for the History of Mathematics in Africa (AMUCHMA). The book contains a preface by Mohamed Hassan, President of the African Academy of Sciences (AAS) and Executive Director of the Academy of Sciences for the Developing World (TWAS). (383 pp.)
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Print: $15.96 Download: $4.00 This volume contains information about 314 doctoral theses by Mozambicans and 319 doctoral dissertations by foreigners about Mozambique. The theses are presented in chronological order. Alphabetic indices of Mozambican doctorate holders and of foreigners with doctoral theses about Mozambique are included. Thematic indices by field of research are presented. A list of Mozambican female doctorate holders is presented. Comparative tables summarize the information given in the catalogues.
This resource may help government, academia, the media, and industry locate needed talent for employment or consultation. (124 pp.)
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Print: $18.95 Download: $4.70 The book “Lunda Geometry” explains how the mathematical concepts of mirror curves and Lunda-designs were discovered in the context of the author’s research of ‘sona’, illustrations traditionally made in the sand by Cokwe storytellers from eastern Angola (a region called Lunda) and neighboring regions of Congo and Zambia. Examples of mirror curves from several cultures are presented. Lunda-designs are aesthetically attractive and display interesting symmetry properties. Examples of Lunda-patterns and Lunda-polyominoes are presented. Some generalizations of the concept of Lunda-design are discussed, like hexagonal Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs. Lunda-designs of Celtic knot designs are constructed.
Several chapters were published in journals like ‘Computers & Graphics’ (Oxford), ‘Visual Mathematics’ (Belgrade), and ‘Mathematics in School’ (UK). (198 pp.)
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Lunda ArtLunda Art (photo book)
Print: $29.90 'Lunda Art' presents original mathematical artwork by Paulus Gerdes. It is inspired by his studies of geometrical properties of 'sona' drawings made by Cokwe story tellers from the Lunda region in Northeast Angola (Africa). Part of 'Lunda Art' was included in the traveling mathematical art exhibition organized by John Sims from the Ringling School of Art and Design, Sarasota, Florida.
Paulus Gerdes, Maputo, Mozambique
Paulus.Gerdes@gmail.com
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Print: $12.97 Download: $4.00 La nouvelle édition de « L’ethnomathématique comme nouveau domaine de recherche en Afrique : Quelques réflexions et expériences du Mozambique » reproduit les cinq chapitres de l’édition originale « Recherche ethnomathématique : une réponse à l’un des plus grands défis à l’enseignement mathématique en Afrique », « Sur le concept de l’ethnomathématique », « Exemples de ‘conscientisation culturelle’ des futurs enseignants de mathématiques », « L’ethnomathématique et l’éducation des enseignants : exemples et illustrations » et « Un motif décoratif amplement diffusé et le Théorème de Pythagore », ainsi qu’inclut deux articles écrits plus tard « Pensée mathématique et exploration géométrique en Afrique et ailleurs » et « Paroles, gestes et symboles ». (148 p.)
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Print: $8.96 Download: $2.50 Aus dem Vorwort:
Leoparden streifen durch die Steppe, Jäger verfolgen Antilopen, Hühner flüchten vor dem Fuchs, Schildkröten suchen sich ihren Weg ... Das Volk der Chokwe im nordöstlichen Angola hat traditionsreiche Techniken entwickelt, um in Sandzeichnungen die typischen Strukturen dieser Pfade darzustellen ...
Paulus Gerdes ... hat in diesem Büchlein die Pfade der Chokwe-Weisen nicht nur in anregenden Zeichnungen wiedergegeben und die Geschichten dieser Pfade erzählt, sondern auch erklärt, welche überraschenden mathematischen Strukturen darin ausgedrückt werden...
Zugleich hat der Autor die anregenden Sandzeichnungen umgesetzt in Aufgaben, mit denen jugendliche Leser eigenständig die geometrischen Strukturen weiter erkunden und insbesondere Erkenntnisse über Graphen gewinnen können.
Das Werk zeichnet sich durch eine vorzügliche Anschaulichkeit aus und führt die Leser in Denk- und Vorstellungsweisen einer afrikanischen Kultur ein.
GERT SCHUBRING
(Universität Bielefeld) (72 S.)
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Print: $8.96 Download: $2.95 Dedicato ai giovani dagli 8 anni in su, 'Disegni africani dall’Angola' ci introduce ad una tradizione africana legata al racconto di favole illustrate con meravigliosi disegni a linea continua tracciati nella sabbia.
Il libro racconta le favole della cicogna ed il leopardo, del gallo ed il volpone, e molte altre tipiche della cultura Cokwe, diffusa in Angola. Spiega come fare i disegni ed invita il lettore (la lettrice) a disegnare tartarughe, antilopi, leoni ed altri animali.
Alcune attività proposte permettono di sperimentare ed esplorare il ‘ritmo’ e la simmetria delle illustrazioni. Giocando, si otterranno risultati matematici sorprendenti, come un sistema per calcolare rapidamente la somma di una sequenza di numeri dispari.
Il libro contiene le risposte alle attività ed ai problemi proposti.
Può essere usato sia in classe, sia a casa.
Presentazione: Bruno D’Amore (Università di Bologna); Traduzione e prefazione: Giovanni Giuseppe Nicosia. (72 p.)
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Print: $22.96 Download: $6.25 Reconstrução de conhecimento matemático e geométrico incorporado na tradição de desenho 'sona' dos Cokwe de Angola e zonas vizinhas do Congo e da Zâmbia. Mais de 350 ilustrações (244 p.)
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Print: $22.95 Download: $5.00 O livro debruçar-se-á sobre práticas na cultura makhuwa que evidenciam considerações geométricas, susceptíveis de uma exploração matemática e educacional.
As práticas a serem apresentadas neste livro provêm da esfera cultural de ‘otthava’ – tecer, entretecer, entrecruzar, entrançar – ou seja, da cestaria e da esteiraria. Constituem temas de análise a fabricação de funis, de chapéus, de armadilhas de pesca, de recipientes, de peneiras, de chocalhos de dança, de carteiras, de tranças decoradas, de cestos, de nós e de esteiras circulares. Em cada capítulo sugerem-se algumas possibilidades de explorar e valorizar, cientifica e didacticamente, os conhecimentos geométricos inerentes às práticas culturais consideradas. Analisam-se simetrias, polígonos e poliedros, espirais, cilindros, hélices, padrões lineares e planares. (292 p.)
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Print: $14.94 Download: FREE “A Numeração em Moçambique:
Contribuição para uma reflexão sobre cultura, língua e educação matemática”
Como se conta nas diversas línguas faladas em Moçambique? Como se desenvolveram os sistemas de numeração? Quais são os principais sistemas de numeração em África? Como fazem os falantes das diversas línguas os seus cálculos mentais? Como se pode melhorar o processo de ensino-aprendizagem da Aritmética nas escolas moçambicanas?
Estas perguntas constituem algumas das questões colocadas no livro A Numeração em Moçambique. Com este livro pretende-se contribuir para uma reflexão sobre cultura, língua e educação matemática básica. (186 p.)
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Print: $15.94 Download: $4.00 No livro apresentam-se alguns aspectos geométricos da fabricação e decoração de cestos na cultura Bora. O povo Bora vive na Amazónia colombiana e peruana.
Após uma breve apresentação do povo Bora, analisam-se vários aspectos da decoração de peneiras e travessas circulares, desde a sua fabricação à composição e colorização de padrões finitos e planares, inclusive uma reflexão sobre as simetrias envolvidas. No Capítulo 10 analisam-se aspectos geométricos da fabricação de cestos de fundo quadrado e de boca circular. No Capítulo 11 apresentam-se algumas sugestões para a incorporação de facetas geométricas da cestaria Bora na educação matemática. Nos últimos capítulos reflecte-se sobre etnomatemática e educação matemática.
O livro pretende contribuir para uma valorização da experiência científica e cultural Bora, em particular, na educação das futuras gerações. (170 p.)
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Print: $8.96 Download: $2.50 O livro “Exemplos de Aplicações da Matemática na Agricultura e na Veterinária” contem quatro capítulos:
1. Matemática aplicada à sementeira;
2. Matemática na adubação;
3. O combate à doença de ‘riquetsiose’ no gado bovino;
4. O combate à doença de ‘coccidiose’ no gado bovino.
O conteúdo do livro constitui um dos temas da disciplina “Aplicações da matemática na vida corrente das populações”, leccionado pelo autor nos primeiros cursos de formação de professores de matemática para as 5ª e 6ª classes na Universidade Eduardo Mondlane, Maputo, Moçambique (1977-1979). (67 p.)
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Print: $10.95 Download: $3.75 “Começando por apresentar alguns teoremas geométricos fascinantes que se conhecem desde a Antiguidade, Gerdes leva o leitor a embrenhar-se no mundo dos triângulos de uma maneira didáctica impressionante. No instante em que comecei a ler a obra, contava fazê-lo apenas por poucas páginas para continuar depois. Cada página que lia, levava-me a prosseguir a leitura - uma leitura emocionante, guiada pela ansiedade de saber o que iria acontecer depois de o autor colocar uma questão que envolve o leitor na procura da resposta. É este estilo que faz experimentar as afirmações apresentadas, que impulsiona reflexões e leva às conjecturas maravilhosas sobre propriedades de triângulos.”
Marcos Cherinda Ph.D.
Universidade Pedagógica, Maputo, Moçambique (114 p.)
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Print: $10.96 Download: $3.75 O livro “Os manuscritos filosófico-matemáticos de Karl Marx sobre o cálculo diferencial. Uma introdução” constitui uma reedição do livro “Karl Marx: ‘Arrancar o véu misterioso à matemática’”, publicado, em 1983, pela Universidade Eduardo Mondlane, Maputo, Moçambique.
Para além da apresentação (2008), o livro contém os seguintes capítulos:
1. Marx matemático?;
2. Porquê é que Marx se dedicou à matemática?;
3. Porquê é que os Manuscritos Matemáticos de Karl Marx ainda são pouco conhecidos pelo ‘grande público’?;
4. Conteúdo e contexto dos Manuscritos Matemáticos de Karl Marx;
5. O método dialéctico de Marx;
6. Sobre o significado dos Manuscritos Matemáticos de Karl Marx;
7. Fonte de inspiração;
8. O Sol aparece no horizonte;
Referências bibliográficas;
Bibliografia adicional (2008). (106 p.)
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Print: $8.96 Download: $2.50 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há nove bisos. Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características (vide o exemplo na capa).
O livro apresenta mais que cinquenta puzzles.
Os puzzles e jogos de bisos podem constituir um passatempo individual, mas também podem ser utilizados por professores como actividade em clubes e ‘círculos de interesse’ ou para aprofundar várias noções do currículo escolar tais como as de polígonos e simetrias.
Os jogos e puzzles de bisos são acessíveis a crianças, jovens e adultos, digamos de seis até cem anos.
Mãos à obra!
Quem não gosta de pegar num puzzle? (68 p.)
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Print: $9.96 Download: $2.50 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há doze bissemis. Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características (vide o exemplo na capa).
O livro apresenta mais que cem puzzles. Inclui uma análise dos jogos e apresenta soluções.
Os puzzles e jogos de bissemis podem constituir um passatempo individual, mas também podem ser utilizados por professores como actividade em clubes e ‘círculos de interesse’ ou para aprofundar várias noções do currículo escolar tais como as de polígonos e simetrias.
Os jogos e puzzles de bissemis são acessíveis a crianças, jovens e adultos, digamos de oito anos até cem anos.
Mãos à obra!
Quem não gosta de pegar num puzzle? (87 p.)
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Print: $9.95 Download: $2.50 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há vinte e três meioquadrados (vide a capa). Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características.
O livro apresenta mais que cem puzzles. Inclui uma análise dos jogos e apresenta soluções.
Os puzzles e jogos de meioquadrados podem constituir um passatempo individual, mas também podem ser utilizados por professores como actividade em clubes e ‘círculos de interesse’ ou para aprofundar várias noções do currículo escolar tais como as de polígonos e simetrias
Os jogos e puzzles de meioquadrados são acessíveis a crianças, jovens e adultos, digamos de dez anos até cem anos.
Mãos à obra!
Quem não gosta de pegar num puzzle? (92 p.)
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Print: $10.44 Download: $2.50 Há vinte e um bitrapézios. Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características (vide o exemplo na capa).
O livro apresenta mais que cem puzzles. Inclui uma análise dos jogos e apresenta soluções.
Os jogos e puzzles de bitrapézios são acessíveis a crianças, jovens e adultos.
CONTEÚDO: Apresentação; 1. Construção de bitrapézios; 2. Construção de sequências de figuras; 3. Construção de figuras simétricas; 4. Construção de figuras com um eixo diagonal de simetria; 5. Construção de figuras com simetria rotacional; 6. Exploração de composições equivalentes; 7. Formar figuras com todos os 21 bitrapézios; 8. O teste de tabuleiro; 9. O teste de contorno; 10. Que figuras convexas se pode formar com 21 bitrapézios?; 11. Construção de figuras convexas não-simétricas; Glossário. (99 p.)
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Print: $15.96 Download: $3.75 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há catorze tetrisos (vide a capa). Com estas catorze peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características. O livro apresenta mais que cem puzzles e soluções.
Os puzzles de tetrisos são acessíveis a pessoas de quase todas as idades.
Conteúdo: Apresentação; 1. Construir poliisos; 2. Mini-puzzles de trisos; 3. Formar figuras com tetrisos; 4. Puzzles com um conjunto de tetrisos; 5. Pesquisa de detective; 6. Puzzles com dois conjuntos de tetrisos; 7. Mosaicos de tetrisos; 8. Pentisos; Anexo: Poliominós e variantes; Epílogo; Glossário.
Mãos à obra!
Quem não gosta de pegar num puzzle? (188 p.)
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Print: $8.96 Download: $2.50 Voor kinderen vanaf 8 jaar.
“Hoe tekenen we een antilope waar een wiskundig patroon in zit? Hoe vindt de ooievaar zijn weg door het moeras en waar zit het ritme in de tekening van de leeuwin? Paulus Gerdes toont het ons. De Tsjokwe bevolking in Angola houdt ervan verhalen te vertellen en deze uit te tekenen met sporen in het zand.
In dit verrassend boekje worden kinderen en jongeren ingeleid in de rijke zandtekeningentraditie van de Tsjokwe.
Via verhalen komen zandtekeningen tot leven en worden kinderen gestimuleerd allerlei figuren te analyseren en na te tekenen waarbij ze een rijkdom aan meetkundige ervaringen opdoen. ...
Paulus Gerdes biedt deze zandtekeningen aan niet alleen als rijke schemata voor het verkennen van meetkundige inhouden maar koppelt er ook procedures aan vast voor een originele exploratie van de getallenwereld.”
Greet Van Keymeulen,
Arteveldehogeschool, Gent (72 blz.)
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Print: $12.38 Download: $5.00 Een ontspannende meetkundige activiteit uit Afrika: Het boek “Lusona: Meetkundige Ontspanning uit Afrika” presenteert problemen van het type “Vind de ontbrekende figuren”. De gegeven figuren zijn in de stijl van de zandtekeningen van de Tsjokwe uit Angola.
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Print: $9.49 Download: $2.50 Wie houdt er niet van een tijdverdrijf dat zowel ontspannend als leerzaam is? Bisospuzzels maken is zo'n activiteit.
Verscheidene puzzels worden in dit boekje voorgesteld. Om de puzzels op te lossen heb je soms enkele, soms de negen stukken van het spel nodig. De stukken heten 'bisos'.
Het puzzelen bestaat uit het maken van figuren die bepaalde eigenschappen hebben.
Deze bisospuzzels en -spelletjes kunnen thuis gebruikt worden of in clubs als leerrijk tijdverdrijf maar ook op school door onderwijzers en leraren om verschillende begrippen (parallellogram, trapezium, ruit, veelhoek, symmetrie,...) die in het leerplan zijn opgenomen, te verdiepen. Antwoorden en oplossingen zijn in het boekje opgenomen.
De bisospuzzels en -spelletjes zijn toegankelijk voor kinderen en volwassenen van zes tot honderd jaar oud.
Het woord vooraf is van de hand van Greet Van Keymeulen, Lector Wiskunde, Arteveldehogeschool, Gent. (76 p.)
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Print: $9.97 Download: $3.75 "Het bisemisspel: Meer dan honderd puzzels" (96 blz.) is een puzzelboek voor jong en oud. Het bisemisspel is een legpuzzel waarbij figuren worden nagelegd. Door aanvullen, verschuiven, draaien, spiegelen of omklappen worden steeds nieuwe en vaak complexe figuren gemaakt. Sommigen daarvan krijgen speelse namen: tent, draaitol, pop, … Woord vooraf: Greet Van Keymeulen, Arteveldehogeschool, Gent.
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Print: $9.99 Download: $2.95 Hierbij weer een boek met puzzels en spelen. Na het bisosspel (met 9 bisos) en het bisemisspel (met 12 bisemis) krijgen we nu een puzzel met maar liefst 23 puzzelstukjes. Deze puzzelstukjes noemen we semiquadrados.
In het eerste hoofdstuk wordt uitgelegd wat semiquadrados zijn. In het tweede hoofdstuk worden meer dan honderd puzzels en spelen voorgesteld. Erop volgen enkele ronden met antwoorden en nieuwe puzzels. Deze semiquadrados puzzels en -spelletjes kunnen thuis gebruikt worden of in clubs als leerrijk tijdverdrijf maar ook op school door leraren om verschillende begrippen (trapezia, veelhoeken, symmetrie, ...) die in het leerplan zijn opgenomen, te verdiepen. Op het eind van het boekje worden een aantal belangrijke begrippen omschreven.
De semiquadrados puzzels en -spelletjes zijn toegankelijk voor kinderen en volwassenen van tien tot honderd jaar oud.
Veel puzzelplezier! (94 blz.) Woord vooraf: Greet van Keymeulen, Arteveldehogeschool, Gent
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Download: $6.25 'Lunda art 14' is original artwork inspired by a geometrical study of traditional 'sona' drawings-illustrations by Cokwe storytellers-educators in the Lunda region of eastern Angola. The colors are locally and globally in balance / harmony / symmetry. Cf. the book 'Lunda Geometry' by Paulus Gerdes, also available from lulu.
Paulus Gerdes, Maputo, Mozambique
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Download: $6.25 'Lunda art 13' is original artwork inspired by a geometrical study of traditional 'sona' drawings-illustrations by Cokwe storytellers-educators in the Lunda region of eastern Angola. The three colors are locally and globally in balance / harmony / symmetry. Cf. the book 'Lunda Geometry' by Paulus Gerdes, also available from lulu.
Paulus Gerdes, Maputo, Mozambique
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Print: $11.99 Download: $6.00 De puzzels in dit boek zijn toegankelijk voor kinderen en volwassenen van tien tot honderd jaar. Ze kunnen individueel of in ‘clubs’ opgelost worden, zowel in de vrije tijd als op school.
In dit boek “Meer puzzelplezier met biLLies” worden honderd puzzels gepresenteerd. Om een puzzel op te lossen hebt je alle biLLies, de stukken van het spel, nodig. Bijvoorbeeld kun je de gelukkige pop op de omslag maken met de veertien biLLies.
De uitdaging van deze puzzels bestaat uit het maken van bepaalde symmetrische patronen. (76 pag.)
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Print: $11.99 Download: $6.00 De puzzels in dit boek zijn toegankelijk voor kinderen en volwassenen van tien tot honderd jaar. Ze kunnen individueel of in ‘clubs’ opgelost worden, zowel in de vrije tijd als op school.
In dit boek “Puzzelplezier met biLLies” worden honderd puzzels gepresenteerd. Om een puzzel op te lossen hebt je alle biLLies, de stukken van het spel, nodig. Bijvoorbeeld kun je de gelukkige pop op de omslag maken met de veertien biLLies.
De uitdaging van deze puzzels bestaat uit het maken van bepaalde symmetrische patronen. (76 pag.)
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Print: $20.08 Download: $8.00 Wie van ons houdt niet van een tijdverdrijf dat zowel ontspannend als leerzaam is? Puzzelen met biLLies is er één van!
De puzzels in dit boek zijn toegankelijk voor tieners en volwassenen van tien tot honderd jaar. Ze kunnen individueel opgelost worden of in ‘clubs’, zowel in de vrije tijd als op school.
Honderden puzzels worden in dit boek “Vermaak je met biLLies puzzels” voorgesteld. Om elk van de puzzels op te lossen heb je sommige of alle veertien ‘biLLies’, de stukken van het spel, nodig. In ieder hoofdstuk worden activiteiten en puzzels gepresenteerd, gevold door één of meer rondes van vragen, antwoorden en oplossingen. (252 pag.)
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Print: $8.95 Download: $2.50 For children from age 8 to 14.
“Drawings from Angola” present an introduction to an African story telling tradition. The tales are illustrated with marvelous drawings made in the sand.
The book conveys the stories of the stork and the leopard, the hunter and the dog, the rooster and the fox, and others. It explains how to execute the drawings. The reader is invited to draw tortoises, antelopes, lions, and other animals. The activities proposed throughout the book invite the reader to experiment and to explore the ‘rhythm’ and symmetry of the illustrations. Surprising results will be playfully obtained, such as in arithmetic, a way to calculate quickly the sum of a sequence of odd numbers. Children will live the beautiful mathematics of the Angolan sanddrawings.
Answers to the activities are provided.
The book can be used both in classrooms and at home. (72 pp.)
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Print: $23.08 Download: $7.00 Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike. They may be explored individually or in clubs, either during leisure time or at school.
The book presents hundreds of puzzles, which you can solve using some, or all, of the fourteen ‘biLLies’, the pieces of the game. “Warming-up exercises” pave the way for the rest of the book. In the second part of the book you are invited to build sequences of rather similar patterns. In the third part you will discover an interesting secret that will allow you to understand why some puzzles are so difficult. You will also be asked to make certain symmetrical patterns. Each chapter presents activities and puzzles, followed by one or more rounds of questions, answers and solutions. The Appendix explains how the ‘biLLies’ were conceived. (252 pp.)
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Print: $11.95 Download: $5.00 Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike, and may be explored individually or in clubs, either in leisure time, or at school.
This book "More puzzle fun with biLLies" presents one hundred puzzles, which you can solve using all fourteen 'biLLies', the pieces of the game. For instance, you can make the happy puppet on the front cover using the fourteen 'biLLies'.
You will be asked to make certain symmetrical patterns.
Have fun with the intriguing and tantalizing 'biLLies'! (76 pp.)
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Print: $11.95 Download: $5.00 Who of us does not like a pastime that can divert and educate at the same time? The puzzles in this book are accessible to teenagers and adults alike, and may be explored individually or in clubs, either in leisure time, or at school.
This book "More puzzle fun with biLLies" presents one hundred puzzles, which you can solve using all fourteen 'biLLies', the pieces of the game. For instance, you can make the happy puppet on the front cover using the fourteen 'biLLies'. You will be asked to make certain symmetrical patterns.
Have fun with the intriguing and tantalizing 'biLLies'! (76 pp.)
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Print: $8.88 Download: $2.94 Who does not like a pastime that can divert and educate at the same time?
More than 50 puzzles will be presented in this booklet. To solve the puzzles one needs some or all nine pieces of the game. We will call the pieces bisos.
The puzzles involve making figures that display certain properties.
For example, with the nine bisos one can form a hexagon (see the front cover).
The bisos puzzles and games could be an individual pastime, but can also be used by teachers as activities in clubs or to deepen various concepts of the school curriculum like those of polygons and symmetries.
The bisos puzzles and games are accessible to children and adults from six to one hundred years of age.
Amuse yourself! (72 pp.)
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Print: $11.96 Download: FREE "Introducing Paulus Gerdes' Ethnomathematics Books: A Collection of Prefaces, Forewords, Afterwords, and Afterthoughts" contains texts by Ubiratan D’Ambrosio, Bruno D’Amore, Maurice Bazin, Jaime Carvalho, Marcos Cherinda, Joan Conolly, Donald Crowe, Peter Damerow, Hippolyte Fofack, Mohamed Hassan, Márcio Imenes, Abdulcarimo Ismael, Mateus Katupha, Aderemi Kuku, Sarifa Magide, Dubner Medina, Alcido Nguenha, Gaston N’Guérékata, Emília Nhalivilo, Giovanni Nicosia, Jan Persens, Arthur Powell, Harald Scheid, Erhard Scholz, Gert Schubring, Greet Van Keymeulen, and the late Dirk Struik.
This black-and-white edition (134 pp.) contains only the texts. The colour edition (156 pp.)contains also a reproduction of the covers of the ethnomathematics books. Both editions are available in print and as free download.
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Print: $51.00 Download: FREE "Introducing Paulus Gerdes' Ethnomathematics Books: A Collection of Prefaces, Forewords, Afterwords, and Afterthoughts" contains texts by Ubiratan D’Ambrosio, Bruno D’Amore, Maurice Bazin, Jaime Carvalho, Marcos Cherinda, Joan Conolly, Donald Crowe, Peter Damerow, Hippolyte Fofack, Mohamed Hassan, Márcio Imenes, Abdulcarimo Ismael, Mateus Katupha, Aderemi Kuku, Sarifa Magide, Dubner Medina, Alcido Nguenha, Gaston N’Guérékata, Emília Nhalivilo, Giovanni Nicosia, Jan Persens, Arthur Powell, Harald Scheid, Erhard Scholz, Gert Schubring, Greet Van Keymeulen, and the late Dirk Struik.
The colour edition (160 pp.) contains also a reproduction of the covers of the ethnomathematics books.
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Print: $15.95 Download: $4.00 “Geometry and Basketry of the Bora in the Peruvian Amazon” presents geometric aspects of the making and decoration of baskets in the Bora culture (Colombian, Brazilian and Peruvian Amazon).
After a brief presentation of the Bora people, various aspects of the decoration of circular trays and cylindrical baskets is analysed, from their design and manufacture to the composition and colouring of finite and plane patterns. Some suggestions for the incorporation of geometrical features of Bora basketry into mathematics education are presented.
This book contributes to an appreciation of the Bora scientific and cultural experience.
Dubner Medina Tuesta, coordinator of the Bilingual Teacher Education Programme, wrote the Preface. The book has 170 pp. Also available from Lulu is a Supplement with images in colours (36 pp.)
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Print: $15.95 Download: $3.75 The supplement contains images in colour of the black-and-white photographs included in the books "Geometry and Basketry of the Bora in the Peruvian Amazon" (Lulu, 2009, 170 pp.) and "Geometria e Cestaria dos Bora na Amazonia Peruana" (Lulu, 2007, 170 pp.)
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Print: $29.96 Download: $5.95 Gitonga speaking basket weavers, mostly women, from Inhambane in the Southeast of Mozambique make colourful 'sipatsi' purses, and handbags. They are very creative in inventing new decorative designs and patterns. This book, resulting from thirty years of enquiring, collecting and observing, is unique. It presents a series of 'snapshots', which collectively constitute a short film that records an unfolding exploration of personal and collective memory, of symmetry, of combinations of colour and pattern, and of variations of order and logic to create new designs. The book includes a catalogue of over 700 different decorative patterns.
In several chapters, activities and problems for exploration in mathematics (teacher) education have been presented, underscoring the scientific and educational wealth of the 'sipatsi' as a mathematical construct. (422 pp.)
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Print: $27.95 Download: $4.95 The supplement (56 pp.) of the book "Sipatsi: Basketry and Geometry in the Tonga Culture of Inhambane (Mozambique, Africa)" (Lulu, 2009, 422 pp.) contains the original colour images of the black-and-white photographs photographs included in the aforementioned book.
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Print: $19.95 Download: $5.00 From the Preface:
“Over the years, Paulus Gerdes has established himself as the pre-eminent expert on patterns in African weaving and basketry, and the broader implications of these patterns. …
This new book is a broad gallery of plaited African designs. These range over much of the continent while concentrating on those parts of Africa that are closest to his Mozambique center, including Kongo, Mbole and Mangbetu from Congo, Cokwe and Lunda from Angola, Digo from Kenya, Soga from Uganda, Zulu from South Africa, and Makhuwa in Mozambique itself, but including such distant peoples as Bamileke in Cameroon.
In Gerdes’ gallery we are shown the love of patterns and symmetries that are the result of centuries of exultant exploration.
Enjoy!”
Donald W. Crowe
Professor of Mathematics, Emeritus
University of Wisconsin (220 pp.)
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Print: $30.50 Download: $6.00 This volume constitutes an updated version of the bibliography published in 2004 by the African Mathematical Union.
The African Studies Association attributed the original edition a ‘special mention’ in the 2006 Conover-Porter Award competition.
The book contains over 1600 bibliographic entries.
The appendices contain additional bibliographic information on (1) mathematicians of the Diaspora, (2) publications by Africans on the history of mathematics outside Africa, (3) time-reckoning and astronomy in African cultures, (4) string figures in Africa, (5) examples of books published by African mathematicians, (6) board games in Africa, (7) research inspired by geometric aspects of the ‘sona’ tradition. The book concludes with several indices (subject, country, region, author, ethnographic and linguistic, journal, mathematicians).
Professor Jan Persens of the University of the Western Cape (South Africa) and president of the African Mathematical Union (2000-2004) wrote the preface. (430 pp.)
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Print: $29.95 Download: $7.95 This volume presents a catalogue of over 2000 doctoral theses by Africans in all fields of mathematics, including applied mathematics, mathematics education and history of mathematics. The introduction contains information about distribution by country, institutions, period, and by gender, about mathematical density, and mobility of mathematicians. Several appendices are included (female doctorate holders, doctorates in mathematics education, doctorates awarded by African universities to non-Africans, doctoral theses by non-Africans about mathematics in Africa, activities of African mathematicians at the service of their communities). Paulus Gerdes compiled the information in his capacity of Chairman of the African Mathematical Union Commission for the History of Mathematics in Africa (AMUCHMA). The book contains a preface by Mohamed Hassan, President of the African Academy of Sciences (AAS) and Executive Director of the Academy of Sciences for the Developing World (TWAS). (383 pp.)
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Print: $15.96 Download: $4.00 This volume contains information about 314 doctoral theses by Mozambicans and 319 doctoral dissertations by foreigners about Mozambique. The theses are presented in chronological order. Alphabetic indices of Mozambican doctorate holders and of foreigners with doctoral theses about Mozambique are included. Thematic indices by field of research are presented. A list of Mozambican female doctorate holders is presented. Comparative tables summarize the information given in the catalogues.
This resource may help government, academia, the media, and industry locate needed talent for employment or consultation. (124 pp.)
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Print: $18.95 Download: $4.70 The book “Lunda Geometry” explains how the mathematical concepts of mirror curves and Lunda-designs were discovered in the context of the author’s research of ‘sona’, illustrations traditionally made in the sand by Cokwe storytellers from eastern Angola (a region called Lunda) and neighboring regions of Congo and Zambia. Examples of mirror curves from several cultures are presented. Lunda-designs are aesthetically attractive and display interesting symmetry properties. Examples of Lunda-patterns and Lunda-polyominoes are presented. Some generalizations of the concept of Lunda-design are discussed, like hexagonal Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs. Lunda-designs of Celtic knot designs are constructed.
Several chapters were published in journals like ‘Computers & Graphics’ (Oxford), ‘Visual Mathematics’ (Belgrade), and ‘Mathematics in School’ (UK). (198 pp.)
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Lunda ArtLunda Art (photo book)
Print: $29.90 'Lunda Art' presents original mathematical artwork by Paulus Gerdes. It is inspired by his studies of geometrical properties of 'sona' drawings made by Cokwe story tellers from the Lunda region in Northeast Angola (Africa). Part of 'Lunda Art' was included in the traveling mathematical art exhibition organized by John Sims from the Ringling School of Art and Design, Sarasota, Florida.
Paulus Gerdes, Maputo, Mozambique
Paulus.Gerdes@gmail.com
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Print: $12.97 Download: $4.00 La nouvelle édition de « L’ethnomathématique comme nouveau domaine de recherche en Afrique : Quelques réflexions et expériences du Mozambique » reproduit les cinq chapitres de l’édition originale « Recherche ethnomathématique : une réponse à l’un des plus grands défis à l’enseignement mathématique en Afrique », « Sur le concept de l’ethnomathématique », « Exemples de ‘conscientisation culturelle’ des futurs enseignants de mathématiques », « L’ethnomathématique et l’éducation des enseignants : exemples et illustrations » et « Un motif décoratif amplement diffusé et le Théorème de Pythagore », ainsi qu’inclut deux articles écrits plus tard « Pensée mathématique et exploration géométrique en Afrique et ailleurs » et « Paroles, gestes et symboles ». (148 p.)
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Print: $8.96 Download: $2.50 Aus dem Vorwort:
Leoparden streifen durch die Steppe, Jäger verfolgen Antilopen, Hühner flüchten vor dem Fuchs, Schildkröten suchen sich ihren Weg ... Das Volk der Chokwe im nordöstlichen Angola hat traditionsreiche Techniken entwickelt, um in Sandzeichnungen die typischen Strukturen dieser Pfade darzustellen ...
Paulus Gerdes ... hat in diesem Büchlein die Pfade der Chokwe-Weisen nicht nur in anregenden Zeichnungen wiedergegeben und die Geschichten dieser Pfade erzählt, sondern auch erklärt, welche überraschenden mathematischen Strukturen darin ausgedrückt werden...
Zugleich hat der Autor die anregenden Sandzeichnungen umgesetzt in Aufgaben, mit denen jugendliche Leser eigenständig die geometrischen Strukturen weiter erkunden und insbesondere Erkenntnisse über Graphen gewinnen können.
Das Werk zeichnet sich durch eine vorzügliche Anschaulichkeit aus und führt die Leser in Denk- und Vorstellungsweisen einer afrikanischen Kultur ein.
GERT SCHUBRING
(Universität Bielefeld) (72 S.)
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Print: $8.96 Download: $2.95 Dedicato ai giovani dagli 8 anni in su, 'Disegni africani dall’Angola' ci introduce ad una tradizione africana legata al racconto di favole illustrate con meravigliosi disegni a linea continua tracciati nella sabbia.
Il libro racconta le favole della cicogna ed il leopardo, del gallo ed il volpone, e molte altre tipiche della cultura Cokwe, diffusa in Angola. Spiega come fare i disegni ed invita il lettore (la lettrice) a disegnare tartarughe, antilopi, leoni ed altri animali.
Alcune attività proposte permettono di sperimentare ed esplorare il ‘ritmo’ e la simmetria delle illustrazioni. Giocando, si otterranno risultati matematici sorprendenti, come un sistema per calcolare rapidamente la somma di una sequenza di numeri dispari.
Il libro contiene le risposte alle attività ed ai problemi proposti.
Può essere usato sia in classe, sia a casa.
Presentazione: Bruno D’Amore (Università di Bologna); Traduzione e prefazione: Giovanni Giuseppe Nicosia. (72 p.)
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Print: $22.96 Download: $6.25 Reconstrução de conhecimento matemático e geométrico incorporado na tradição de desenho 'sona' dos Cokwe de Angola e zonas vizinhas do Congo e da Zâmbia. Mais de 350 ilustrações (244 p.)
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Print: $22.95 Download: $5.00 O livro debruçar-se-á sobre práticas na cultura makhuwa que evidenciam considerações geométricas, susceptíveis de uma exploração matemática e educacional.
As práticas a serem apresentadas neste livro provêm da esfera cultural de ‘otthava’ – tecer, entretecer, entrecruzar, entrançar – ou seja, da cestaria e da esteiraria. Constituem temas de análise a fabricação de funis, de chapéus, de armadilhas de pesca, de recipientes, de peneiras, de chocalhos de dança, de carteiras, de tranças decoradas, de cestos, de nós e de esteiras circulares. Em cada capítulo sugerem-se algumas possibilidades de explorar e valorizar, cientifica e didacticamente, os conhecimentos geométricos inerentes às práticas culturais consideradas. Analisam-se simetrias, polígonos e poliedros, espirais, cilindros, hélices, padrões lineares e planares. (292 p.)
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Print: $14.94 Download: FREE “A Numeração em Moçambique:
Contribuição para uma reflexão sobre cultura, língua e educação matemática”
Como se conta nas diversas línguas faladas em Moçambique? Como se desenvolveram os sistemas de numeração? Quais são os principais sistemas de numeração em África? Como fazem os falantes das diversas línguas os seus cálculos mentais? Como se pode melhorar o processo de ensino-aprendizagem da Aritmética nas escolas moçambicanas?
Estas perguntas constituem algumas das questões colocadas no livro A Numeração em Moçambique. Com este livro pretende-se contribuir para uma reflexão sobre cultura, língua e educação matemática básica. (186 p.)
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Print: $15.94 Download: $4.00 No livro apresentam-se alguns aspectos geométricos da fabricação e decoração de cestos na cultura Bora. O povo Bora vive na Amazónia colombiana e peruana.
Após uma breve apresentação do povo Bora, analisam-se vários aspectos da decoração de peneiras e travessas circulares, desde a sua fabricação à composição e colorização de padrões finitos e planares, inclusive uma reflexão sobre as simetrias envolvidas. No Capítulo 10 analisam-se aspectos geométricos da fabricação de cestos de fundo quadrado e de boca circular. No Capítulo 11 apresentam-se algumas sugestões para a incorporação de facetas geométricas da cestaria Bora na educação matemática. Nos últimos capítulos reflecte-se sobre etnomatemática e educação matemática.
O livro pretende contribuir para uma valorização da experiência científica e cultural Bora, em particular, na educação das futuras gerações. (170 p.)
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Print: $8.96 Download: $2.50 O livro “Exemplos de Aplicações da Matemática na Agricultura e na Veterinária” contem quatro capítulos:
1. Matemática aplicada à sementeira;
2. Matemática na adubação;
3. O combate à doença de ‘riquetsiose’ no gado bovino;
4. O combate à doença de ‘coccidiose’ no gado bovino.
O conteúdo do livro constitui um dos temas da disciplina “Aplicações da matemática na vida corrente das populações”, leccionado pelo autor nos primeiros cursos de formação de professores de matemática para as 5ª e 6ª classes na Universidade Eduardo Mondlane, Maputo, Moçambique (1977-1979). (67 p.)
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Print: $10.95 Download: $3.75 “Começando por apresentar alguns teoremas geométricos fascinantes que se conhecem desde a Antiguidade, Gerdes leva o leitor a embrenhar-se no mundo dos triângulos de uma maneira didáctica impressionante. No instante em que comecei a ler a obra, contava fazê-lo apenas por poucas páginas para continuar depois. Cada página que lia, levava-me a prosseguir a leitura - uma leitura emocionante, guiada pela ansiedade de saber o que iria acontecer depois de o autor colocar uma questão que envolve o leitor na procura da resposta. É este estilo que faz experimentar as afirmações apresentadas, que impulsiona reflexões e leva às conjecturas maravilhosas sobre propriedades de triângulos.”
Marcos Cherinda Ph.D.
Universidade Pedagógica, Maputo, Moçambique (114 p.)
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Print: $10.96 Download: $3.75 O livro “Os manuscritos filosófico-matemáticos de Karl Marx sobre o cálculo diferencial. Uma introdução” constitui uma reedição do livro “Karl Marx: ‘Arrancar o véu misterioso à matemática’”, publicado, em 1983, pela Universidade Eduardo Mondlane, Maputo, Moçambique.
Para além da apresentação (2008), o livro contém os seguintes capítulos:
1. Marx matemático?;
2. Porquê é que Marx se dedicou à matemática?;
3. Porquê é que os Manuscritos Matemáticos de Karl Marx ainda são pouco conhecidos pelo ‘grande público’?;
4. Conteúdo e contexto dos Manuscritos Matemáticos de Karl Marx;
5. O método dialéctico de Marx;
6. Sobre o significado dos Manuscritos Matemáticos de Karl Marx;
7. Fonte de inspiração;
8. O Sol aparece no horizonte;
Referências bibliográficas;
Bibliografia adicional (2008). (106 p.)
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Print: $8.96 Download: $2.50 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há nove bisos. Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características (vide o exemplo na capa).
O livro apresenta mais que cinquenta puzzles.
Os puzzles e jogos de bisos podem constituir um passatempo individual, mas também podem ser utilizados por professores como actividade em clubes e ‘círculos de interesse’ ou para aprofundar várias noções do currículo escolar tais como as de polígonos e simetrias.
Os jogos e puzzles de bisos são acessíveis a crianças, jovens e adultos, digamos de seis até cem anos.
Mãos à obra!
Quem não gosta de pegar num puzzle? (68 p.)
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Print: $9.96 Download: $2.50 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há doze bissemis. Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características (vide o exemplo na capa).
O livro apresenta mais que cem puzzles. Inclui uma análise dos jogos e apresenta soluções.
Os puzzles e jogos de bissemis podem constituir um passatempo individual, mas também podem ser utilizados por professores como actividade em clubes e ‘círculos de interesse’ ou para aprofundar várias noções do currículo escolar tais como as de polígonos e simetrias.
Os jogos e puzzles de bissemis são acessíveis a crianças, jovens e adultos, digamos de oito anos até cem anos.
Mãos à obra!
Quem não gosta de pegar num puzzle? (87 p.)
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Print: $9.95 Download: $2.50 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há vinte e três meioquadrados (vide a capa). Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características.
O livro apresenta mais que cem puzzles. Inclui uma análise dos jogos e apresenta soluções.
Os puzzles e jogos de meioquadrados podem constituir um passatempo individual, mas também podem ser utilizados por professores como actividade em clubes e ‘círculos de interesse’ ou para aprofundar várias noções do currículo escolar tais como as de polígonos e simetrias
Os jogos e puzzles de meioquadrados são acessíveis a crianças, jovens e adultos, digamos de dez anos até cem anos.
Mãos à obra!
Quem não gosta de pegar num puzzle? (92 p.)
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Print: $10.44 Download: $2.50 Há vinte e um bitrapézios. Com estas peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características (vide o exemplo na capa).
O livro apresenta mais que cem puzzles. Inclui uma análise dos jogos e apresenta soluções.
Os jogos e puzzles de bitrapézios são acessíveis a crianças, jovens e adultos.
CONTEÚDO: Apresentação; 1. Construção de bitrapézios; 2. Construção de sequências de figuras; 3. Construção de figuras simétricas; 4. Construção de figuras com um eixo diagonal de simetria; 5. Construção de figuras com simetria rotacional; 6. Exploração de composições equivalentes; 7. Formar figuras com todos os 21 bitrapézios; 8. O teste de tabuleiro; 9. O teste de contorno; 10. Que figuras convexas se pode formar com 21 bitrapézios?; 11. Construção de figuras convexas não-simétricas; Glossário. (99 p.)
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Print: $15.96 Download: $3.75 Para divertir-se, para enfrentar um desafio, para descansar, para concentrar-se, para confortar-se, ou simplesmente como um passatempo, um puzzle é sempre bem-vindo.
Há catorze tetrisos (vide a capa). Com estas catorze peças pode-se tentar compor diversas figuras. Cada puzzle consiste em juntar as peças de tal modo que apareça uma figura proposta ou com determinadas características. O livro apresenta mais que cem puzzles e soluções.
Os puzzles de tetrisos são acessíveis a pessoas de quase todas as idades.
Conteúdo: Apresentação; 1. Construir poliisos; 2. Mini-puzzles de trisos; 3. Formar figuras com tetrisos; 4. Puzzles com um conjunto de tetrisos; 5. Pesquisa de detective; 6. Puzzles com dois conjuntos de tetrisos; 7. Mosaicos de tetrisos; 8. Pentisos; Anexo: Poliominós e variantes; Epílogo; Glossário.
Mãos à obra!
Quem não gosta de pegar num puzzle? (188 p.)
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Print: $8.96 Download: $2.50 Voor kinderen vanaf 8 jaar.
“Hoe tekenen we een antilope waar een wiskundig patroon in zit? Hoe vindt de ooievaar zijn weg door het moeras en waar zit het ritme in de tekening van de leeuwin? Paulus Gerdes toont het ons. De Tsjokwe bevolking in Angola houdt ervan verhalen te vertellen en deze uit te tekenen met sporen in het zand.
In dit verrassend boekje worden kinderen en jongeren ingeleid in de rijke zandtekeningentraditie van de Tsjokwe.
Via verhalen komen zandtekeningen tot leven en worden kinderen gestimuleerd allerlei figuren te analyseren en na te tekenen waarbij ze een rijkdom aan meetkundige ervaringen opdoen. ...
Paulus Gerdes biedt deze zandtekeningen aan niet alleen als rijke schemata voor het verkennen van meetkundige inhouden maar koppelt er ook procedures aan vast voor een originele exploratie van de getallenwereld.”
Greet Van Keymeulen,
Arteveldehogeschool, Gent (72 blz.)
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Print: $12.38 Download: $5.00 Een ontspannende meetkundige activiteit uit Afrika: Het boek “Lusona: Meetkundige Ontspanning uit Afrika” presenteert problemen van het type “Vind de ontbrekende figuren”. De gegeven figuren zijn in de stijl van de zandtekeningen van de Tsjokwe uit Angola.
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Print: $9.49 Download: $2.50 Wie houdt er niet van een tijdverdrijf dat zowel ontspannend als leerzaam is? Bisospuzzels maken is zo'n activiteit.
Verscheidene puzzels worden in dit boekje voorgesteld. Om de puzzels op te lossen heb je soms enkele, soms de negen stukken van het spel nodig. De stukken heten 'bisos'.
Het puzzelen bestaat uit het maken van figuren die bepaalde eigenschappen hebben.
Deze bisospuzzels en -spelletjes kunnen thuis gebruikt worden of in clubs als leerrijk tijdverdrijf maar ook op school door onderwijzers en leraren om verschillende begrippen (parallellogram, trapezium, ruit, veelhoek, symmetrie,...) die in het leerplan zijn opgenomen, te verdiepen. Antwoorden en oplossingen zijn in het boekje opgenomen.
De bisospuzzels en -spelletjes zijn toegankelijk voor kinderen en volwassenen van zes tot honderd jaar oud.
Het woord vooraf is van de hand van Greet Van Keymeulen, Lector Wiskunde, Arteveldehogeschool, Gent. (76 p.)
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Print: $9.97 Download: $3.75 "Het bisemisspel: Meer dan honderd puzzels" (96 blz.) is een puzzelboek voor jong en oud. Het bisemisspel is een legpuzzel waarbij figuren worden nagelegd. Door aanvullen, verschuiven, draaien, spiegelen of omklappen worden steeds nieuwe en vaak complexe figuren gemaakt. Sommigen daarvan krijgen speelse namen: tent, draaitol, pop, … Woord vooraf: Greet Van Keymeulen, Arteveldehogeschool, Gent.
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Print: $9.99 Download: $2.95 Hierbij weer een boek met puzzels en spelen. Na het bisosspel (met 9 bisos) en het bisemisspel (met 12 bisemis) krijgen we nu een puzzel met maar liefst 23 puzzelstukjes. Deze puzzelstukjes noemen we semiquadrados.
In het eerste hoofdstuk wordt uitgelegd wat semiquadrados zijn. In het tweede hoofdstuk worden meer dan honderd puzzels en spelen voorgesteld. Erop volgen enkele ronden met antwoorden en nieuwe puzzels. Deze semiquadrados puzzels en -spelletjes kunnen thuis gebruikt worden of in clubs als leerrijk tijdverdrijf maar ook op school door leraren om verschillende begrippen (trapezia, veelhoeken, symmetrie, ...) die in het leerplan zijn opgenomen, te verdiepen. Op het eind van het boekje worden een aantal belangrijke begrippen omschreven.
De semiquadrados puzzels en -spelletjes zijn toegankelijk voor kinderen en volwassenen van tien tot honderd jaar oud.
Veel puzzelplezier! (94 blz.) Woord vooraf: Greet van Keymeulen, Arteveldehogeschool, Gent
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Download: $6.25 'Lunda art 14' is original artwork inspired by a geometrical study of traditional 'sona' drawings-illustrations by Cokwe storytellers-educators in the Lunda region of eastern Angola. The colors are locally and globally in balance / harmony / symmetry. Cf. the book 'Lunda Geometry' by Paulus Gerdes, also available from lulu.
Paulus Gerdes, Maputo, Mozambique
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Download: $6.25 'Lunda art 13' is original artwork inspired by a geometrical study of traditional 'sona' drawings-illustrations by Cokwe storytellers-educators in the Lunda region of eastern Angola. The three colors are locally and globally in balance / harmony / symmetry. Cf. the book 'Lunda Geometry' by Paulus Gerdes, also available from lulu.
Paulus Gerdes, Maputo, Mozambique
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Print: $11.99 Download: $6.00 De puzzels in dit boek zijn toegankelijk voor kinderen en volwassenen van tien tot honderd jaar. Ze kunnen individueel of in ‘clubs’ opgelost worden, zowel in de vrije tijd als op school.
In dit boek “Meer puzzelplezier met biLLies” worden honderd puzzels gepresenteerd. Om een puzzel op te lossen hebt je alle biLLies, de stukken van het spel, nodig. Bijvoorbeeld kun je de gelukkige pop op de omslag maken met de veertien biLLies.
De uitdaging van deze puzzels bestaat uit het maken van bepaalde symmetrische patronen. (76 pag.)
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Print: $11.99 Download: $6.00 De puzzels in dit boek zijn toegankelijk voor kinderen en volwassenen van tien tot honderd jaar. Ze kunnen individueel of in ‘clubs’ opgelost worden, zowel in de vrije tijd als op school.
In dit boek “Puzzelplezier met biLLies” worden honderd puzzels gepresenteerd. Om een puzzel op te lossen hebt je alle biLLies, de stukken van het spel, nodig. Bijvoorbeeld kun je de gelukkige pop op de omslag maken met de veertien biLLies.
De uitdaging van deze puzzels bestaat uit het maken van bepaalde symmetrische patronen. (76 pag.)
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Print: $20.08 Download: $8.00 Wie van ons houdt niet van een tijdverdrijf dat zowel ontspannend als leerzaam is? Puzzelen met biLLies is er één van!
De puzzels in dit boek zijn toegankelijk voor tieners en volwassenen van tien tot honderd jaar. Ze kunnen individueel opgelost worden of in ‘clubs’, zowel in de vrije tijd als op school.
Honderden puzzels worden in dit boek “Vermaak je met biLLies puzzels” voorgesteld. Om elk van de puzzels op te lossen heb je sommige of alle veertien ‘biLLies’, de stukken van het spel, nodig. In ieder hoofdstuk worden activiteiten en puzzels gepresenteerd, gevold door één of meer rondes van vragen, antwoorden en oplossingen. (252 pag.)
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