Anaxagoras and the Size of the Sun

Plutarch and others report that Anaxagoras compared the size of the sun with the Peloponnesus. It is the aim of this paper to show that this was a fair estimate, from his point of view, which is that of a flat earth. More precisely, I will show that, with the instruments and the geometrical knowledge available, Anaxagoras must have been able to use the procedures and perform the calculations needed to reach approximately his result

Dioptra

O uso de Geometria elementar foi essencial num número variado de aplicações, sobretudo na área da topografia, arquitetura e engenharia, tendo sido o seu uso de extrema importância para medir fisicamente distâncias e alturas com instrumentos de medição simples. A dioptra é um bom exemplo de um instrumento que permitiu o cálculo de distâncias inacessíveis recorrendo ao uso de Geometria elementar.info:eu-repo/semantics/publishedVersio

Hispania: huellas de la conquista romana. Aproximación al estudio de los fosos de los asentamientos militares peninsulares

Los asentamientos militares jugaron un papel destacado en la conquista de la Peninsula Ibérica por las armas romanas tanto a nivel de pernocta y refugio de legiones como de elementos de asedio y cerco de nucleos indígenas. Hispania es un terreno privilegiado y casi único en cuanto a la riqueza de vestigios de este tipo documentados en nuestro suel

The Roman centuriated landscape: conception, genesis and development as inferred from the Ager Tarraconensis case

Although centuriation was only one system of Roman land division, its impact on the landscape and its visibility in modern field arrangements make it the most commonly recognized expression of Roman landscapes. Centuriated grid systems are usually analyzed from a materialistic point of view and consequently regarded as an assertion of Roman dominance over conquered territories. In this sense, their productive function is clear. The hinterland of Tarraco (the ancient capital of the Roman province of Tarraconensis) offers one of the most clearly documented examples of multiple-grid centuriated systems. From 2006 to 2010, the Landscape Archaeology Research Group (GIAP) of the Catalan Institute of Classical Archaeology employed a wide array of digital and field methodologies at Tarraco to record the traces of centuriated land divisions and their Roman origin. Most importantly, these methods have allowed research to move beyond pure description of the traces to explore the concepts and ideas behind the making of a centuriated landscape. By using Tarraco as a case study, this article shows how centuriation was not only a system for dividing the land but also a conceptual appropriation of the landscape based on a strong mythical and religious backgroun

An early abridgement of Fibonacci’s De practica geometrie

AbstractIn this article I will show that sometime before the end of the 14th century a now lost abridgement of Fibonacci’s De practica geometrie (1220) was made, and that three closely related Italian treatises on geometry from the 14th and 15th centuries were copied from this abridgement. The contents of the three manuscripts are compared closely with those of De pratica geometrie. Rather than being a chapter-by-chapter description of the treatises, my comparison is organized under the headings Basic Definitions, Pisan Measurements, Figures to be Measured, Tools for Measuring, and Examples of Measurements

Close Mapping of St. Olav’s Pilgrimage Path Through Gudbrandsdal Norway: Probabilities of a Designed, Land Surveyed Concept of a Large-Scale Christianised Landscape

This exercise in Norway ‘close-maps’ accurate, existing geometries between thirty-two latitude / longitude points of mostly medieval churches and other sites on the major pilgrimage path through Gudbrandsdal to Trondheimsfjord where the martyr St.Olav was venerated. Site data and basic path routes are taken from the Pilegrimsleden website, popular today with religious or recreational tourists. The inclusion of the largest prehistoric monumental mound in Scandinavia as an important early stop on the pilgrimage provides the first clue to the eventual mapping of a large-scale ‘system’ of land surveyed patterns. This symbolic anchor in the south, is connected to likely ancient religious sites to the north in Trondheimsfjord where St. Olav was killed in battle. Discovered are several early church sites key to site integration but not included as part of today’s pilgrim path. The Gudbrandsdal route appears to have been laid out earlier than the smaller volume, overlapping, Østerdal path immediately to the east. To distinguish formally designed geometric large-scale patterns from random phenomena, test areas are created where equal numbers of random points replace the existing. Combinations of three-point alignments, cardinal (N-S. E-W) alignments between two points, and right-angle relationships between three points are tested at increasing complexities of combination at accuracies of 0.06° angular deviation or less, mostly around 0.04°. The ‘systemic’ map pattern that tests show to be highly probable as designed and land surveyed - occurring about 1 in 100,000 random sets - shows considerable overlap with the Gudbrandalsleden map created by the Norwegian website, but variation and omission of important sites occur. The conclusion raises final questions about the value of this real, close-map information to the modern ‘pilgrim’, and to more academic historians and archaeologists. Can today’s path experience be heightened by the creation of a more holistic and symbolic concept of modern Norwegian landscape, this is considered together with insights into how historically such a concept may have moderated civil conflict and integrated an imported book-based religion with ancient Norse ritual practice

Urbanise in roman times: rituality and practicality. Proposal for an approved execution procedure

En época romana la orientación conferida a las construcciones solía tener significados simbólicos, reflejos de una ritualidad, especialmente en el caso de ciudades o santua - rios. Aunque también podía responder simplemente a cuestio - nes de tipo práctico. En cualquier caso, el beneplácito de los dioses era condición sine qua non para iniciar la obra y dibu - jar sobre el terreno el diseño de la misma. Frente a la cuestión de su significado, se plantea una pregunta: ¿cuál fue el proce - dimiento de ejecución? En publicaciones precedentes, nues - tra propuesta iba encaminada a identificar sistemas utiliza - dos para conferir a las obras una orientación determinada. En este artículo planteamos un modelo de operar que va en para - lelo con las interpretaciones dadas a las orientaciones, ya sean simbólicas o prácticas, proponiendo como modo de ejecución el explicado por Nypsius en el siglo I d.C. al describir la téc - nica de la varatio.In Roman times, the orientation given to the build - ings usually had symbolic meanings, reflection of a ritual, es - pecially in the case of cities or sanctuaries, although the ori - entation could also simply respond to practical issues. In any case, the gods’ support was essential for the beginning of the works, and the drawing of the design on the ground. Besides the topic of the meaning of the orientations, another question arises: what was the procedure? In previous publications, our proposal was intended to identify the systems used to give the works a certain orientation. In this paper we propose im - plementation rules which run parallel with the symbolic or pragmatic interpretations of orientations, proposing as the ex - ecution procedure the one explained by Nypsius in the first century AD when he describes the technique of varatio

Pure geometry and geometric cognition

The cognitive basis of pure geometry is basically unknown. Even the ‘simpler’ issue of what kind of representation of geometric object we have. In this work, we set forward a model of the representation of geometric objects at a neurological level for the case of the pure geometry of Euclid. To arrive at the model, we take into account historical aspects of practical and pure geometry together. This enables us to arrive at a coherent model of geometric objects consistent with the historical record