Mathematics in Ancient Egypt

2016 ◽  
Author(s):  
Annette Imhausen
Keyword(s):  
Mathematical Knowledge ◽  
Ancient Egypt ◽  
Middle Kingdom ◽  
Old Kingdom ◽  
Material Resources ◽  
Greco Roman ◽  
Unit Fractions ◽  
Egyptian Culture ◽  
Mathematical Techniques ◽  
Egyptian History

This book traces the development of Egyptian mathematics, from the end of the fourth millennium BC—and the earliest hints of writing and number notation—to the end of the pharaonic period in Greco-Roman times. The book surveys three thousand years of Egyptian history to present an integrated picture of theoretical mathematics in relation to the daily practices of Egyptian life and social structures. It shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. The book looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. It draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why. Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, the book sheds new light on a civilization's unique mathematical evolution.

A World Upturned

2009 ◽  
Author(s):  
Roland Enmarch
Keyword(s):  
Reception History ◽  
Ancient Egypt ◽  
Literary Analysis ◽  
Middle Kingdom ◽  
Human Motivation ◽  
The Core ◽  
Divine Justice ◽  
Egyptian Culture ◽  
Egyptian Literature ◽  
Literary Composition

The Dialogue of Ipuwer and the Lord of All is one of the major works from the golden age of Egyptian literature, the Middle Kingdom (c. 1980–1630 bc). The poem provides one of the most searching explorations of human motivation and divine justice to survive from ancient Egypt, and its stark pessimism questions many of the core ideologies that underpinned the Egyptian state and monarchy. It begins with a series of laments portraying an Egypt overwhelmed by chaos and destruction, and develops into an examination of why these disasters should happen, and who bears responsibility for them: the gods, the king, or humanity. This volume provides the first full literary analysis of this poem for a century. It provides a detailed study of questions such as: its date of composition; its historicity; the identity of its protagonists and setting; its reception history within Egyptian culture; and whether it really is a unified literary composition, or a redacted collection of texts of heterogenous origin.

Mathematical texts

2020 ◽  
pp. 1032-1040
Author(s):  
Annette Imhausen
Keyword(s):  
Mathematical Knowledge ◽  
Primary Source ◽  
Ancient Egypt ◽  
Source Material ◽  
Ancient Egyptian ◽  
Modern Analysis ◽  
Mathematical Techniques ◽  
Mathematical Texts ◽  
The Way

Approximately a dozen mathematical papyri have survived from ancient Egypt. Based on their script (but also their stage of the Egyptian language) they fall into two groups—hieratic and demotic texts. These papyri constitute our primary source material to learn about ancient Egyptian mathematics. Because of the procedural style that they were written in, it is assumed that they were used in teaching junior scribes the mathematical techniques they would need for their job; however, the procedural format may also have constituted the way of collecting mathematical knowledge at the time. It is only if this format is taken into account in the (modern) analysis of Egyptian mathematical texts that their sophistication becomes visible, and a deeper understanding of Egyptian mathematics beyond rudimentary similarities to modern equivalents can therefore be achieved.

The Old Kingdom and First Intermediate Period

2020 ◽  
pp. 618-637
Author(s):  
Nigel Strudwick
Keyword(s):  
Ancient Egypt ◽  
Old Kingdom ◽  
Modern Culture ◽  
Intermediate Period ◽  
Time Period ◽  
Early Dynastic ◽  
History Of ◽  
First Intermediate Period ◽  
First Time ◽  
Egyptian History

The Old Kingdom is usually characterized as the first great epoch of Egyptian history, when the phenomenal cultural, iconographical and political developments of the late Predynastic Period and the Early Dynastic Period coalesced to give an eminently visible culture that says ‘ancient Egypt’ to the modern audience. This development may best be symbolized by the pyramid, the most persistent image of the era. For its part, the First Intermediate Period is the first clear manifestation in Egyptian history of the periods of disunity and systemic weakness that have affected every long-lasting ancient and modern culture in one form or the other. The time-period covered in this section illustrates for the first time both the highs and lows of ancient Egypt. The Old Kingdom is usually defined as consisting of the Third to Eighth Dynasties of Manetho (c.2686–2125 bc), and the First Intermediate Period of the Ninth and Tenth and roughly two-thirds of the Eleventh Dynasty (c.2160–2016 bc).

The Oxford Handbook of Egyptology

2015 ◽  
Keyword(s):  
Ancient Egypt ◽  
Environmental Aspects ◽  
Ancient Egyptian ◽  
Current State ◽  
Egyptian Culture ◽  
The Subject ◽  
Current Characteristics ◽  
The Many ◽  
Key Aspects ◽  
Egyptian History

The Oxford Handbook of Egyptology presents a series of articles by colleagues working across the many archaeological, philological and cultural subdisciplines within the study of ancient Egypt from prehistory through to the end of the Roman Period. The volume seeks to place Egyptology within its theoretical, methodological, and historical contexts, both indicating how the subject has evolved and discussing its distinctive contemporary problems, issues and potential. Transcending conventional boundaries between archaeological and ancient textual analysis, it stresses the need for Egyptology to seek multidisciplinary methods and broader collaborations if it is to remain contemporary and relevant. It therefore serves as a reference work not only for those working within the discipline, but also as a gateway into Egyptology for archaeologists, anthropologists, sociologists and linguists. The book is organized into ten parts, the first of which examines the many different historical and geographical perspectives that have influenced the development and current characteristics of the discipline. Part II addresses the various environmental aspects of the subject: landscapes, climate, flora, fauna and the mineral world. Part III considers a variety of practical aspects of the ways in which Egyptologists survey, characterize and manage landscapes. Part IV discusses materials and technology, from domestic architecture and artefacts through to religious and funerary items. Part V deals with Egypt’s relations with neighbouring regions and peoples, while Part VI explores the sources and interpretive frameworks that characterize different phases of ancient Egyptian history. Part VII is concerned with textual and iconographic approaches to Egyptian culture, and Part VIII comprises discussions of the key aspects of ancient Egyptian scripts and philology. Part IX presents summaries of the current state of the subject in relation to a variety of textual genres, from letters and autobiographies to socio-economic, magical and mathematical texts. The final section covers different aspects of museology and conservation.

Transnasal excerebration surgery in ancient Egypt

2012 ◽  
Vol 116 (4) ◽  
pp. 743-748 ◽  
Author(s):  
Andrew A. Fanous ◽  
William T. Couldwell
Keyword(s):  
Skull Base ◽  
Surgical Techniques ◽  
Ancient Egypt ◽  
Transnasal Approach ◽  
Old Kingdom ◽  
Greco Roman ◽  
Ancient Egyptian ◽  
Transnasal Surgery ◽  
The One

Ancient Egyptians were pioneers in many fields, including medicine and surgery. Our modern knowledge of anatomy, pathology, and surgical techniques stems from discoveries and observations made by Egyptian physicians and embalmers. In the realm of neurosurgery, ancient Egyptians were the first to elucidate cerebral and cranial anatomy, the first to describe evidence for the role of the spinal cord in the transmission of information from the brain to the extremities, and the first to invent surgical techniques such as trepanning and stitching. In addition, the transnasal approach to skull base and intracranial structures was first devised by Egyptian embalmers to excerebrate the cranial vault during mummification. In this historical vignette, the authors examine paleoradiological and other evidence from ancient Egyptian skulls and mummies of all periods, from the Old Kingdom to Greco-Roman Egypt, to shed light on the development of transnasal surgery in this ancient civilization. The authors confirm earlier observations concerning the laterality of this technique, suggesting that ancient Egyptian excerebration techniques penetrated the skull base mostly on the left side. They also suggest that the original technique used to access the skull base in ancient Egypt was a transethmoidal one, which later evolved to follow a transsphenoidal route similar to the one used today to gain access to pituitary lesions.

Metrological Systems

2016 ◽  
Author(s):  
Annette Imhausen
Keyword(s):  
Building Materials ◽  
Ancient Egypt ◽  
Specific Kind ◽  
Old Kingdom ◽  
Agricultural Resources ◽  
Egyptian History

The development of metrology constituted the foundation of the quantitative control of agricultural resources, which then enabled the cultural achievements of ancient Egypt. Note that while some units remained the same and were used throughout Egyptian history, others became obsolete or changed. This chapter focuses on metrological units, which are attested in the Old Kingdom. Some metrological units were linked to a specific kind of object to be measured; thus it is to be expected that there were different units for assessing volumes of grain, liquids, or building materials. The discussions cover length units, area units, capacity units, and weights.

Mathematical Texts (II): Tradition, Transmission, Development

2016 ◽  
Author(s):  
Annette Imhausen
Keyword(s):  
Roman Period ◽  
Greco Roman ◽  
Mathematical Problems ◽  
Egyptian Culture ◽  
The Moment ◽  
Egyptian History ◽  
Mathematical Texts

The Greco-Roman Period is the second time in Egyptian history for which a significant corpus of mathematical texts happens to be extant. They are written in the Egyptian script and language of that time, that is, demotic, and are, therefore, commonly known as “demotic mathematical texts.” This chapter presents an overview of the extant sources and some questions that can be raised—as our knowledge of the Egyptian culture during that period is still growing rapidly at the moment. It also outlines some significant changes in Egyptian mathematics that happened in the nearly 1500 years are between the hieratic and demotic mathematical texts and considers selected examples of demotic mathematical problems.

First Steps in Archaeology

Antiquity ◽  
1961 ◽  
Vol 35 (137) ◽  
pp. 8-13 ◽  
Author(s):  
Margaret Murray
Keyword(s):  
English Translation ◽  
British Museum ◽  
Middle Kingdom ◽  
Old Kingdom ◽  
Biblical Archaeology ◽  
Exact Date ◽  
Great Pyramid ◽  
University College London ◽  
Painted Pottery ◽  
Egyptian History

To trace the rise of archaeology is practically to write the biography of one man, Flinders Petrie.I first went to University College, London, as a student of Egyptology in January 1894. Petrie was then in Egypt, digging at Koptos, having in the previous year electrified the learned world by his discoveries at Tell el Amarna. Dr J. H. Walker was in charge of the Egyptology department (then and for years afterwards known as the Edwards Library), and Mr F. Ll. Griffith of the British Museum came twice a week to take a class in hieroglyphs. When Miss Amelia B. Edwards founded the Edwards Professorship of Egyptology, it was with the intention that it should be for the training of students in Egyptian archaeology as distinct from the Egyptian language. She had a small but well chosen collection of Egyptian antiquities which she bequeathed as a nucleus of a teaching collection, and with it her Egyptological library. One show case held the collection, and two bookcases held the library. There were also three ‘cradles’ which held the enormous tomes of Rosselini, La Description de Z’Egypte, and Lepsius’s Denkmäler. It is difficult for any modern archaeologist to realize how few books there were on any archaeological subject. For Egypt there were the early volumes of the ‘Egypt Exploration Fund (including the disastrous Bubastis) and Petrie’s early volumes, including Kahun, with its shattering suggestion that certain peculiar painted pottery found in a Middle Kingdom site (c. 2000 B.C.) came from the Aegean. Mariette and Heinrich Brugsch were well represented in the Edwards Library, and the Proceedings of the Society of Biblical Archaeology was the chief journal in which to publish short articles. Erman’s Aegyptische Grammatik, with its English translation by Breasted had just appeared and was being carefully studied by all Orientalists. Egyptian history began at the 4th dynasty, nothing was known of anything beyond Khufu and the Great Pyramid, except the fragments of Manetho’s history, the lists of Kings, of which the Tablet of Abydos was one, Herodotus, Josephus, and a few scattered items in other ancient authors. The Biblical record concerning Egypt dates from Abraham’s visit, but as the ruler of that country is called Pharaoh without his personal name the exact date is uncertain, but is definitely after the Old Kingdom.

The Nile Delta during the Early Dynastic and Old Kingdom periods. Preliminary remarks on the evolution of settlement landscape

2020 ◽  
pp. 13-61
Author(s):  
Natalia Małecka-Drozd
Keyword(s):  
Nile Delta ◽  
Ancient Egypt ◽  
The Other ◽  
Old Kingdom ◽  
The Third ◽  
Other Hand ◽  
Early Dynastic ◽  
Territorial Structure ◽  
Settlement Landscape ◽  
New Settlements

The 3rd millennium BC appears to be a key period of development of the historical settlement landscape in ancient Egypt. After the unification of the country, the process of disappearance of the predynastic socio-political structures and settlement patterns associated with them significantly accelerated. Old chiefdoms, along with their centres and elites, declined and vanished. On the other hand, new settlements emerging in various parts of the country were often strictly related to the central authorities and formation of the new territorial administration. Not negligible were climatic changes, which influenced the shifting of the ecumene. Although these changes were evolutionary in their nature, some important stages may be recognized. According to data obtained during surveys and excavations, there are a number of sites that were considerably impoverished and/or abandoned before and at the beginning of the Old Kingdom. On the other hand, during the Third and Fourth Dynasties some important Egyptian settlements have emerged in the sources and begun their prosperity. Architectural remains as well as written sources indicate the growing interest of the state in the hierarchy of landscape elements and territorial structure of the country.

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