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This deliverable focuses on the formation of the Eratosthenes Centre of Excellence thematic research clusters of Environment & Climate, the Resilient Society and Big Earth Data Analytics in terms of the operations, research collaborations, tools to facilitate research, agreeing internal structures and allocating staff responsibilities. This deliverable will focus on the integration of recruited research personnel, research equipment and the Strategic Partners’ expertise to meet the needs of the research groups.

This deliverable provides an extensive analysis of the dissemination activities and workshops organisation of the EXCELSIOR H2020 Teaming Project. The analysis starts with the report on our participation in conferences (11) and how the project was promoted through it. Then, we explain about the participation of our team members in talks (17), workshops (7) and seminars (12) as invited speakers. The deliverable continues with a thorough presentation of the lectures by invited speakers (8), the webinar (1) and the workshops (2) organized by our team. Additionally, we document about our participation in other events (i.e., European Researcher’s Night 2021 and SpaceUPCyprus 2021 Live). The last chapter provides the publications, journal papers, conference papers, and book sections for the reporting time period. The deliverable concludes by providing information on the outcome of the reported activities and how they have contributed to the progress of the EXCELSIOR H2020 Teaming Project. It is concluded that there is a strong need to establish links in the EMMENA region and connect with them. This has not been achieved yet, but a strategy was prepared to raise awareness about the EXCELSIOR Project in the EMMENA region and establish partnerships, starting with targeted stakeholders’ workshop in autumn 2021, where selected stakeholders from the region will be invited to be informed them about the project and provide them the space to discuss their needs and identify common scientific interests and ways of collaboration.

This document represents the ‘Workplan for transfer of knowledge and experience’ (deliverable D.6.2) for the EXCELSIOR project. It focuses on the scope and activities of WP6 ”Knowledge Transfer and Capacity Building”. The main objective of WP6 is to coordinate and manage the knowledge transfer and capacity building that will take place during the EXCELSIOR project with Strategic Partners. The document will provide a workplan of how knowledge transfer and capacity building will take place between the Strategic Partners via workshops, seminars and secondments. This plan relies heavily on the extensive work done at the preparation of the project in defining the seminars, workshops and secondments that will take place between the Strategic Partners. This deliverable focuses on the initial workplan developed for Capacity Building Scheme A, which runs from M26 to M44. The deliverable includes the capacity building and knowledge transfer activities that will be conducted by the Strategic Partners DLR, NOA and TROPOS. The course description and program for selected trainings can be found in the appendices. The present document constitutes the ‘Workplan for transfer of knowledge and experience’ for Capacity Building Scheme period ‘A’ in the framework of the EXCELSIOR project, dedicated to Task T6.1 ‘Personnel Mobility Scheme’ under work package WP6 ‘Knowledge Transfer and Capacity Building’. D6.2 focuses on the trainings that will take place during the Capacity Building Scheme A of the project. This document provides a guideline of the knowledge transfer activities, but it is not limited to the activities that will take place during Capacity Building Scheme A. The Strategic Partners suggested that a flexible workplan is needed in order to identify the gaps and needs of the researchers of the ECoE, especially during the first Capacity Building Scheme and adjust the workplan as needed in order to facilitate more effective knowledge transfer and capacity building. The secondments will be selected by the Strategic Partners as needed, during the knowledge transfer activities, parallel to the demonstration projects in WP7. Selected descriptions of knowledge transfer activities are featured in Appendix A and Appendix B.

Eratosthenes arrested Polemarchus, following the orders of the Thirty to seize the money of the metics, and then he brought him to the Council, where he was condemned to death without a proper trial. Eratosthenes could not deny that he had arrested Polemarchus but he hoped to be acquitted by distorting the recent past, which the jurors ignored in all its details. An examination of the questions and answers of Lysias and Eratosthenes, and an assessment of their arguments shows that Lysias was right to regard his opponent as guilty, but the latter still had chances to be acquitted.

This work aims to present an approach to teaching the content of similarity of triangles, based on elements of the History of Mathematics, through historical narratives. The qualitative study uses bibliographic research as a strategy for the construction of a historical narrative that aims to assist the teaching of similarity of triangles from a story focused on the calculation of the circumference of the Earth. The historical facts taken as the main elements in the process of narrative construction and chosen in a way that were related to the contents intended to be taught, were constituted from fragments of history presented in the works of the authors Lasky (2001), Vinagre e Lunazzi (2002) and Asger (1984). Through this proposal, the dynamic of teaching methodologies is emphasized, through the use of interdisciplinary elements that promote qualitative changes in the teaching and learning process, and also enable new ways of addressing content in the classroom and a more active participation of the student in the learning process. Este trabalho tem o objetivo de apresentar uma abordagem para o ensino do conteúdo de semelhança de triângulos, com base em elementos da História da Matemática, por meio de narrativas históricas. O estudo, de abordagem qualitativa, faz uso da pesquisa bibliográfica como estratégia para a construção de uma narrativa histórica que visa auxiliar o ensino de semelhança de triângulos a partir de uma história voltada ao cálculo da circunferência da Terra. Os fatos históricos tomados como principais elementos no processo de construção da narrativa e escolhidos de forma que estivessem relacionados aos conteúdos que se pretende ensinar, foram constituídos a partir de fragmentos da história apresentados nos trabalhos dos autores Lasky (2001), Vinagre e Lunazzi (2002) e Asger (1984). Acentua-se, através dessa proposta, a dinamização das metodologias de ensino, por meio do uso de elementos interdisciplinares que promovam mudanças qualitativas no processo de ensino e aprendizagem, e ainda possibilitem novas formas de abordagem do conteúdo na sala de aula e uma participação mais ativa do estudante no processo de aprendizagem.

Prime numbers are unique numbers. Prime numbers are numbers that only have a dividing factor consisting of numbers 1 and the number itself. The prime numbers from 1 to n that are relatively small can be generated manually, but a prime number generator algorithm is needed to generate prime numbers on a large scale. This study compares three prime number generator algorithms, namely: The Sieve of Eratosthenes, The Sieve of Atkins, and The Sieve of Sundaram. These three sieve algorithms have their own differences in generating prime numbers. The Sieve of Eratosthenes uses a simpler method by crossing multiples of prime numbers and marking them as non-prime numbers. The Sieve of Atkins uses several requirements for quadratic equations and modulus in determining prime numbers. The Sieve of Sundaram has an algorithm similar to The Sieve of Atkins, but there are requirements for linear equations to determine prime numbers. This study aims to see a comparison of these three algorithms in terms of accuracy and speed in generating prime numbers on a large scale. The results of this study indicate The Sieve of Eratosthenes, Atkins and Sundaram algorithms can generate large numbers of prime numbers with good accuracy, this was tested by the Fermat Primality Test Algorithm. The conclusion that can be drawn from this study, The Sieve of Eratosthenes have a faster time to generate prime numbers on a large scale than the other two algorithms.

The tenth prefatory letter of Pollux’ Onomasticon transmits two otherwise unattested pieces of information concerning the existence of an anonymous commentary on Xenophon and of a treatise by Eratosthenes of Cyrene entitled Σκευογραφικός. The corrupt state of the text in the manuscript tradition, which the standard edition by E. Bethe has not improved, has so far hindered the full understanding of this passage. This article (a) argues that two corrections should be introduced in 10.2–3 Bethe; (b) suggests that the anonymous commentary on Xenophon quoted by Pollux concerned not only the Περὶ ἱππικῆς, as traditionally assumed, but also the Ἱππαρχικός; and (c) re-examines the evidence supporting the hypothesis that Eratosthenes’ Σκευογραφικός was not part of the better-known Περὶ τῆς ἀρχαίας κωμῳδίας, but an independent work.

Autori rada analiziraju Lisijinu besedu sačuvanu u korpusu pod brojem 12. Ova beseda predstavlja živ opis društvenopolitičkih prilika odmah nakon restauracije demokratije u Atini 403. godine pre n. ere, ali i događaja koji su doveli do njenog rušenja godinu dana ranije. Beseda Protiv Eratostena je višeslojna, a dopuna je glavnim istorijskim izvorima, Ksenofontovoj Helenskoj istoriji i Aristotelovom Ustavu atinskom, predstavljajući događaje iz drugog ideološkog ugla. Against Eratosthenes is the only oration delivered personally by Lysias. It was the occasion on which he, although being an alien - metoikos istoteles, accused an Athenian citizen of murder, i.e. Eratosthenes for arresting and murdering Polemarchus, Lysias' brother. The orator took advantage of a case in the field of the general amnesty practice, which excluded only the crimes committed by the Thirty. Having this case in mind, Lysias took Eratosthenes to trial for murder. This trial was probably a private one, but since Eratosthenes was a prominent figure of the previous regime, actually one of the Thirty, drew the attention of many. By means of this oration Lysias as a foreigner, who did not have the right to actively participate in the political life of Athens, announced his political views on the past and recent events, on the nature of the regime of the Thirty, on their main leaders Critias and especially on Theramenes, to whom he put the most of the blame for the subversion of democracy. In his other speech on a Charge of Overthrowing the Democracy, which was delivered several years later, Lysias, this time in the role of the logographos, also disagreed with the common views on collective guilt, expressing his disapproval on leaving crimes unpunished and emphasized the importance of naming every perpetrator and his crime(s), not generalizing them.

In the third century B.C.E., Eratosthenes of Cyrene made a famous measurement of the circumference of the Earth. This was not the first such measurement, but it is the earliest for which significant details are preserved. Cleomedes gives a short account of Eratosthenes’ method, his numerical assumptions, and the final result of 250,000 stades. However, many ancient sources attribute to Eratosthenes a result of 252,000 stades. Historians have attempted to explain the second result by supposing that Eratosthenes later made better measurements and revised his estimate or that the original result was simply rounded to 252,000 to have a number conveniently divisible by 60 or by 360. These explanations are speculative and untestable. However, Eratosthenes’ estimates of the distances of the Sun and Moon from the Earth are preserved in the doxographical literature. This essay shows that Eratosthenes’ result of 252,000 stades for the Earth’s circumference follows from a solar distance that is attributed to him. Thus it appears that Eratosthenes computed not only a lower limit for the size of the Earth, based on the assumption that the Sun is at infinity, but also an upper limit, based on the assumption that the Sun is at a finite distance. The essay discusses the consequences for our understanding of his program. Fil: Carman, Christian Carlos. Universidad Nacional de Quilmes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Evans, James. University Of Puget Sound; Estados Unidos

This paper places the concept of ‘common sense geography’ as developed by the members of Topoi research group C-5 within the context of ancient geographical literature. For the first time, a consistent model of arranging and classifying Greek and Roman geographical texts from a historical perspective is presented.

From immemorial time, many Tyrrhenian places of ancient Sicily and Italy were identified (also by the local people) with the main stages of the return of Ulysses (Cyclopes, Aeolus, Circe, etc.). Some Hellenistic critics (for example Aristarchus and Polybius) assumed that it was from the various ancient and pre-Homeric myths that Homer drew inspiration, in the same way that he did with the myth of the Trojan War, which certainly occurred before him. Thus, the voyage of Ulysses, after his losing the course because of the storm at Cape Malea, had to be located in those sites. But how can one explain the fact that Homer places the voyage from Circe to the Hades over the Ocean? Is it only a pseudo-geographic poetic touch, aimed to magnify the exploit? Crates of Mallus did not think so: in his opinion, only some of the numerous adventures had taken place in the Tyrrhenian Sea, whereas Homer had purposefully placed some other exactly on the Atlantic Ocean, beyond the Pillars of Hercules (the ancient name given to the Straits of Gibraltar). Whichever of the two models one chooses, the route of Ulysses seems to be completely unlikely, both from the point of view of objective reality and from the point of view of poetic imagination (if one desires to retain at least some plausibility). It appears to be a senseless coming and going that takes the shape of some sort of a labyrinth. Furthermore, the navigation times suggested by the text do not accord at all (even approximately) with the distances among the real sites. For this reason, Eratosthenes held that, from Cape Malea onwards, Ulysses switched from the real world to that of fantasy, or better still to the world of some narrative fable that does not heed geography at all. The modern critics are inclined to agree with him and this thesis is nowadays the most popular one. Yet, a very serious objection can be raised here: the myth and the epos (since the most archaic era), are strictly linked to the geography and the topography as well – they are radically refractory to a narrative fable that totally contradicts the then realities of time and space. Why should Ulysses plunge from Cape Malea onwards straight into the Neverland kingdom? If we combine Odyssey’s data with those we can reconstruct for the earliest form of the Argonautic saga (taking also into account the chronology of the Greek western colonization), then we get the solution that neither the ancient nor the modern critics have guessed correctly: up to around the middle of the 8th century B.C., the Greeks thought the Ocean to flow just after the Sicily Channel, essentially coinciding with the so-called Tyrrhenian Sea, still completely unknown at that time. This new perspective can well justify the objective disorder of Ulysses’ route. Above all, it also bears a deeper poetic sense: the Hero had the chance to know and to experience not only some far and exotic countries in general terms (as it can happen to any off-course sailor), but he also met the very boundaries of the surfacing lands and the rushing waters which encircle the terrestrial disc, bordering the external cosmic abyss. Ulysses came back home alive. He was able to tell the stories about the lands where no human being could ever sail. This borderline that geographically is clearly located marks at the same time the insurmountable chasm between the physical and the meta-physical world.

Bello Peloponnesiaco confecto, Atheniensium res publica ob morum temporumque inclinationem nec felix amplius nec prospera fuit. Mulieres quoque, occasionem nactae, ut ex Aristophanis Euripidisque fabulis comperimus, maiorem sibi libertatem vindicare coeperunt. Rebus funditus mutatis, divites brevi ditiores fiunt. In quibus est Euphiletus, Atheniensis, ditissimus agrorum possessor, qui sibi amplas ac sumptuosas in urbe exstruxit aedes. Euphiletus autem, ut ex Lysiae oratione comperitur, ut terrae fructus contra fures et servos tueatur, dintius in agris moratur. Uxor contra, cui domus cura est commissa, in urbe manet sola. Sed, serva quadam conscia et ministra, cuiusdam Eratosthenis pellex fit. Quo commercio detecto, Euphiletus rivalem necat et in ius vocatur.

L’aspetto originale del lavoro è nel considerare l’Epitome come ciò che resta di un testo nato insieme alle sue illustrazioni; queste illustrazioni si sono conservate, almeno in parte, nei manoscritti latini dei traduttori di Arato. Il rapporto del testo con le sue precise illustrazioni delle costellazioni ne consente una migliore comprensione. La ricerca ha portato anche all’identificazione della mappa celeste contenuta nel manoscritto Aberystwyth, NLW 735 f. 10r 1000 ca., come la più fedele rappresentazione del cielo descritto nei Catasterismi che ci sia stata conservata nella tradizione dei manoscritti latini di Aratea.

This paper deals with the development of scientific geography during Antiquity from its mythical background before the seventh century BC to Claudius Ptolemy during the second century AD. The main focus is on questions concerning the shape of the earth, its place in the universe, size and mapping of the earth. Already before 400 BC, the idea of the earth as a globe was firmly estabished. During classical time, Aristotle used empirical and rational arguments to prove that the earth was a sphere and that it was situated motionless in the center of the universe. In the third century BC, the first reasonably correct measurements of the circumference of the earth was carried out by Eratosthenes. Later, a lower, incorrect measurement of the circumference of the earth was made by Poseidonius. His measurement was for some reason accepted by later geographers.The first map of the earth that we know of is on a clay tablet from Mesopotamia from c. 600 BC. The first useful maps were constructed during the Roman era.

I examine what do we know about Eratosthenes' mathematical Works, in particular about means., J'examine ce que l'on peut savoir au sujet des travaux mathématiques d'Ératosthène, en particulier sur les médiétés.

Can the movement be allowed in geometry, and in which sense ? The paper studies the contrasting answers of some ancient philosophers (Plato, Aristotle, Proclus) and compare them with the practise of geometers (Euclid, Archimedes, ... al-Khayyâm), Le mouvement a-t-il droit de cité en géométrie et, si oui, en quel sens ? L'article examine les réponses contrastées de quelques philosophes anciens (Platon, Aristote, Proclus) et les confrontent à la pratique des géomètres (Euclide, Archimède, ..., al-Khayyâm).

La utilización por vez primera del manuscrito Edimburgensis Adv. 18.7.15, arquetipo de toda la tradición planudeana, cuestiona las ediciones de los Catasterismos de Eratóstenes publicadas hasta el momento. Este ejemplar, autógrafo de Planudes, fue corregido por una segunda mano -muy probablemente por Demetrio Triclinio. Por otra parte, el manuscrito Parisinus Graecus 1310 contiene un breve extracto de la edición tricliniana de los Catasterismos. Collated for the first time, the manuscript Edimburgensis Adv. 18.7.15 challenges the editions of Eratosthenes' Catasterisms published so far. This codex, an autograph by Maximus Planudes, was corrected by a second hand (most probably by Demetrius Triclinius). On the other side, the manuscript Parisinus Graecus 1310 contains a brief extract from the Triclinian edition of the Catasterisms.