ID:
509314
Duration (hours):
48
CFU:
6
SSD:
GEOMETRIA
Year:
2025
Overview
Date/time interval
Secondo Semestre (23/02/2026 - 22/05/2026)
Syllabus
Course Objectives
The educational objectives are: familiarity with the concepts taught during the course and with the texts that will be assigned for reading. The results will be assessed through an examination.
Course Prerequisites
The following concepts are required: simple Euclidean geometry, basic notions of elementay number theory, some knowledge of Galois theory, and elementary notions of analysis.
Teaching Methods
The teaching methods will be based primarily on traditional, in-person lectures delivered by the instructor, through which the main topics and concepts of the course will be presented and explained directly to the students.
Assessment Methods
The method of assessment for this course will take the form of a formal oral examination, personally conducted by the instructor. During this evaluation, the student will be expected not merely to recite information, but to exhibit a thorough and nuanced understanding of the range of topics addressed throughout the course. This includes the ability to engage with the material in a critical and reflective manner, articulating insights, connections, and interpretations that demonstrate both depth and sophistication. Moreover, the student should display a well-grounded familiarity with the primary sources and the essential reference texts introduced during the lectures, showing the capacity to contextualize these works within the broader framework of the subject matter. In essence, the examination will serve as an opportunity for the student to reveal the extent to which they have internalized, contemplated, and are able to communicate the intellectual substance of the course, thereby translating acquired knowledge into reasoned, articulate discourse before the instructor.
Texts
The textbooks will be:
• Heath, Thomas Little. A history of Greek mathematics. Vol. 1-2. Claren- don, 1921.
• Netz, Reviel. A new history of Greek mathematics. Cambridge University Press, 2022.
The passages we will comment are found in:
• Thomas, Ivor. Greek Mathematical Works: Volume I, Thales to Euclid. (Loeb Classical Library No. 335). 1939.
• Thomas, Ivor. Selections illustrating the history of Greek mathematics. Vol. II. From Aristarchus to Pappus, Loeb Classical Library.
Other useful general works are:
• Becker, Oskar. Das mathematische Denken der Antike. No. 3. Vanden- hoeck & Ruprecht, 1966.
• Youschkevitch, Adolf-P. Les Math ́ematiques Arabes: Viiie-Xve Si`ecles. (1976).
• Rashed, Roshdi. Encyclopedia of the history of Arabic science. Routledge, 2002.
• Netz, Reviel. The shaping of deduction in Greek mathematics: A study in cognitive history. Vol. 51. Cambridge University Press, 2003.
• Netz, Reviel. The transformation of mathematics in the early Mediter- ranean world: From problems to equations. Cambridge University Press, 2004.
• Christianidis, Jean, ed. Classics in the history of Greek mathematics. Vol. 240. Springer Science & Business Media, 2004.
• Zhmud, Leonid. The origin of the History of Science in Classical Antiq- uity. Walter de Gruyter, 2006.
On special problems
(A star * denotes particularly recommended references.)
2
Egyptian, Babylonian
• * Neugebauer, Otto. The exact sciences in antiquity. Providence, Rhode Island: Brown University Press (1957).
• * Neugebauer, Otto. Mathematische Keilschrift-Texte: mathematical cuneiform texts. Springer-Verlag, 2013.
• Vogel, Kurt. Vorgriechische Mathematik. Vol. 2. H. Schroedel, 1958.
• * Høyrup, Jens. Lengths, widths, surfaces: A portrait of old Babylonian
algebra and its kin. Springer Science & Business Media, 2013. Pythagoreans
• Burkert, Walter. Lore and science in ancient Pythagoreanism. Harvard University Press, 1972.
• Zhmud, Leonid J. Wissenschaft, Philosophie Und Religion Im Fru ̈hen Pythagoreismus. (1997).
• Huffmann, Carl. Archytas of Tarentum: Pythagorean, philosopher and mathematician king. Cambridge University Press, 2005.
• Zhmud, Leonid. Pythagoras and the early Pythagoreans. Oxford Univer- sity Press, 2012.
• Huffman, Carl A., ed. A History of Pythagoreanism. Cambridge Univer- sity Press, 2014.
Huffman, Carl A., Archytas of Tarentum: Pythagorean, philosopher and math- ematician king., Cambridge University Press, 2005.
Hippokrates
• Becker, Oskar. Zur Textgestaltung des eudemischen Berichts u ̈ber die Quadratur der M ̈ondchen durch Hippokrates von Chios. Springer, 1936.
• Lloyd, Geoffrey. The alleged fallacy of Hippocrates of Chios. Apeiron 20.2 (1987): 103-128.
• Netz, Reviel. Eudemus of Rhodes, Hippocrates of Chios and the earliest form of a Greek mathematical text. Centaurus 46.4 (2004): 243-286.
• Høyrup, Jens. Hippocrates of Chios–his Elements and his lunes: A critique of circular reasoning. AIMS mathematics 5.1 (2020): 158-184.
• Heath, Thomas Little. A history of Greek mathematics. Vol. 1-2. Claren- don, 1921.
• Netz, Reviel. A new history of Greek mathematics. Cambridge University Press, 2022.
The passages we will comment are found in:
• Thomas, Ivor. Greek Mathematical Works: Volume I, Thales to Euclid. (Loeb Classical Library No. 335). 1939.
• Thomas, Ivor. Selections illustrating the history of Greek mathematics. Vol. II. From Aristarchus to Pappus, Loeb Classical Library.
Other useful general works are:
• Becker, Oskar. Das mathematische Denken der Antike. No. 3. Vanden- hoeck & Ruprecht, 1966.
• Youschkevitch, Adolf-P. Les Math ́ematiques Arabes: Viiie-Xve Si`ecles. (1976).
• Rashed, Roshdi. Encyclopedia of the history of Arabic science. Routledge, 2002.
• Netz, Reviel. The shaping of deduction in Greek mathematics: A study in cognitive history. Vol. 51. Cambridge University Press, 2003.
• Netz, Reviel. The transformation of mathematics in the early Mediter- ranean world: From problems to equations. Cambridge University Press, 2004.
• Christianidis, Jean, ed. Classics in the history of Greek mathematics. Vol. 240. Springer Science & Business Media, 2004.
• Zhmud, Leonid. The origin of the History of Science in Classical Antiq- uity. Walter de Gruyter, 2006.
On special problems
(A star * denotes particularly recommended references.)
2
Egyptian, Babylonian
• * Neugebauer, Otto. The exact sciences in antiquity. Providence, Rhode Island: Brown University Press (1957).
• * Neugebauer, Otto. Mathematische Keilschrift-Texte: mathematical cuneiform texts. Springer-Verlag, 2013.
• Vogel, Kurt. Vorgriechische Mathematik. Vol. 2. H. Schroedel, 1958.
• * Høyrup, Jens. Lengths, widths, surfaces: A portrait of old Babylonian
algebra and its kin. Springer Science & Business Media, 2013. Pythagoreans
• Burkert, Walter. Lore and science in ancient Pythagoreanism. Harvard University Press, 1972.
• Zhmud, Leonid J. Wissenschaft, Philosophie Und Religion Im Fru ̈hen Pythagoreismus. (1997).
• Huffmann, Carl. Archytas of Tarentum: Pythagorean, philosopher and mathematician king. Cambridge University Press, 2005.
• Zhmud, Leonid. Pythagoras and the early Pythagoreans. Oxford Univer- sity Press, 2012.
• Huffman, Carl A., ed. A History of Pythagoreanism. Cambridge Univer- sity Press, 2014.
Huffman, Carl A., Archytas of Tarentum: Pythagorean, philosopher and math- ematician king., Cambridge University Press, 2005.
Hippokrates
• Becker, Oskar. Zur Textgestaltung des eudemischen Berichts u ̈ber die Quadratur der M ̈ondchen durch Hippokrates von Chios. Springer, 1936.
• Lloyd, Geoffrey. The alleged fallacy of Hippocrates of Chios. Apeiron 20.2 (1987): 103-128.
• Netz, Reviel. Eudemus of Rhodes, Hippocrates of Chios and the earliest form of a Greek mathematical text. Centaurus 46.4 (2004): 243-286.
• Høyrup, Jens. Hippocrates of Chios–his Elements and his lunes: A critique of circular reasoning. AIMS mathematics 5.1 (2020): 158-184.
Contents
Program of the course
1. Introduction, the sources for the history of Ancient and Greek Mathemat- ics.
2. Egyptian Mathematics.
3. Babylonian Mathematics.
4. The dawn of Greek speculation. Eupalinos, Hecateus, Thales and the Ionians.
5. The Pythagoreans. Arithmetic, Music, Geometry and Application of Ar- eas.
6. Hippokrates, Theodorus, Theetetus and the problem of Irrationals.
7. Parmenides, Zeno and Democritus, the problem of Motion and Infinitesi- mals.
8. The Mathematics of Plato’s Academy.
9. Eudoxus, Astronomy and Theory of Proportions.
10. Mathematics and Metaphysics in Aristotle.
11. Alexandrian Mathematics and Science. Euclid’s Elements.
12. Archimedes.
13. Apollonius and Diophantus.
14. The transmission of Greek Mathematics to the Arabs. A sketch of Arabic Mathematics.
1. Introduction, the sources for the history of Ancient and Greek Mathemat- ics.
2. Egyptian Mathematics.
3. Babylonian Mathematics.
4. The dawn of Greek speculation. Eupalinos, Hecateus, Thales and the Ionians.
5. The Pythagoreans. Arithmetic, Music, Geometry and Application of Ar- eas.
6. Hippokrates, Theodorus, Theetetus and the problem of Irrationals.
7. Parmenides, Zeno and Democritus, the problem of Motion and Infinitesi- mals.
8. The Mathematics of Plato’s Academy.
9. Eudoxus, Astronomy and Theory of Proportions.
10. Mathematics and Metaphysics in Aristotle.
11. Alexandrian Mathematics and Science. Euclid’s Elements.
12. Archimedes.
13. Apollonius and Diophantus.
14. The transmission of Greek Mathematics to the Arabs. A sketch of Arabic Mathematics.
Course Language
Italian
More information
At the present time, it does not appear to be necessary to provide any additional information regarding this course beyond what has already been outlined and discussed in the preceding sections. The details previously presented are considered sufficient to give a clear and comprehensive understanding of the nature, objectives, and structure of the course, and no further specifications are deemed required at this stage.
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