5000 Years of Geometry

Scriba, Christoph J.; Schreiber, Peter

doi:10.1007/978-3-0348-0898-9

Cited by 18 publications

(5 citation statements)

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“…There are many mathematical cuneiform tablets which deal with the problems of inclines, proportions, cones, etc. Diagonals and a small Part outside the Triangle, but connected per definition, the Arrow, were explicitly used for this [50,27,47](for instance BM 085194,Db2-146). We find this especially together and connected with a geometry within a circle.…”

Section: Discussion Of the Robson Criteriamentioning

confidence: 99%

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On the evidence of a trigonometric function value system in Babylon

KLEB¹

2021

Preprint

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Ratios and coefficients are used to simplify calculations. For geometric usage these values also called function values. Like in Egypt also in Babylon such a value system can be shown. The reconstructed calculation sequence, of the Plimpton 322 cuneiform tablet, presented and described here, shows in its completeness that, around 3800 years ago there already was a systematically applied exact measuring system, with the usage of trigonometric function values. With this approach one can plausibly explain that, as we still it practice today, a geometry of the circle has been used for this calculation. It is based on, but not only, of the usage of the regularities, which 1200 years later, were named after Pythagoras. During a second calculation step, for an intended scaled documentation, presentation or transfer to other locations, the dimensionless calculated function value, was extended, with a fractional part, or more exact spelled a common factor. This transformation creates a real measurable length from the ratios, always related to the smallest unit. The systematic usage by means of inclining triangles already in old Babylonian times, goes far beyond the previously known level of this age. The accuracy of the individual calculation is just as verifiable and on exactly the same level as the trigonometric functions used today. However, at least at this point in time, the Babylonians were content with dividing a quarter circle into at least 150 inclining triangles. This old Babylonian trigonometric function value system, together with the here described "Babylonian diagonal calculation", is thus the forerunner of the Greek chord calculation and the Indo-Arabic trigonometric functions of the early Middle Ages, which we still use today. In addition, the new approach to Plimpton 322 plausible explains why and how such values could have been used.

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Section: Discussion Of the Robson Criteriamentioning

confidence: 99%

“…In conclusion, it can be stated, that the calculation principles of Plimpton 322 which have been sought since Neugebauer and Sachs 1945 [40] and also been requested by Scriba and Schreiber [49], [50], have not yet been satisfactorily described [45, p. 4].…”

Section: Proportions and Function Values Evidence And Usagementioning

confidence: 99%

On the evidence of a trigonometric function value system in Babylon

KLEB¹

2021

Preprint

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“…Las raíces de estos procedimientos se encuentran en una larga tradición de tratados sobre los fundamentos de la geometría, producidos en la Grecia clásica (450-300 a. de C.) (RÍBNIKOV, 1987;SCRIBA;SCHREIBER, 2015). De estos tratados, los Elementos de Euclides han sido la obra más difundida e influyente entre la comunidad científica por más de veinte siglos.…”

Section: Saber Acerca De Las Contrucciones Euclidianas Con Geogebraunclassified

Construcciones euclidianas con GeoGebra y procesos de objetivación: Un estudio con futuros profesores de matemáticas

Arredondo

2021

REMATEC

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Producir construcciones geométricas con regla y compás o mediante algún software dinámico, así como justificar y explicar los procedimientos empleados con un lenguaje geométrico, son parte del saber necesario para la enseñanza de la geometría en Chile. En este artículo, analizamos el aprendizaje de este saber a partir de los procesos de objetivación ocurridos durante el trabajo conjunto de dos futuros profesores de matemáticas y el formador ante una tarea que demandaba la construcción con GeoGebra de un triángulo rectángulo con ciertas propiedades. Los resultados mostraron que las contradicciones inherentes a la respuesta de una estudiante impulsaron las acciones de los participantes hacia el logro del objetivo de la actividad. Además, el uso coordinado de palabras, gestos y notación geométrica permitieron hacer aparente las intenciones y acciones de estos sujetos durante el encuentro con el saber movilizado. Finalmente, destacamos el rol de algunos participantes en el aprendizaje evidenciado.

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“…La percepción visual es un fenómeno inherente a la experiencia cotidiana de las personas videntes. A su vez, este fenómeno se ha estudiado en distintos periodos históricos y entornos culturales (Scriba y Schreiber, 2015). En esta investigación, nos propusimos caracterizar dificultades que surgen en el proceso de resolución que realizan estudiantes de secundaria al abordar un problema del mundo real con sustento histórico-cultural en el ámbito de la percepción visual, lo que conlleva el uso del teorema del ángulo inscrito.…”

Section: Conclusionesunclassified