This paper presents an ultra-high definition simulator for the teaching of human anatomy in class... more This paper presents an ultra-high definition simulator for the teaching of human anatomy in class. The simulator in question consists of hardware and software specially developed for this purpose. The hardware seeks to meet the requirements of real-scale representation of models, visual acuity, color, texture, depth perception e touch-based interactivity. The software, in turn, offers a set of dissecting tools typically used in anatomical studies, in addition to allowing connectivity to educational environments and the Internet. The characteristic that stands out most in this simulator is the fact that it is not an anatomical atlas, but a dissecting table that uses models from real bodies, which differentiates it from most of the simulators and anatomical atlases developed
O escopo do presente trabalho e investigar as conexoes interdisciplinares entre a Neurociencia, a... more O escopo do presente trabalho e investigar as conexoes interdisciplinares entre a Neurociencia, a Historia da Matematica e a Musica. Serao discutidos avancos da Neurociencia, como a Lei de Weber-Fechner, sistemas de representacao de valores numericos, com enfase no (ANS-Approximate Number System) e como as fracoes seao representacoes inatas nao simbolicas de magnitudes analogicas. Com base nesses avancos, serao analisadas quais escalas musicais, cujas fracoes intercalares a Historia da Matematica registra, melhor se adequem ao sistema ANS.
ABSTRACT O presente volume estuda o nascimento da matemática, quando surgiu, quais suas primeiras... more ABSTRACT O presente volume estuda o nascimento da matemática, quando surgiu, quais suas primeiras manifestações e em que contexto se originou. Dá um tratamento inédito, multidisciplinar, sistêmico à questão. Procura respostas à Ur-questôes como: quem veio primeiro: a geometria ou os números, quando, como, porquê, onde, etc. Atenção especial é dada à Neurofisiologia da Matemática, ou seja, como o cérebro processa suas questões. Prefácio de Ubiratan D'Ambrósio.
The discovery of a fragment of ochre inscribed with a geometric pattern by Christopher Henshiwool... more The discovery of a fragment of ochre inscribed with a geometric pattern by Christopher Henshiwoold in South Africa, with a 77,000-year age, in 2,000, is, so far, the oldest testimony of geometric mathematics activity performed by man. His character shows the apprehension of elementary geometrical concepts by Homo Sapiens Sapiens, such as parallelism, distance, angle and geometric shapes (rectangles, parallelograms). The discovery of fragments of ostrich eggs 270 in the shelter of Diepkoloof, South Africa, in 2010, with an age of 66,000 years, also covered with geometric patterns, records a tradition of inscription of geometric patterns in South Africa, the oldest known. These findings belong to the techno-complexes of Still Bay and Howiesons Poort, respectively, reputed for their advances in terms of prehistoric technologies. Subsequent communications about these discoveries, where deeper studies about the same are presented, clarify how these inscriptions were held. This will allow us to rebuild, in this work, based on these studies, how these geometric patterns were outlined, as well as which elementary geometrical concepts were employed. The sequence of the inscription of the strokes shows the constructive process employed in the pattern, or, in other words, shows the way to trace his geometric design. In this way we will be able to clarify how the earliest geometric designs, such as today are named, registered to date, were stroked. Therefore, from a historical-mathematician point of view, archaeological discoveries will be employed to assist in the elucidation of the origins of concepts of a proto-geometry and the construction processes of its forms. Arguments based on informations of Ethnography allow to assume what people were responsible for these discoveries. These considerations will assist in understanding the evolution of cognitive processes employed in the study of geometry. This makes it possible to contribute to laying the foundations of the study of prehistory of the discipline today called geometric design.
Tally prehistoric sticks are artifacts that connect the object to be counted to an incision on a ... more Tally prehistoric sticks are artifacts that connect the object to be counted to an incision on a stick (bone, stone, etc.), through a matching one-to-one, and are the oldest evidence of processes for counting used by Homo Sapiens. The use of one-to-one correlation can also be done through associations with pebbles, beads, coconuts, various calculi, body parts, etc. However, with these media's materials happens that: either their set is scattered or cannot be linked with processes of countings, or cannot survive archaeologically. In prehistoric times counting processes were necessarily orals, numerals only emerged at the end of the Neolithic, with the invention of writing (c.3.400-3.000 BC), which provided tangible record of your results. Ethnography shows that the use of tally sticks as a counting process was, and still is, a widely used material resource employed by primitive people around the globe. Inscriptions in bones, ocher, stone or other material substrates can withstand the ravages of time, remaining as practically the only material evidence of primitive processes of counting capable of archaeological discoveries. The importance of the study of prehistoric tally sticks lies in the fact that they can identify the use of the most rudimentary concept of number of objects by the man, in order to distinguish between one, more than one and many, probably even before the onset of the association with names of numbers, indicating thus the oldest symbols of quantities. In this study will be presented and discussed some of the oldest known evidences of your employment.
Archaeological discoveries made in two techno-complexes in southern Africa, known as Still Bay (S... more Archaeological discoveries made in two techno-complexes in southern Africa, known as Still Bay (SB) and Howiesons Poort (HP), have recently been the subjects of intense attention from the academic world because they have characteristics that signal what is called "modern behavior" of our specie, point at the start of "modernity" and the behavior that distinguishes Homo Sapiens Sapiens from other animal species. They point to the use of culturally symbols, foreshadowing the human capacity for abstraction, intrinsic characteristic of mathematics. Some artifacts of these findings can register the earliest examples of geometric patterns and numerical records known to the present. Based on its reconstruction we can restore the mathematical knowledge known in these periods, the basic elements of a (proto) geometry and a (proto) arithmetic, foundations of a Prehistoric Mathematics. Rudiments of mathematical concepts are identified, such as symmetry, parallelism, (equi) distance, angle and also geometric shapes (rectangles, parallelograms). We can see the seizure of notions of counting’s processes, of the concept of number, because the amounts are expressed through correspondences one-to-one recorded in tally sticks. In these periods probably were made the first geometric patterns and the first mathematical artifacts in that are preserved numerical records, roots of a (proto) geometry and a (proto) arithmetic. Recent reanalysis of findings of origins organic from Border Cave, South Africa, point to a possible connection between the people of SB and HP and the San of the Kalahari Desert. The work discusses the continuity of these traditions. Keywords: Origins of Mathematics, Ethnomatematics, Still Bay, Howiesons Poort.
Aborda-se as Origens da Matemática, dando ênfase à Hipótese de Van de Waerden - Seidenberg. Igual... more Aborda-se as Origens da Matemática, dando ênfase à Hipótese de Van de Waerden - Seidenberg. Igualmente discute-se o conceito de número, a matemática megalítica, os indo-europeus, as matemáticas: babilônica, chinesa, egípcia, grega e hindu.
Notched tally sticks were first used at least forty thousand years ago. They might seem to be a p... more Notched tally sticks were first used at least forty thousand years ago. They might seem to be a primitive method of accounting, but they haved certainly proved their value as a permanent register of legal documents. The technique has remained much the same through many centuries of historical and cultural changes, right down to the present day. The biblical text Tb 5, 1-3 may record one of the oldest employment of notched tally sticks for legal purposes. God’s convenant with Abraham and its ancient ritual may also receive a new interpretation in terms of notched tally sticks functions, if we consider the parallelism amongst both symbolisms.
1 Manoel de Campos Almeida 2 RESUMO Numerais são signos capazes de representar números. Quando e ... more 1 Manoel de Campos Almeida 2 RESUMO Numerais são signos capazes de representar números. Quando e como surgiram os primeiros numerais verdadeiros interessa aos historiadores e aos matemáticos. O presente trabalho analisa e sintetiza o estágio atual do conhecimento sobre o assunto. Apresenta a evolução dos processos de contagem e do conceito de número, indicando a origem dos primeiros numerais puros. Mostra que a origem dos numerais está ligada à emergência da escrita. Analisa tanto o aparecimento da escrita nas civilizações Sumeriana, Egípcia, do vale do Indo e Vinča, como o presente debate sobre qual escrita foi a primeira. ABSTRACT The numerals are signs able to represent numbers. When and how the first true numbers came from it is what actually matter for the historians and mathematicians. The present study synthesize and analyse the current knowledge stage on this subject. It presents the number concept and counting processes pointing to the pure first numerals rising. It puts in...
O objetivo deste livro é proceder a uma reavaliação da Teoria dos Número Figurados, mostrando que... more O objetivo deste livro é proceder a uma reavaliação da Teoria dos Número Figurados, mostrando que esta teoria, conjuntamente com a concepção platônica da estrutura da matéria, pode reaparecer inopinadamente na física moderna. Aborda a Conjectura de Kepler e introduz os números poliedrais regulares, propiciando uma nova visão ao tema.
The wolf’s radius discovered by Karl Absolon in Dolní Vĕstonice may not be a conclusive proof of ... more The wolf’s radius discovered by Karl Absolon in Dolní Vĕstonice may not be a conclusive proof of the employment of the base 5 by the Palaeolithic men, because really there isn’t groups of five incisions on it. In : Anais do V Seminário Nacional de História da Matemática. SP:SBHMat-Unesp, 2003, p. 341-351.
O número da besta (666) geralmente é apresentado no textos de história da matemática como um mero... more O número da besta (666) geralmente é apresentado no textos de história da matemática como um mero exemplo de aplicação da gematria. Essa visão é apenas parcial, porque não o configura dentro do contexto em que realmente surge, ou seja, o da literatura apocalíptica, como mostraremos no presente trabalho. The beast number (666) is generally introduced in the mathematics history texts as a plain example of gematry. This is only part of the truth, because it take no notice of the context where it appears, that is, inside the apocalyptic literature, as we will show in the present work.
This paper presents an ultra-high definition simulator for the teaching of human anatomy in class... more This paper presents an ultra-high definition simulator for the teaching of human anatomy in class. The simulator in question consists of hardware and software specially developed for this purpose. The hardware seeks to meet the requirements of real-scale representation of models, visual acuity, color, texture, depth perception e touch-based interactivity. The software, in turn, offers a set of dissecting tools typically used in anatomical studies, in addition to allowing connectivity to educational environments and the Internet. The characteristic that stands out most in this simulator is the fact that it is not an anatomical atlas, but a dissecting table that uses models from real bodies, which differentiates it from most of the simulators and anatomical atlases developed
O escopo do presente trabalho e investigar as conexoes interdisciplinares entre a Neurociencia, a... more O escopo do presente trabalho e investigar as conexoes interdisciplinares entre a Neurociencia, a Historia da Matematica e a Musica. Serao discutidos avancos da Neurociencia, como a Lei de Weber-Fechner, sistemas de representacao de valores numericos, com enfase no (ANS-Approximate Number System) e como as fracoes seao representacoes inatas nao simbolicas de magnitudes analogicas. Com base nesses avancos, serao analisadas quais escalas musicais, cujas fracoes intercalares a Historia da Matematica registra, melhor se adequem ao sistema ANS.
ABSTRACT O presente volume estuda o nascimento da matemática, quando surgiu, quais suas primeiras... more ABSTRACT O presente volume estuda o nascimento da matemática, quando surgiu, quais suas primeiras manifestações e em que contexto se originou. Dá um tratamento inédito, multidisciplinar, sistêmico à questão. Procura respostas à Ur-questôes como: quem veio primeiro: a geometria ou os números, quando, como, porquê, onde, etc. Atenção especial é dada à Neurofisiologia da Matemática, ou seja, como o cérebro processa suas questões. Prefácio de Ubiratan D'Ambrósio.
The discovery of a fragment of ochre inscribed with a geometric pattern by Christopher Henshiwool... more The discovery of a fragment of ochre inscribed with a geometric pattern by Christopher Henshiwoold in South Africa, with a 77,000-year age, in 2,000, is, so far, the oldest testimony of geometric mathematics activity performed by man. His character shows the apprehension of elementary geometrical concepts by Homo Sapiens Sapiens, such as parallelism, distance, angle and geometric shapes (rectangles, parallelograms). The discovery of fragments of ostrich eggs 270 in the shelter of Diepkoloof, South Africa, in 2010, with an age of 66,000 years, also covered with geometric patterns, records a tradition of inscription of geometric patterns in South Africa, the oldest known. These findings belong to the techno-complexes of Still Bay and Howiesons Poort, respectively, reputed for their advances in terms of prehistoric technologies. Subsequent communications about these discoveries, where deeper studies about the same are presented, clarify how these inscriptions were held. This will allow us to rebuild, in this work, based on these studies, how these geometric patterns were outlined, as well as which elementary geometrical concepts were employed. The sequence of the inscription of the strokes shows the constructive process employed in the pattern, or, in other words, shows the way to trace his geometric design. In this way we will be able to clarify how the earliest geometric designs, such as today are named, registered to date, were stroked. Therefore, from a historical-mathematician point of view, archaeological discoveries will be employed to assist in the elucidation of the origins of concepts of a proto-geometry and the construction processes of its forms. Arguments based on informations of Ethnography allow to assume what people were responsible for these discoveries. These considerations will assist in understanding the evolution of cognitive processes employed in the study of geometry. This makes it possible to contribute to laying the foundations of the study of prehistory of the discipline today called geometric design.
Tally prehistoric sticks are artifacts that connect the object to be counted to an incision on a ... more Tally prehistoric sticks are artifacts that connect the object to be counted to an incision on a stick (bone, stone, etc.), through a matching one-to-one, and are the oldest evidence of processes for counting used by Homo Sapiens. The use of one-to-one correlation can also be done through associations with pebbles, beads, coconuts, various calculi, body parts, etc. However, with these media's materials happens that: either their set is scattered or cannot be linked with processes of countings, or cannot survive archaeologically. In prehistoric times counting processes were necessarily orals, numerals only emerged at the end of the Neolithic, with the invention of writing (c.3.400-3.000 BC), which provided tangible record of your results. Ethnography shows that the use of tally sticks as a counting process was, and still is, a widely used material resource employed by primitive people around the globe. Inscriptions in bones, ocher, stone or other material substrates can withstand the ravages of time, remaining as practically the only material evidence of primitive processes of counting capable of archaeological discoveries. The importance of the study of prehistoric tally sticks lies in the fact that they can identify the use of the most rudimentary concept of number of objects by the man, in order to distinguish between one, more than one and many, probably even before the onset of the association with names of numbers, indicating thus the oldest symbols of quantities. In this study will be presented and discussed some of the oldest known evidences of your employment.
Archaeological discoveries made in two techno-complexes in southern Africa, known as Still Bay (S... more Archaeological discoveries made in two techno-complexes in southern Africa, known as Still Bay (SB) and Howiesons Poort (HP), have recently been the subjects of intense attention from the academic world because they have characteristics that signal what is called "modern behavior" of our specie, point at the start of "modernity" and the behavior that distinguishes Homo Sapiens Sapiens from other animal species. They point to the use of culturally symbols, foreshadowing the human capacity for abstraction, intrinsic characteristic of mathematics. Some artifacts of these findings can register the earliest examples of geometric patterns and numerical records known to the present. Based on its reconstruction we can restore the mathematical knowledge known in these periods, the basic elements of a (proto) geometry and a (proto) arithmetic, foundations of a Prehistoric Mathematics. Rudiments of mathematical concepts are identified, such as symmetry, parallelism, (equi) distance, angle and also geometric shapes (rectangles, parallelograms). We can see the seizure of notions of counting’s processes, of the concept of number, because the amounts are expressed through correspondences one-to-one recorded in tally sticks. In these periods probably were made the first geometric patterns and the first mathematical artifacts in that are preserved numerical records, roots of a (proto) geometry and a (proto) arithmetic. Recent reanalysis of findings of origins organic from Border Cave, South Africa, point to a possible connection between the people of SB and HP and the San of the Kalahari Desert. The work discusses the continuity of these traditions. Keywords: Origins of Mathematics, Ethnomatematics, Still Bay, Howiesons Poort.
Aborda-se as Origens da Matemática, dando ênfase à Hipótese de Van de Waerden - Seidenberg. Igual... more Aborda-se as Origens da Matemática, dando ênfase à Hipótese de Van de Waerden - Seidenberg. Igualmente discute-se o conceito de número, a matemática megalítica, os indo-europeus, as matemáticas: babilônica, chinesa, egípcia, grega e hindu.
Notched tally sticks were first used at least forty thousand years ago. They might seem to be a p... more Notched tally sticks were first used at least forty thousand years ago. They might seem to be a primitive method of accounting, but they haved certainly proved their value as a permanent register of legal documents. The technique has remained much the same through many centuries of historical and cultural changes, right down to the present day. The biblical text Tb 5, 1-3 may record one of the oldest employment of notched tally sticks for legal purposes. God’s convenant with Abraham and its ancient ritual may also receive a new interpretation in terms of notched tally sticks functions, if we consider the parallelism amongst both symbolisms.
1 Manoel de Campos Almeida 2 RESUMO Numerais são signos capazes de representar números. Quando e ... more 1 Manoel de Campos Almeida 2 RESUMO Numerais são signos capazes de representar números. Quando e como surgiram os primeiros numerais verdadeiros interessa aos historiadores e aos matemáticos. O presente trabalho analisa e sintetiza o estágio atual do conhecimento sobre o assunto. Apresenta a evolução dos processos de contagem e do conceito de número, indicando a origem dos primeiros numerais puros. Mostra que a origem dos numerais está ligada à emergência da escrita. Analisa tanto o aparecimento da escrita nas civilizações Sumeriana, Egípcia, do vale do Indo e Vinča, como o presente debate sobre qual escrita foi a primeira. ABSTRACT The numerals are signs able to represent numbers. When and how the first true numbers came from it is what actually matter for the historians and mathematicians. The present study synthesize and analyse the current knowledge stage on this subject. It presents the number concept and counting processes pointing to the pure first numerals rising. It puts in...
O objetivo deste livro é proceder a uma reavaliação da Teoria dos Número Figurados, mostrando que... more O objetivo deste livro é proceder a uma reavaliação da Teoria dos Número Figurados, mostrando que esta teoria, conjuntamente com a concepção platônica da estrutura da matéria, pode reaparecer inopinadamente na física moderna. Aborda a Conjectura de Kepler e introduz os números poliedrais regulares, propiciando uma nova visão ao tema.
The wolf’s radius discovered by Karl Absolon in Dolní Vĕstonice may not be a conclusive proof of ... more The wolf’s radius discovered by Karl Absolon in Dolní Vĕstonice may not be a conclusive proof of the employment of the base 5 by the Palaeolithic men, because really there isn’t groups of five incisions on it. In : Anais do V Seminário Nacional de História da Matemática. SP:SBHMat-Unesp, 2003, p. 341-351.
O número da besta (666) geralmente é apresentado no textos de história da matemática como um mero... more O número da besta (666) geralmente é apresentado no textos de história da matemática como um mero exemplo de aplicação da gematria. Essa visão é apenas parcial, porque não o configura dentro do contexto em que realmente surge, ou seja, o da literatura apocalíptica, como mostraremos no presente trabalho. The beast number (666) is generally introduced in the mathematics history texts as a plain example of gematry. This is only part of the truth, because it take no notice of the context where it appears, that is, inside the apocalyptic literature, as we will show in the present work.
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Papers by Manoel Almeida
Keywords: Origins of Mathematics, Ethnomatematics, Still Bay, Howiesons Poort.
Keywords: Origins of Mathematics, Ethnomatematics, Still Bay, Howiesons Poort.