Stela Segev | Herzog College (original) (raw)

Papers by Stela Segev

WTM-Verlag eBooks, Dec 31, 2022

During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th c... more During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th centuries on scientific and especially mathematical topics have been deciphered. In these works, one can find mainly topics like arithmetic and geometry. Apart from the mathematical content, however, we can sometimes find (especially in each introduction but not only there), more information about other topics. Below are presented examples of the diverse information that can be found in the introductions to mathematical works written in Hebrew during the 12th–16th centuries, with a special focus on information that allows us to learn about the didactic views of the authors of these works. As research in teaching in general and research in mathematics education are relatively new research disciplines, these views are particularly interesting. Here we find evidence of didactic thinking long before the subject of mathematics teaching became a canonical university discipline. Scholars and students studying mathematics education will be interested in discovering that didactic issues in mathematics teaching are as old as mathematics itself. Special attention will be paid to Elijah Mizrahi's Book of the Number (posthumous print in 1533), a unique figure among the authors of mathematical books in Hebrew from the 12th–16th centuries.

Between the 12 th and 16 th centuries, many arithmetical texts were written in Hebrew. These text... more Between the 12 th and 16 th centuries, many arithmetical texts were written in Hebrew. These texts include a variety of topics: arithmetic operations with integers, simple fractions, and fractions in sexagesimal system, extracting roots, ratios, and word problems. However, no in-depth study has been conducted so far about simple fractions in these texts. In this paper, we present both the mathematical content (definitions, theorems, proofs), and the didactic content (how to present the concept of fraction, the choice of algorithms, the types of explanations, and reasonings), as they appear in Hebrew texts.

“DIG WHERE YOU STAND” 7, 2022

During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th c... more During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th centuries on scientific and especially mathematical topics have been deciphered. In these works, one can find mainly topics like arithmetic and geometry. Apart from the mathematical content, however, we can sometimes find (especially in each introduction but not only there), more information about other topics. Below are presented examples of the diverse information that can be found in the introductions to mathematical works written in Hebrew during the 12th–16th centuries, with a special focus on information that allows us to learn about the didactic views of the authors of these works. As research in teaching in general and research in mathematics education are relatively new research disciplines, these views are particularly interesting. Here we find evidence of didactic thinking long before the subject of mathematics teaching became a canonical university discipline. Scholars and students studying mathematics education will be interested in discovering that didactic issues in mathematics teaching are as old as mathematics itself. Special attention will be paid to Elijah Mizrahi's Book of the Number (posthumous print in 1533), a unique figure among the authors of mathematical books in Hebrew from the 12th–16th centuries.

ThirteenthCongressoftheEuropeanSocietyforResearchinMathe- matics Education(CERME13),AlfrédRényiInstituteofMathematics;EötvösLorándUniversityof Budapest,Jul2023,Budapest,Hungary.￿hal-04422642￿, 2023

Between the 12th and 16th centuries, many arithmetical texts were written in Hebrew. These texts ... more Between the 12th and 16th centuries, many arithmetical texts were written in Hebrew. These texts include a variety of topics: arithmetic operations with integers, simple fractions, and fractions in sexagesimal system, extracting roots, ratios, and word problems. However, no in-depth study has been conducted so far about simple fractions in these texts. In this paper, we present both the mathematical content (definitions, theorems, proofs), and the didactic content (how to present the concept of fraction, the choice of algorithms, the types of explanations, and reasonings), as they appear in Hebrew texts.

Sourcebook in the Mathematics of Medieval Europe and North Africa

This chapter covers mathematics written in Hebrew between the eleventh and sixteenth centuries in... more This chapter covers mathematics written in Hebrew between the eleventh and sixteenth centuries in Europe. It starts with the practical and scholarly—as well as earlier and later—Hebrew expositions of arithmetic, from Ibn Ezra's foundational twelfth-century The Book of Number, to Levi ben Gershon's early-fourteenth-century arithmetic. The chapter then follows with two discussions of combinatorics: Ibn Ezra's calculations of the number of possible conjunctions of a given number of planets from among the seven planets, and Ben Gershon's abstract and general discussion of permutations and combinations. Finally, this chapter discusses two important treatises that summarize geometric knowledge in a semi-practical style as well as measurements in a religious context.

Books by Stela Segev

Sourcebook in the Mathematics of Medieval Europe and North Africa-Prince, 2017

Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the... more 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 proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman 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. The 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.

WTM-Verlag eBooks, Dec 31, 2022

During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th c... more During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th centuries on scientific and especially mathematical topics have been deciphered. In these works, one can find mainly topics like arithmetic and geometry. Apart from the mathematical content, however, we can sometimes find (especially in each introduction but not only there), more information about other topics. Below are presented examples of the diverse information that can be found in the introductions to mathematical works written in Hebrew during the 12th–16th centuries, with a special focus on information that allows us to learn about the didactic views of the authors of these works. As research in teaching in general and research in mathematics education are relatively new research disciplines, these views are particularly interesting. Here we find evidence of didactic thinking long before the subject of mathematics teaching became a canonical university discipline. Scholars and students studying mathematics education will be interested in discovering that didactic issues in mathematics teaching are as old as mathematics itself. Special attention will be paid to Elijah Mizrahi's Book of the Number (posthumous print in 1533), a unique figure among the authors of mathematical books in Hebrew from the 12th–16th centuries.

Between the 12 th and 16 th centuries, many arithmetical texts were written in Hebrew. These text... more Between the 12 th and 16 th centuries, many arithmetical texts were written in Hebrew. These texts include a variety of topics: arithmetic operations with integers, simple fractions, and fractions in sexagesimal system, extracting roots, ratios, and word problems. However, no in-depth study has been conducted so far about simple fractions in these texts. In this paper, we present both the mathematical content (definitions, theorems, proofs), and the didactic content (how to present the concept of fraction, the choice of algorithms, the types of explanations, and reasonings), as they appear in Hebrew texts.

“DIG WHERE YOU STAND” 7, 2022

During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th c... more During the last decade, many works in Hebrew (manuscripts and printed books) from the 12th–16th centuries on scientific and especially mathematical topics have been deciphered. In these works, one can find mainly topics like arithmetic and geometry. Apart from the mathematical content, however, we can sometimes find (especially in each introduction but not only there), more information about other topics. Below are presented examples of the diverse information that can be found in the introductions to mathematical works written in Hebrew during the 12th–16th centuries, with a special focus on information that allows us to learn about the didactic views of the authors of these works. As research in teaching in general and research in mathematics education are relatively new research disciplines, these views are particularly interesting. Here we find evidence of didactic thinking long before the subject of mathematics teaching became a canonical university discipline. Scholars and students studying mathematics education will be interested in discovering that didactic issues in mathematics teaching are as old as mathematics itself. Special attention will be paid to Elijah Mizrahi's Book of the Number (posthumous print in 1533), a unique figure among the authors of mathematical books in Hebrew from the 12th–16th centuries.

ThirteenthCongressoftheEuropeanSocietyforResearchinMathe- matics Education(CERME13),AlfrédRényiInstituteofMathematics;EötvösLorándUniversityof Budapest,Jul2023,Budapest,Hungary.￿hal-04422642￿, 2023

Between the 12th and 16th centuries, many arithmetical texts were written in Hebrew. These texts ... more Between the 12th and 16th centuries, many arithmetical texts were written in Hebrew. These texts include a variety of topics: arithmetic operations with integers, simple fractions, and fractions in sexagesimal system, extracting roots, ratios, and word problems. However, no in-depth study has been conducted so far about simple fractions in these texts. In this paper, we present both the mathematical content (definitions, theorems, proofs), and the didactic content (how to present the concept of fraction, the choice of algorithms, the types of explanations, and reasonings), as they appear in Hebrew texts.

Sourcebook in the Mathematics of Medieval Europe and North Africa

This chapter covers mathematics written in Hebrew between the eleventh and sixteenth centuries in... more This chapter covers mathematics written in Hebrew between the eleventh and sixteenth centuries in Europe. It starts with the practical and scholarly—as well as earlier and later—Hebrew expositions of arithmetic, from Ibn Ezra's foundational twelfth-century The Book of Number, to Levi ben Gershon's early-fourteenth-century arithmetic. The chapter then follows with two discussions of combinatorics: Ibn Ezra's calculations of the number of possible conjunctions of a given number of planets from among the seven planets, and Ben Gershon's abstract and general discussion of permutations and combinations. Finally, this chapter discusses two important treatises that summarize geometric knowledge in a semi-practical style as well as measurements in a religious context.

Sourcebook in the Mathematics of Medieval Europe and North Africa-Prince, 2017

Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the... more 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 proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman 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. The 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.