Bibliography
Behroozi, F. “A Fresh Look at the Catenary.” European Journal of Physics 35, no. 5 (2014): 055007. https://doi.org/10.1088/0143-0807/35/5/055007.
Bostan, Alin, Frédéric Chyzak, Grégoire Lecerf, Bruno Salvy, and Éric Schost. “Differential Equations for Algebraic Functions.” In Proceedings of ISSAC 2007, 25–32. New York: ACM, 2007. https://arxiv.org/abs/cs/0703121.
Branson, William B. “Solving the Cubic with Cardano.” Convergence. September 2013. https://doi.org/10.4169/convergence20131001. Mathematical Association of America.
Cajori, Florian. A History of Mathematical Notations. Vol. 2, Notations Mainly in Higher Mathematics. Chicago: Open Court Publishing Company, 1929. https://webhomes.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf.
Cardano, Girolamo. The Great Art; or, The Rules of Algebra. Translated and edited by T. Richard Witmer. Cambridge, MA: MIT Press, 1968.
Chun, Byung-Kyu, Andy Liu, and Daniel van Vliet. “Dissecting Squares into Similar Rectangles.” Crux Mathematicorum 22 (1996): 241–248. https://www.cms.math.ca/wp-content/uploads/crux-pdfs/CRUXv22n6.pdf.
“Complex Number.” Encyclopedia of Mathematics. https://encyclopediaofmath.org/wiki/Complex_number.
Confalonieri, Sara. The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations: Gerolamo Cardano’s De Regula Aliza. Wiesbaden: Springer Spektrum, 2015.
de Spinadel, Vera W., and Antonia Redondo Buitrago. “Towards van der Laan’s Plastic Number in the Plane.” Journal for Geometry and Graphics 13, no. 2 (2009): 163–175. https://www.heldermann-verlag.de/jgg/jgg13/j13h2spin.pdf.
Euclid. Elements. Book VI, definition 3. Online edition by David E. Joyce. Clark University. Accessed October 14, 2026. https://mathcs.clarku.edu/~djoyce/elements/bookVI/defVI3.html.
Euler, Leonhard. Introductio in analysin infinitorum. Vol. 1. Lausanne: Marc-Michel Bousquet, 1748. https://archive.org/details/introductioanaly00eule.
Galois, Évariste. “Œuvres mathématiques d’Évariste Galois.” With introduction by Joseph Liouville. Journal de mathématiques pures et appliquées, 1st ser., 11 (1846): 381–444. https://www.numdam.org/item/JMPA_1846_1_11__381_0.pdf.
Hartshorne, Robin. “Viète’s Construction of the Regular Heptagon.” University of California, Berkeley, Department of Mathematics. https://math.berkeley.edu/~robin/Viete/construction.html.
Helfgott, Harald, and Michel Helfgott. “A Modern Vision of the Work of Cardano and Ferrari on Quartics.” Convergence, February 2010. https://doi.org/10.4169/loci003312.
Houzel, Christian. “The Work of Niels Henrik Abel.” In The Legacy of Niels Henrik Abel, edited by Olav Arnfinn Laudal and Ragni Piene. Berlin: Springer, 2004. https://abelprisen.no/sites/default/files/2021-05/houzel_the_work.pdf.
Huang, Hua-Lin, Shengyuan Ruan, Xiaodan Xu, and Yu Ye. “Solving Algebraic Equations by Completing Powers.” American Mathematical Monthly 132, no. 3 (2025): 218–236. https://doi.org/10.1080/00029890.2024.2421145. Earlier preprint version: “Solving Cubic Equations by Completing the Cube and Higher Degree Equations by Completing Powers,” arXiv:2301.07375v3 (March 13, 2024), https://arxiv.org/html/2301.07375v3.
Jawalgekar, Prasad, D. G. Sooryanarayan, and K. Ramasubramanian. “Gaṇitakaumudī of Nārāyaṇa Paṇḍita: A Gem among the Pāṭīgaṇita Texts in Indian Mathematics.” Bhāvanā 7, no. 1 (January 2023). https://bhavana.org.in/ga%E1%B9%87itakaumudi-of-naraya%E1%B9%87a-pa%E1%B9%87%E1%B8%8Dita/.
Jones, Alexander. Numbers on Clay. New York: Institute for the Study of the Ancient World, New York University, 2010. https://isaw.nyu.edu/exhibitions/before-pythagoras/pamphlet.pdf.
Katscher, Friedrich. “Who Is Tartaglia Really?” Convergence. Mathematical Association of America, December 2006. https://old.maa.org/press/periodicals/convergence/who-is-tartaglia-really.
Lucian. “A Slip of the Tongue in Salutation.” In The Works of Lucian of Samosata. Translated by H. W. Fowler and F. G. Fowler. Oxford: Clarendon Press, 1905. Section 5. https://lucianofsamosata.info/wiki/doku.php?id=home:texts_and_library:essays:a-slip-of-the-tongue-in-salutation.
Merriam-Webster. “Trigonometry.” Merriam-Webster.com Dictionary. Accessed October 14, 2026. https://www.merriam-webster.com/dictionary/trigonometry.
Miller, Jeff. “Cosine.” In “Earliest Known Uses of Some of the Words of Mathematics (C).” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 14, 2026. https://mathshistory.st-andrews.ac.uk/Miller/mathword/c/.
Neugebauer, Otto, and Abraham J. Sachs. Mathematical Cuneiform Texts. American Oriental Series 29. New Haven: American Oriental Society, 1945.
O’Connor, J. J., and E. F. Robertson. “Babylonian Mathematics.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 3, 2026. https://mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_mathematics/.
O’Connor, J. J., and E. F. Robertson. “François Viète.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 14, 2026. https://mathshistory.st-andrews.ac.uk/Biographies/Viete/.
O’Connor, J. J., and E. F. Robertson. “The Fundamental Theorem of Algebra.” MacTutor History of Mathematics Archive. University of St Andrews. https://mathshistory.st-andrews.ac.uk/HistTopics/Fund_theorem_of_algebra/.
O’Connor, J. J., and E. F. Robertson. “Girolamo Cardano.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 3, 2026. https://mathshistory.st-andrews.ac.uk/Biographies/Cardan/.
O’Connor, J. J., and E. F. Robertson. “Lodovico Ferrari.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 3, 2026. https://mathshistory.st-andrews.ac.uk/Biographies/Ferrari/.
O’Connor, J. J., and E. F. Robertson. “Niels Henrik Abel.” MacTutor History of Mathematics Archive. University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Abel/.
O’Connor, J. J., and E. F. Robertson. “Nine Chapters on the Mathematical Art.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 14, 2026. https://mathshistory.st-andrews.ac.uk/HistTopics/Nine_chapters/.
O’Connor, J. J., and E. F. Robertson. “Pythagoras’s Theorem in Babylonian Mathematics.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 14, 2026. https://mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_Pythagoras/.
O’Connor, J. J., and E. F. Robertson. “Quadratic, Cubic and Quartic Equations.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 3, 2026. https://mathshistory.st-andrews.ac.uk/HistTopics/Quadratic_etc_equations/.
O’Connor, J. J., and E. F. Robertson. “Rafael Bombelli.” MacTutor History of Mathematics Archive. University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Bombelli/.
O’Connor, J. J., and E. F. Robertson. “Scipione del Ferro.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 14, 2026. https://mathshistory.st-andrews.ac.uk/Biographies/Ferro/.
O’Connor, J. J., and E. F. Robertson. “Tartaglia.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 3, 2026. https://mathshistory.st-andrews.ac.uk/Biographies/Tartaglia/.
O’Connor, J. J., and E. F. Robertson. “Tartaglia versus Cardan.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 3, 2026. https://mathshistory.st-andrews.ac.uk/HistTopics/Tartaglia_v_Cardan/.
O’Connor, J. J., and E. F. Robertson. “Trigonometric Functions.” MacTutor History of Mathematics Archive. University of St Andrews. June 1996. https://mathshistory.st-andrews.ac.uk/HistTopics/Trigonometric_functions/.
O’Connor, J. J., and E. F. Robertson. “Vincenzo Riccati.” MacTutor History of Mathematics Archive. University of St Andrews. Accessed October 15, 2026. https://mathshistory.st-andrews.ac.uk/Biographies/Riccati_Vincenzo/.
The On-Line Encyclopedia of Integer Sequences. “A092526.” Accessed October 14, 2026. https://oeis.org/A092526.
Osborn, G. “109. [D. 6. d.] Mnemonic for Hyperbolic Formulae.” The Mathematical Gazette 2, no. 34 (July 1902): 189. https://doi.org/10.2307/3602492.
Pápay, Gyula. “Mercator’s Geometric Method in the Construction of His Projection from 1569.” KN – Journal of Cartography and Geographic Information 72 (2022): 261–267. https://doi.org/10.1007/s42489-022-00115-5.
Pepe, Luigi. “Teoria generale delle equazioni … (1799).” Matematica Italiana. Il Giardino di Archimede, Università di Firenze. https://archimede.dimai.unifi.it/archimede/matematicaitaliana/schede_opere/5ruffini99.html.
Prodanov, Emil M. “The Siebeck–Marden–Northshield Theorem and the Real Roots of the Symbolic Cubic Equation.” Results in Mathematics 77, article 126 (2022). https://doi.org/10.1007/s00025-022-01667-8.
Rashed, Roshdi, and Bijan Vahabzadeh. Omar Khayyam, the Mathematician. New York: Bibliotheca Persica Press, 2000.
Redondo Buitrago, Antonia. “Polygons, Diagonals, and the Bronze Mean.” Nexus Network Journal 9 (2007): 321–326. https://doi.org/10.1007/s00004-007-0046-x.
Rothman, Tony. “Cardano v Tartaglia: The Great Feud Goes Supernatural.” Author preprint, 2013. https://arxiv.org/abs/1308.2181.
Rothman, Tony. “Genius and Biographers: The Fictionalization of Évariste Galois.” American Mathematical Monthly 89, no. 2 (1982): 84–106. https://doi.org/10.1080/00029890.1982.11995389.
Smithsonian Institution, National Museum of American History. “Linear Slide Rules.” https://www.si.edu/spotlight/slide-rules/linear-slide-rules.
Stipp, David. A Most Elegant Equation: Euler’s Formula and the Beauty of Mathematics. New York: Basic Books, 2017.
Swinton, Jonathan, Erinma Ochu, and The MSI Turing’s Sunflower Consortium. “Novel Fibonacci and Non-Fibonacci Structure in the Sunflower: Results of a Citizen Science Experiment.” Royal Society Open Science 3, no. 5 (2016): 160091. https://doi.org/10.1098/rsos.160091.
Vahabzadeh, Bijan. “Khayyam, Omar xiv. As Mathematician.” Encyclopaedia Iranica. Published May 7, 2014. Updated August 29, 2017. https://www.iranicaonline.org/articles/khayyam-omar/khayyam-omar-xiv-as-mathematician/.
Whipple Museum of the History of Science, University of Cambridge. “Tables.” https://www.whipplemuseum.cam.ac.uk/explore-whipple-collections/calculating-devices/tables.
Wilson, Robin. Euler’s Pioneering Equation: The Most Beautiful Theorem in Mathematics. Oxford: Oxford University Press, 2018.
Zhivkov, Angel. “Resolution of Degree ≤6 Algebraic Equations by Genus Two Theta Constants.” Preprint, 2002. https://doi.org/10.18452/2623.
Image Credits
Figure 1.1. Cuneiform tablet: fragment of a mathematical problem text, ca. late 1st millennium BCE. Clay. The Metropolitan Museum of Art, New York, Purchase, 1886, 86.11.404. The Met Open Access, CC0.