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Sourcebook in the mathematics of medieval Europe and North Africa /
Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments providing results on the conchoid--a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Muʹtaman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. This book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics. -- Inside jacket flap.
Book
La question de Blaise de Parme sur le contact entre une sphère et un plan
This article contains a critical edition and a French translation of the question \"Utrum spericum tangit planum in puncto\" by Blasius of Parma (†1416). These two parts are preceded by a historical and doctrinal introduction. The question of whether a sphere touches a plane surface in one point only, which had originally emerged in the context of a passage in Aristotle's \"Treatise on the Soul,\" had become an independent issue in thirteenth century. The text edited in this article is the seventh question of Blasius' commentary on the first book of the \"Treatise in the Soul,\" which was however transmitted separately in an Oxford manuscript. Blasius of Parma there investigates the status of objects such as the point, the line and the plane, and analyses the possibility of a contact between a sphere and a plane, intertwining logical, physical and mathematical arguments. In his own answer to the problem, he distinguishes between a mathematical and physical point of view.
Journal Article
Between Copernicus and Galileo
Between Copernicus and Galileo is the story of Christoph Clavius, the Jesuit astronomer and teacher whose work helped set the standards by which Galileo's famous claims appeared so radical, and whose teachings guided the intellectual and scientific agenda of the Church in the central years of the Scientific Revolution. Though relatively unknown today, Clavius was enormously influential throughout Europe in the late sixteenth and early seventeenth centuries through his astronomy books—the standard texts used in many colleges and universities, and the tools with which Descartes, Gassendi, and Mersenne, among many others, learned their astronomy. James Lattis uses Clavius's own publications as well as archival materials to trace the central role Clavius played in integrating traditional Ptolemaic astronomy and Aristotelian natural philosophy into an orthodox cosmology. Although Clavius strongly resisted the new cosmologies of Copernicus and Tycho, Galileo's invention of the telescope ultimately eroded the Ptolemaic world view. By tracing Clavius's views from medieval cosmology the seventeenth century, Lattis illuminates the conceptual shift from Ptolemaic to Copernican astronomy and the social, intellectual, and theological impact of the Scientific Revolution.
eBook
Desire of teachers and realities in textbooks: dealing with history of mathematics in the new French curriculum and its impact on teacher training
Many international studies focus empirically on integrating the history of mathematics in mathematics education. Over the last 2 decades, some studies also revealed theoretical elements concerning the implementation of learning sessions and/or their didactical analysis and effectiveness. This paper has the aim of complementing these empirical studies with a more systematic approach in the French context. Defended for decades within the IREM (Institut de recherche sur l’enseignement des mathématiques), the history of mathematics is now officially introduced in the French curriculum. Nevertheless, is it really sufficient for teachers to change their habits by implementing the history of mathematics in their practices? To answer this question, I first present an unpublished survey with secondary school mathematics teachers (pupils from 10- to 18 years old) about the introduction of the history of mathematics in their classes. This survey allows the comparison of teachers’ desires (‘history of mathematics
in potentiality
’) and realities in classrooms (‘history of mathematics
in actuality
’). Then I focus on French mathematics textbooks (for pupils from 15- to 18 years old) in order to question their effectiveness as tools for the introduction of a historical perspective. I describe the historical/mathematical tasks available in these textbooks focusing on their reference to Fibonacci. Finally, I present a proposition to implement the history of mathematics in mathematics education starting from the textbooks, aiming to help mathematics teachers to redesign the tasks of their textbooks so as to be more relevant.
Journal Article
Finding Fibonacci : the quest to rediscover the forgotten mathematical genius who changed the world
In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers--which, it so happens, he didn't invent--Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci--the \"Book of Calculation\"--Introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him. -- Back cover.
Book
Spiritual Calculations
Medieval English sermons teem with examples of quantitative reasoning, ranging from the arithmetical to the numerological, and regularly engage with numerical concepts. Examining sermons written in Middle English and Latin, this book reveals that popular English-speaking audiences were encouraged to engage in a wide range of numerate operations in their daily religious practices.
Medieval sermonists promoted numeracy as a way for audiences to appreciate divine truth. Their sermons educated audiences in a hybrid form of numerate practice—one that relied on individuals' pragmatic quantitative reasoning, which, when combined with spiritual interpretations of numbers provided by the preacher, created a deep and rich sense in which number was the best way to approach the sacred mysteries of the world as well as to learn how one could best live as a Christian. Analyzing both published and previously unpublished sermons and sermon cycles, Christine Cooper-Rompato explores the use of numbers, arithmetic, and other mathematical operations to better understand how medieval laypeople used math as a means to connect with God.
Spiritual Calculations enhances our understanding of medieval sermons and sheds new light on how receptive audiences were to this sophisticated rhetorical form. It will be welcomed by scholars of Middle English literature, medieval sermon studies, religious experience, and the history of mathematics.
eBook