I'm looking for problems about quadratic function across the ages. For example, in the Babylonian civilization, there are problems which are related with quadratic equation. Besides that, the concept of function was developed through relation between numbers. On the other hand, in Greek Culture the problems were focusing in geometrical interpretation for solving quadratic equation. Al-Khwarizmi, in the Islamic Culture, was the most important scholar because he posed a formula to solve quadratic equation. I've been reading some Al-Khwarizmi's problems and his solution , which could be solved through algebraic ideas.

My principal references are

Swetz, F. J. (2012). Mathematical expeditions: Exploring word problems across the ages. JHU Press.

Kline, M. (1990). Mathematical thought from ancient to modern times (Vol.1, 2 y 3). Oxford University Press.

Boyer, C. B., & Merzbach, U. C. (2011). A history of mathematics. John Wiley & Sons.

Irving, R. (2013). Beyond the quadratic formula. Washington, D.C.: Mathematical Association of America.

Bashmakova, I. G., & Smirnova, G. S. (2000). The beginnings and evolution of algebra (No. 23). Cambridge University Press.

My focus is to study problems posed about quadratic function in some scenes of history of mathematics.

Please, could you help me in this endeavour?

  • $\begingroup$ Sorry, but to me it's still not completely clear what you are asking for. Could you try to make it more clear/precise? What exactly do you expect or want a good answer to address? $\endgroup$ – Danu Aug 31 '15 at 15:40
  • $\begingroup$ You may find the discussion in André Weil, Number Theory: An Approach Through History from Hammurapi to Legendre, useful. $\endgroup$ – Tony Solomonides Sep 3 '15 at 21:03

If you read the papers under with keywords "Holomorphic dynamics", "Mandelbrot set", and MLC conjecture, you discover that quadratic functions are still a hot research topic. A. Douady and J. Hubbard recalled in the late 90s, that when in the early 80-s they were asked "what problems are you working on now ?", they replied "we study quadratic polynomials (of one variable)". A typical reaction was: "Do you hope to find something new about them???"

Since then, two Fields medals were awarded for results on quadratic polynomials:-) So you do not have to restrict yourself to Babylonian mathematics.

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Toomer’s excellent article ‘al-Khwārizmī’ in the Complete Dictionary of Scientific Biography offers a rather more cautious evaluation of al-Khwārizmī’s contribution to the history of algebra. He shows in particular that “both Greek and Hindu algebra had advanced well beyond the elementary stage of al-Khwārizmī’s work”.

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  • $\begingroup$ I agree. John Derbyshire in his book Unknown Quantity also gives details about the algebra of al-Khwārizmī’ and compares it to that to, for example, Diophantus. He judges that Diophantus is the actual father of algebra and used symbols to represent quadratic equations. al-Khwārizmī’ only used words, such as the Greeks before Diophantus. $\endgroup$ – Rory Daulton Aug 30 '15 at 23:49

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