Journal articles: 'Babylonian mathematics'

1

Brack-Bernsen*, Lis, and Olaf Schmidt**. "Bisectable Trapezia in Babylonian Mathematics." Centaurus 33, no. 1 (April 1990): 1–38. http://dx.doi.org/10.1111/j.1600-0498.1990.tb00718.x.

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Steele, John. "Babylonian Shadow-Length Schemes: Between Mathematics and Astronomy." Claroscuro. Revista del Centro de Estudios sobre Diversidad Cultural, no. 20 (December 30, 2021): 1–25. http://dx.doi.org/10.35305/cl.vi20.82.

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A simple mathematical scheme to represent the variation in the length of the shadow cast by a vertical gnomon at different times of day and in different months of the year is presented in the early astronomical compendium MUL.APIN. A small number of texts composed in the Late Babylonian period investigate and expand this scheme. These texts have previously been studied and understood as part of Babylonian astronomy. In this article, I suggest that two of these later texts can be better understood as mathematical texts. As such they provide evidence for the influence of astronomy on Late Babylonian mathematics, either or both as the context for simple mathematical problems and/or as a topic of mathematical investigation.

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Friberg (book author), Jöran, and Nathan Sidoli (review author). "Unexpected Links between Egyptian and Babylonian Mathematics and Amazing Traces of a Babylonian Origin in Greek Mathematics." Aestimatio: Critical Reviews in the History of Science 5 (December 21, 2015): 142–47. http://dx.doi.org/10.33137/aestimatio.v5i0.25867.

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Muroi, Kazuo. "Extraction of Cube Roots in Babylonian Mathematics." Centaurus 31, no. 3 (October 1988): 181–88. http://dx.doi.org/10.1111/j.1600-0498.1988.tb00736.x.

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Depuydt, Leo. "Unexpected links between Egyptian and Babylonian mathematics." Mathematical Intelligencer 30, no. 3 (June 2008): 72–74. http://dx.doi.org/10.1007/bf02985385.

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Knill, Ronald J. "A Modified Babylonian Algorithm." American Mathematical Monthly 99, no. 8 (October 1992): 734. http://dx.doi.org/10.2307/2324239.

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Høyrup, Jens. "On a Collection of Geometrical Riddles and their Role in the Shaping of Four to Six “Algebras”." Science in Context 14, no. 1-2 (June 2001): 85–131. http://dx.doi.org/10.1017/s0269889701000047.

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For more than a century, there has been some discussion about whether medieval Arabic al-jabr (and hence also later European algebra) has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 BCE, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later the geometry of Elements II (where the techniques are submitted to theoretical investigation). The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European (Latin and abbaco) mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles.

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Bidwell, James K. "A Babylonian Geometrical Algebra." College Mathematics Journal 17, no. 1 (January 1986): 22. http://dx.doi.org/10.2307/2686867.

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9

Flenner, H. "Babylonian tower theorems for coverings." Archiv der Mathematik 57, no. 3 (September 1991): 299–304. http://dx.doi.org/10.1007/bf01196861.

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HØYRUP, JENS. "On Old Babylonian Mathematical Terminology and its Transformations in the Mathematics of Later Periods." GANITA BHARATI 40, no. 1 (August 9, 2019): 53–99. http://dx.doi.org/10.32381/gb.2018.40.01.3.

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Schumann, Andrew. "On the Origin of Logical Determinism in Babylonia." Logica Universalis 15, no. 3 (August 16, 2021): 331–57. http://dx.doi.org/10.1007/s11787-021-00282-5.

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AbstractIn this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs (omens) which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal event (including past and future events) is actual. In divination lists in Akkadian presented as codes we can reconstruct Boolean matrices showing that the Babylonians used some logical-algebraic structures in their reasoning. The idea of logical contingency was introduced within a new mood of thinking presented by the Greek prose – historical as well as philosophical narrations. In the Jewish genre ’aggādōt, the logical determinism is supposed to be in opposition to the Greek prose.

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Flenner, Hubert. "Babylonian tower theorems on the punctured spectrum." Mathematische Annalen 271, no. 1 (March 1985): 153–60. http://dx.doi.org/10.1007/bf01455804.

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Duke, Dennis. "Greek angles from Babylonian numbers." Archive for History of Exact Sciences 64, no. 3 (March 23, 2010): 375–94. http://dx.doi.org/10.1007/s00407-010-0058-x.

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Fowler, David, and Eleanor Robson. "Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context." Historia Mathematica 25, no. 4 (November 1998): 366–78. http://dx.doi.org/10.1006/hmat.1998.2209.

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Høyrup, Jens. "A Note on Old Babylonian Computational Techniques." Historia Mathematica 29, no. 2 (May 2002): 193–98. http://dx.doi.org/10.1006/hmat.2002.2343.

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Swerdlow, N. M. "Acronychal Risings in Babylonian Planetary Theory." Archive for History of Exact Sciences 54, no. 1 (April 1, 1999): 49–65. http://dx.doi.org/10.1007/s004070050033.

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Dold-Samplonius, Yvonne. "2000 Years Transmission of Mathematical Ideas: Exchange and Influence from Late Babylonian Mathematics to Early Renaissance Science." Nexus Network Journal 2, no. 1-2 (June 2000): 204. http://dx.doi.org/10.1007/s00004-999-0030-8.

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Gray, J. M. K., and J. M. Steele. "Studies on Babylonian goal-year astronomy II: the Babylonian calendar and goal-year methods of prediction." Archive for History of Exact Sciences 63, no. 6 (July 15, 2009): 611–33. http://dx.doi.org/10.1007/s00407-009-0048-z.

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Evans, James, and Christián C. Carman. "Babylonian solar theory on the Antikythera mechanism." Archive for History of Exact Sciences 73, no. 6 (September 20, 2019): 619–59. http://dx.doi.org/10.1007/s00407-019-00237-9.

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de Jong, Teije, and Hermann Hunger. "Babylonian observations of a unique planetary configuration." Archive for History of Exact Sciences 74, no. 6 (August 3, 2020): 587–603. http://dx.doi.org/10.1007/s00407-020-00252-1.

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Abstract In this paper, we discuss Babylonian observations of a “massing of the planets” reported in two Astronomical Diaries, BM 32562 and BM 46051. This extremely rare astronomical phenomenon was observed in Babylon between 20 and 30 March 185 BC shortly before sunrise when all five planets were simultaneously visible for about 10 to 15 min close to the horizon in the eastern morning sky. These two observational texts are not only interesting as records of an extremely rare planetary configuration, but also because (1) the observers appear to be confused by the presence of all planets simultaneously and mix them up in their reports, and (2) the two reports of the same observations are so different that we are forced to conclude that they were carried out by two different observers. There is an additional astronomical event which makes this planetary configuration even more unique: the exact conjunction of the planets Mars and Jupiter in the afternoon of 25 March 185 BC. An exact conjunction, where two planets are so close together that they appear as one object in the sky, is also extremely rare. Although this exact conjunction between Mars and Jupiter occurred during the day so that it was not observable, it was correctly predicted by the Babylonian scholars: a remarkable achievement and a nice illustration of their astronomical craftsmanship. Finally, our study clearly exposes one of the limitations of Babylonian naked-eye astronomy. When first appearances of the planets Mercury, Mars and Saturn are expected around the same date, it is nearly impossible to correctly identify them because their expected positions are only approximately known while they have about the same visual magnitude so that they become visible at about the same altitude above the horizon.

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García, José Barrios. "A New Look at Old Texts – Rethinking the Relations Between Egyptian and Babylonian Mathematics." Metascience 16, no. 2 (May 4, 2007): 295–98. http://dx.doi.org/10.1007/s11016-007-9105-x.

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Hannah, John. "The Doctrines of Triangles: A History of Modern Trigonometry by Glen Van Brummelen." Aestimatio: Sources and Studies in the History of Science 3, no. 1 (September 30, 2023): 134–43. http://dx.doi.org/10.33137/aestimatio.v3i1.41820.

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The Doctrine of Triangles is the second half of Glen Van Brummelen’s history of trigonometry. The first part, The Mathematics of the Heavens and the Earth [Van Brummelen 2009] dealt with the early history of trigonometry, from “precursors” in ancient Egyptian and Babylonian sources (dating from the second millennium BC), through to the trigonometric tables of Georg Rheticus in the 16th century AD. The present volume begins with a brief account of the story so far and then continues the story through to the early 20th century. It will be helpful to review briefly that “story so far”.

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Steele, J. M., and E. L. Meszaros. "A study of Babylonian records of planetary stations." Archive for History of Exact Sciences 75, no. 4 (February 18, 2021): 415–38. http://dx.doi.org/10.1007/s00407-021-00272-5.

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Brack-Bernsen, Lis. "Babylonian astronomy: a new understanding of column Φ." Archive for History of Exact Sciences 74, no. 6 (August 6, 2020): 605–40. http://dx.doi.org/10.1007/s00407-020-00254-z.

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Abstract The most discussed and mysterious column within the Babylonian astronomy is column Φ. It is closely connected to the lunar velocity and to the duration of the Saros. This paper presents new ideas for the development and interpretation of column Φ. It combines the excellent Goal-Year method (for the prediction of Lunar Six time intervals) with old ideas and practices from the “schematic astronomy”. Inspired by the old “TU11” rule for prediction of times of lunar eclipses, it proposes that column Φ, in a similar way, used the sum of the Lunar Four to predict times of lunar eclipses as well as the duration of one, 6, and 12 months by means of what usually is called “R–S” schemes. It also explains fully the structure and development of such schemes, a fact that strongly supports the new interpretation of column Φ.

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Bakirov, Denys. "REX IUDÆORUM: FROM THORNBUSH TO THE CROWN OF THORNS." 66, no. 66 (November 25, 2022): 47–51. http://dx.doi.org/10.26565/2226-0994-2022-66-5.

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The aim of this study is to trace the development of the messianic thought from its pre-monarchic roots (Pre-Temple) to the monarchic period (First Temple), to the post-exilic period (Second Temple), and to the post-Second Temple period. I hypothesise that the first identification of the messiah (the anointed) with the military leader was an intellectual and religious endorsement of the “original sin” of kingship described in the allegory of the trees (Judges 9:8-15). However, the Babylonian exile catalysed the process by which Jews learned to abstract their expectation of the messiah from the “pagan” worship of the extant commander-in-chief. I trace this gradual process of learning to its acme in the Qumran literature: where historical and extraterrestrial strains of messianic thought are reconciled. Then I follow Mack and Juel in arguing that Mark the Evangelist used the wisdom pattern (learned after the Babylonian exile) as the foundation on which to rethink the concept of kingship from scratch. Thus it was no longer kingship that “seemed” divine but wisdom that “seemed” royal. The significance of Jesus’s scandalous ministry could only be captured by the irony which Mark uses to narrate his Gospel: Jesus’s coronation as a king could only happen as mockery because his claim to kingship does not make the slightest sense. Hence the idea of messianism was liberated from the confusion with the powers-that-be by being identified with the powerless teacher whose life embodied the wisdom tale pattern at the heart of Israel’s history – Egyptian slavery and Exodus, trial and vindication, exile and homecoming, death and resurrection.

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BRITTON, JOHN P., and ALEXANDER JONES. "A New Babylonian Planetary Model in a Greek Source." Archive for History of Exact Sciences 54, no. 4 (January 2000): 349–73. http://dx.doi.org/10.1007/pl00007553.

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27

Proust, Christine. "The sexagesimal place-value system inside and outside texts." Claroscuro. Revista del Centro de Estudios sobre Diversidad Cultural, no. 20 (December 30, 2021): 1–20. http://dx.doi.org/10.35305/cl.vi20.81.

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This article proposes a contribution to the reflection on the invention of the sexagesimal place-value notation, a way of representing numbers which was at the basis of the so-called “Babylonian” mathematics (mathematical texts written in cuneiform script in the Ancient Near East from the 3rd to the 1st millennium BCE). The history of the sexagesimal place-value notation has already been the subject of numerous studies. It is proposed here to shed some new light on this question not only by examining texts, but also by taking into account the environment of the texts: what happens outside the text itself? What are the activities that accompany the act of writing?

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Gabriel, Gösta Ingvar. "An Exemplificational Critique of Violence: Re-Reading the Old Babylonian Epic Inūma ilū awīlum (a.k.a. Epic of Atramḫasīs)." Journal of Ancient Near Eastern History 5, no. 1-2 (October 25, 2018): 179–213. http://dx.doi.org/10.1515/janeh-2018-0011.

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AbstractThe article approaches the mythical epic Inūma ilū awīlum with respect to its narrative structure and procedure. Within this framework, it investigates the ideas pertaining to the nature of violence that is communicated through the sequence of events within the poem. The mode chosen to inform the epic’s reader is understood as narrative exemplification, being an equivalent to the demonstration of general principles through representative examples that can often be found in other epistemic contexts in ancient Mesopotamia, e. g. in mathematics or divination. Thus, the paper not only reconstructs a specific concept of violence but also elaborates on the more general question of whether and how these intellectual means might represent some form of a Babylonian philosophy.

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de Jong, Teije. "A study of Babylonian planetary theory I. The outer planets." Archive for History of Exact Sciences 73, no. 1 (September 24, 2018): 1–37. http://dx.doi.org/10.1007/s00407-018-0216-0.

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de Jong, Teije. "A study of Babylonian planetary theory II. The planet Venus." Archive for History of Exact Sciences 73, no. 4 (March 29, 2019): 309–33. http://dx.doi.org/10.1007/s00407-019-00224-0.

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31

Steele, John. "Combining Science and History: Lis Brack-Bernsen’s Contributions to the History of Babylonian Astronomy." Notices of the American Mathematical Society 70, no. 03 (March 1, 2023): 1. http://dx.doi.org/10.1090/noti2650.

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Mersin, Nazan, Mehmet Akif Karabörk, and Soner Durmuş. "Awareness of Preservice Mathematics Teachers about Prehistoric and Ancient Number Systems." Malikussaleh Journal of Mathematics Learning (MJML) 3, no. 2 (October 30, 2020): 57. http://dx.doi.org/10.29103/mjml.v3i2.2904.

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This study seeks to analyse the awareness of the pre-service teachers on the counting methods, systems and tools used in the prehistoric method and the Ancient period and to examine the distribution of this awareness by gender. A total of 42 sophomore-level students studying at a university in the Western Black Sea region, Turkey, participated in this exploratory case study. The data were obtained through a form consisting of 6 questions, one of which is open-ended, after the 14-week course of history of mathematics. The data collection tool included questions on the counting methods used in the pre-historic period and the Ancient Egyptian, Ancient Roman, Babylonian, Ancient Greek and Mayan number systems. The data were analysed through descriptive analysis and content analysis. The findings indicated that the pre-service teachers most reported the methods of tallying, tying a knot, token, circular disc. Also, the question on the Ancient Egyptian number system was answered correctly by all pre-service teachers, the lowest performance was observed in the question on the Mayan number system. Analysis of the answers by gender revealed that the male pre-service teachers were more likely to give false answers compared to the female pre-service teachers.

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Britton, John P. "Studies in Babylonian Lunar Theory: Part II. Treatments of Lunar Anomaly." Archive for History of Exact Sciences 63, no. 4 (April 18, 2009): 357–431. http://dx.doi.org/10.1007/s00407-009-0041-6.

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M. Izmirli, Ilhan. "An Important Historical Milestone: The Classification of the Cubic Equations." Global Research in Higher Education 6, no. 2 (April 13, 2023): p32. http://dx.doi.org/10.22158/grhe.v6n2p32.

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This article investigates the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics, using the history of the cubic equation as a specific example.Cubic equations arise intrinsically in many applications in natural sciences and mathematics. For example, in physics, the solutions of the equations of state in thermodynamics, or the computation of the speed of seismic Rayleigh waves require the solutions of cubic equations. In mathematics, they are instrumental in solving the quartic equations, for in the process, these are reduced to cubic equations. The impossibility of trisecting an angle or doubling a cube using only a straightedge and compass is equivalent to solving some cubic equations. As the name implies, the cubic spline approximation, an important tool in numerical analysis, also entails working with cubic functions. Although cubic equations were explored by the ancient Babylonian, Greek, Chinese, Indian, and Egyptian scholars, it took the collective work of many well-known mathematicians such as Diophantus, Archimedes, Fibonacci, del Ferro, Khayyam, Tartaglia, Cardano, Viète, Descartes, and Lagrange to finally obtain a full solution. Our goal in this paper is to investigate one of the most formidable steps in this extensive and prolific history, namely the complete classification of the cubic equations by Omar Khayyam in eleventh century, who was the first scholar to classify cubic equation and hence facilitate a methodical and logical approach to obtaining a general solution.

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Hamilton, Norman T., and Asger Aaboe. "A Babylonian Venus Text Computed According to System A: ACT No. 1050." Archive for History of Exact Sciences 53, no. 3-4 (November 1998): 215–21. http://dx.doi.org/10.1007/s004070050028.

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Britton, John P. "Studies in Babylonian lunar theory: part III. The introduction of the uniform zodiac." Archive for History of Exact Sciences 64, no. 6 (September 14, 2010): 617–63. http://dx.doi.org/10.1007/s00407-010-0064-z.

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Ossendrijver, Mathieu. "Bisecting the trapezoid: tracing the origins of a Babylonian computation of Jupiter’s motion." Archive for History of Exact Sciences 72, no. 2 (March 2018): 145–89. http://dx.doi.org/10.1007/s00407-018-0204-4.

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Dusan Vallo, Lucia Rumanová, and Veronika Bočková. "Elements of Algorithmic Thinking in the Teaching of School Geometry through the Application of Geometric Problems." International Journal of Emerging Technologies in Learning (iJET) 18, no. 14 (July 31, 2023): 229–43. http://dx.doi.org/10.3991/ijet.v18i14.40341.

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Algorithmic thinking and the creation of algorithms have traditionally been associated with mathematics. It is based on the general perception of an algorithm as a logically unambiguous and precise prescription for performing a certain set of operations, through which we reach a result in real time in a finite number of steps. There are well-known examples from history, such as the division algorithm used by ancient Babylonian mathematicians, Eratosthenes algorithm for finding prime numbers, Euclid’s algorithm for finding the greatest common divisor of two numbers, and cryptographic algorithm for coding and breaking, invented by Arabic mathematicians in the 9th century. Although the usage of algorithms and the development of algorithmic thinking currently fall within the domain of computer science, algorithms still play a role in mathematics and its teaching today. Contemporary mathematics, and especially its teaching in schools of all grades, prefers specific algorithms in arithmetic, algebra, and calculus. For example, operations with numbers, modifications of algebraic expressions, and derivation of functions. Teaching geometry in schools involves solving a variety of problems, many of which are presented as word problems. Algorithmization of school geometric tasks is therefore hardly visible and possible at first glance. However, there are ways to solve examples of a certain kind and to establish a characteristic and common algorithmic procedure for them. Algorithmic thinking in geometry and the application of algorithms in the teaching of thematic parts of school geometry are specific issue that we deal with in this study. We will focus on a detailed analysis of the possibilities of developing algorithmic thinking in school geometry and the algorithmization of geometric tasks.

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Britton, John P. "Studies in Babylonian Lunar Theory: Part I. Empirical Elements for Modeling Lunar and Solar Anomalies." Archive for History of Exact Sciences 61, no. 2 (January 25, 2007): 83–145. http://dx.doi.org/10.1007/s00407-006-0121-9.

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Artemenko, Mykyta. "ONTOLOGICAL SYSTEM OF BARDAISAN – FREE WILL AND “ETHICAL COSMOLOGY”." 66, no. 66 (November 25, 2022): 52–58. http://dx.doi.org/10.26565/2226-0994-2022-66-6.

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The article is devoted to the reconstruction of the ontological system of Bardaisan. A specific view of ethics as an ontological construct is characteristic of the Middle Eastern philosophical tradition. The teachings of Bardaisan lie at the origins of the Syrian religious philosophy, therefore the reconstruction of his teachings allows us to understand the main sources that formed the Eastern philosophical tradition in its originality. A detailed philosophical analysis of the concept of fate in the teachings of Bardaisan has not previously been undertaken. In addition, most of the studies paid more attention to the history of borrowings and the origin of various concepts of the Bardaisanite philosophy and their doxography, while the analysis of individual concepts was usually left out of brackets. The study of Bardaisan as a philosopher from the point of view of the modern philosophical tradition is undertaken for the first time. The article pays great attention to the phenomenon of free will, the construct underlying Bardaisan's “ethical cosmology”. The transformation of Babylonian astrology and Jewish symbolism serves as a civilizational backdrop against which Bardaisan weaves Christian ethics, Zoroastrian ontology, and Stoic anthropology. Understanding the peculiarities of citing Greek philosophy, as well as building the main ontological constructs, provides the key to understanding the Middle Eastern philosophical tradition. The dialogue "Book of Laws and Countries", which is considered in the article, is a vivid example of a treatise-mesekhet, a multilevel discourse, the space of a language game, images and tropes. The article examines models of interaction of various discourses and various strategies for building a philosophical treatise. Plato's dialogue, using Middle Eastern metaphor, reveals the space of language play and intertextuality, dissemination.

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Unguru, Sabetai. "Jöran Friberg. Amazing Traces of a Babylonian Origin in Greek Mathematics. xx + 476 pp., apps., bibl., index. Singapore: World Scientific Publishing, 2007. $98 (cloth)." Isis 99, no. 4 (December 2008): 821–22. http://dx.doi.org/10.1086/597750.

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Gray, J. M. K., and J. M. Steele. "Studies on Babylonian goal-year astronomy I: a comparison between planetary data in Goal-Year Texts, Almanacs and Normal Star Almanacs." Archive for History of Exact Sciences 62, no. 5 (July 1, 2008): 553–600. http://dx.doi.org/10.1007/s00407-008-0027-9.

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ACERBI, FABIO. "JÖRAN FRIBERG, Amazing Traces of a Babylonian Origin in Greek Mathematics. Hackensack, NJ - U.S.A.: World Scientific Press, 2007. xx+476 pp., ISBN 978-981-270-452-8." Nuncius 24, no. 1 (January 1, 2009): 190–91. http://dx.doi.org/10.1163/221058709x00114.

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Mak, Bill M. "The Date and Nature of Sphujidhvaja’s Yavanajātaka Reconsidered in the Light of Some Newly Discovered Materials." History of Science in South Asia 1 (May 1, 2013): 1. http://dx.doi.org/10.18732/h2rp4t.

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Since Pingree's 1978 publication of his work on the Yavanajātaka, the text had established itself as one of the most important historical documents in various fields of Indology, from the history of mathematics and astral science, to Indian chronology and historical contacts among ancient cultures. A number of Pingree's discoveries concerning the text were widely quoted by scholars in the past decades. These discoveries may be summarized as follows: The Yavanajātaka was an astrological/astronomical work composed in 269/270 CE. by Sphujidhvaja, an "Indianized Greek" who lived in the realm of the Western Kṣatrapas. The work was a versification of a prose original in Greek composed by Yavaneśvara in Alexandria in 149/150 CE. The work, though highly corrupted and clumsily expressed, contains algorithms of "ultimately Babylonian origin" and the earliest reference to the decimal place-value with a symbol for zero (bindu). Pingree's discoveries were based largely on readings from the last section of the Yavanajātaka, described by him as "Chapter 79 - Horāvidhiḥ", an exposition of mathematical astronomy. In the recent years, scholars including Shukla (1989) and Falk (2001) pointed out some major flaws in some of Pingree's interpretations and reconstitution of the text. However, further progress of a proper reevaluation of the controversial contents of this chapter has so far been hampered by the lack of a better manuscript. In 2011-2012, additional materials including a hitherto unreported copy of the Yavanajātaka became available to the present author. This paper will therefore be the first attempt to reexamine Pingree's key interpretations of the Yavanajātaka, focusing on this last chapter, in the light of the new textual evidences.

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Steele, J. M. "Planetary Latitudes in Babylonian Mathematical Astronomy." Journal for the History of Astronomy 34, no. 3 (August 2003): 269–89. http://dx.doi.org/10.1177/002182860303400302.

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Bacelar Valente, Mario. "On the correctness of problem solving in ancient mathematical procedure texts." Revista de Humanidades de Valparaíso, no. 16 (January 21, 2021): 169. http://dx.doi.org/10.22370/rhv2020iss16pp169-189.

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It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive.

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Abbey, Tristan. "In the Shadow of the Palms: The Selected Works of David Eugene Smith." Perspectives on Science and Christian Faith 75, no. 2 (September 2023): 135–37. http://dx.doi.org/10.56315/pscf9-23abbey.

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IN THE SHADOW OF THE PALMS: The Selected Works of David Eugene Smith by Tristan Abbey, ed. Alexandria, VA: Science Venerable Press, 2022. xii + 155 pages, including a Glossary of Biosketches. Paperback; $22.69. ISBN: 9781959976004. *David Eugene Smith (1860-1944) may not be a household name for readers of this journal, but he deserves to be better known. An early-twentieth-century world traveler and antiquarian, his collaboration with publisher and bibliophile George Arthur Plimpton led to establishing the large Plimpton and Smith collections of rare books, manuscripts, letters, and artefacts at Columbia University in 1936. He was one of the founders (1924) and an early president (1927) of the History of Science Society, whose main purpose at the time was supporting George Sarton's ongoing management of the journal ISIS, begun a dozen years earlier. Smith also held several offices in the American Mathematical Society over the span of two decades and was a charter member (1915) and President (1920-1921) of the Mathematical Association of America (MAA). *Smith is best known, however, for his pioneering work in mathematics education, both nationally and internationally. In 1905, he proposed setting up an international commission devoted to mathematics education (now the International Commission on Mathematical Instruction) to explore issues of common concern to mathematics teachers on all levels, worldwide. He was actively involved in reviving this organization after its dissolution during the First World War and served as its President from 1928 to 1932. Nationally, Smith was instrumental in inaugurating the field of mathematics education, advancing this discipline professionally both in his role as mathematics professor at the prestigious Teachers College, Columbia University (1901-1926) and as an author of numerous best-selling mathematics textbooks for elementary and secondary schools. These texts were not focused solely on mathematical content; they also dealt substantively with teaching methodology, applications, rationales for studying the material, and significant historical developments. *Throughout his life Smith championed placing mathematics within the wider liberal arts setting of the humanities, highlighting history, art, and literary connections in his many talks, articles, and textbooks. For him there was no two-cultures divide, as it later came to be known. While acknowledging the value of utilitarian arguments for studying mathematics (he himself published a few textbooks with an applied focus), he considered such a rationale neither sufficient nor central. For him, mathematics was to be studied first of all for its own sake, appreciating its beauty, its reservoir of eternal truths, and its training in close logical reasoning. But again, for him this did not mean adopting a narrow mathematical focus. In particular, given his wide-ranging interest in how mathematics developed in other places and at other times, he tended to incorporate historical narratives in whatever he wrote. *This interest led him later in life to write a popular two-volume History of Mathematics. The first volume (1923) was a chronological survey from around 2200 BC to AD 1850 that focused on the work of key mathematicians in Western and non-Western cultures; the second volume (1925) was organized topically around subjects drawn from the main subfields of elementary mathematics. His History of Mathematics was soon supplemented by a companion Source Book in Mathematics (1929), which contained selected excerpts in translation from mathematical works written between roughly 1475 and 1875. Smith wrote at a time when the history of mathematics was beginning to expand beyond the boundaries of Greek-based Western mathematics to include developments from non-Western cultures (Egyptian, Babylonian, Indian, Chinese, Japanese, and Arabic), a trend he approved of and participated in professionally. *Smith's interest in broader issues extended even to exploring possible linkages between religion and mathematics. His unprecedented parting address to members of the MAA as its outgoing President is titled "Religio Mathematici," a reflection on mathematics and religion that was reproduced a month later as a ten-page article in The American Mathematical Monthly (1921) and subsequently reprinted several times. Smith's article "Mathematics and Religion" appearing in the National Council of Teachers of Mathematics' sixth yearbook Mathematics in Modern Life (1931) touched on similar themes. These two essays maintain that mathematics and religion are both concerned with infinity, with eternal truths, with valid reasoning from assumptions, and with the existence of the imaginary and higher dimensions, "the great beyond," enabling one to draw fairly strong parallels between them. Thus, a deep familiarity with these facets of mathematics may help one to appreciate the essentials of religion. Mathematics itself was thought of in quasi-religious terms, as "the Science Venerable." Smith's farewell address partly inspired Francis Su in his own presidential retirement address to the MAA in 2017 and in its 2020 book-length expansion Mathematics for Human Flourishing (see PSCF 72, no. 3 [2020]: 179-81). Su's appreciation of Smith's ideas also led him to contribute a brief Foreword to the booklet under review, to which we now turn. *First a few publication details: In the Shadow of the Palms is an attractive booklet produced as a labor of love by someone obviously enamored with his subject. Tristan Abbey is a podcaster with broad interests that include being a "math history enthusiast," but whose primary professional experience up to now has been focused on the environmental politics of energy and mineral resources. This work is the initial (and so far the only) offering by a publication company Abbey set up. Its name, Science Venerable Press, was chosen in honor of Smith's designation for mathematics. *One might classify this work non-pejoratively as a coffee-table booklet. It contains 50 excerpts (Su terms them "short meditations") from a wide range of Smith's writings, selected, categorized, and annotated by Abbey, along with full-page reproductions of eight postcards mailed back home by Smith on his world travels, and two photos, including Smith's Columbia-University-commissioned portrait. Smith's excerpted writing occupies only 109 of the total 167 pages, nearly two dozen of which are less than half full. The amply spaced text appears on 3.25 inches of the 7 inch-wide pages, the outer margins being reserved for Abbey's own auxiliary notes explaining references and allusions that appear in the excerpt. This gives the book lots of white space; in fact, eighteen pages of the booklet are completely blank. Another nine pages contain 75 short biographical sketches of mathematicians taken from Smith's historical writings; these are unlinked to any of the excerpts, but they do indicate the breadth of his historical interests. Unfortunately, no index of names or subjects is provided for the reader who wants to learn whether a person or a topic is treated anywhere in the booklet; the best one can do in this regard is consult the titles Abbey assigns the excerpts in the Table of Contents. *The booklet gives a gentle introduction to Smith's views on mathematics, mathematics education, and the history of mathematics. The excerpts chosen are more often literary than discursive. Smith was a good writer, able to keep the reader's attention and convey the sentiments intended, but these excerpts do not develop his ideas in any real length. They portray mathematics in radiant--sometimes fanciful--terms that a person disposed toward the humanities might find attractive but nevertheless judge a bit over-the-top: mathematicians are priests lighting candles in the chapel of Pythagoras; mathematics is "the poetry of the mind"; learning geometry is like climbing a tall mountain to admire the grandeur of the panoramic view; progress in mathematics hangs lanterns of light on major thoroughfares of civilization; and retirement is journeying through the desert to a restful oasis "in the shadow of the palms." Some passages are parables presented to help the reader appreciate what mathematicians accomplished as they overcame great obstacles. *While the excerpts occasionally recognize that mathematics touches everyday needs and is a necessary universal language for commerce and science, without which our world would be unrecognizable, their main emphasis--in line with Smith's fundamental outlook--is on mathematics' ability on its own to deliver joy and inspire admiration of its immortal truths. These are emotions many practicing mathematicians and mathematics educators share; Smith's references to music, art, sculpture, poetry, and religion are calculated to convey to those who are not so engaged, some sense of how thoughtful mathematicians value their field--as a grand enterprise of magnificent intrinsic worth. *In the Shadow of the Palms offers snapshots of the many ideas found in Smith's prolific writings about mathematics, mathematics education, and history of mathematics. It may not attract readers, though, who do not already understand and appreciate Smith's significance for these fields. Abbey himself acknowledges that his booklet "only scratches the surface of [Smith's] contributions" (p. 4). A recent conference devoted to David Eugene Smith and the Historiography of Mathematics (Paris, 2019) is a step toward recognizing Smith's importance, but a comprehensive scholarly treatment of Smith's work within his historical time period remains to be written. *Reviewed by Calvin Jongsma, Professor of Mathematics Emeritus, Dordt University, Sioux Center, IA 51250.

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Steele, J. M. "Book Review: Moving beyond ‘Act’, Babylonian Mathematical Astronomy: Procedure Texts." Journal for the History of Astronomy 44, no. 3 (August 2013): 363–64. http://dx.doi.org/10.1177/002182861304400307.

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Alivernini, Sergio. "MATHEMATICAL ASPECTS OF EARTH-MOVING LINKED TO HYDRAULIC WORKS IN UR III UMMA." Iraq 80 (October 8, 2018): 15–34. http://dx.doi.org/10.1017/irq.2018.8.

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This paper studies mathematical aspects of earthwork projects in the Ur III city of Umma, c.2053–2032 b.c. The main purpose of this paper is to describe the practical procedures involved in moving earth for hydraulic works around Umma. It also shows how Old Babylonian pedagogical “mathematical texts” about earthworks, from the early second millennium b.c., are indebted to the practical procedures adopted by Ur III officials.

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MUROI, Kazuo. "Some Remarks on the Babylonian Mathematical Text Db2-146. (IM 67118)." Bulletin of the Society for Near Eastern Studies in Japan 32, no. 1 (1989): 140–47. http://dx.doi.org/10.5356/jorient.32.140.

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Journal articles on the topic 'Babylonian mathematics'

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