Today I had a student in my college algebra class ask me why "Quadratic Equations" are so named. If we have a polynomial of degree 3 set equal to zero, we call it a cubic equation and that makes sense to these students. However, this particular student is curious because she sees "Q-U-A-D" in quadratic and thinks of four, yet the polynomial in such an equation is only of degree 2. I've never encountered this question before and I was at a loss for an explanation. Does anyone know the origin of the term "quadratic equation"? I would be very grateful to receive an answer.
Thank you in advance.
Jeff Darrow Idaho State University
Jeff, Look in Chapter V of "The Great Art or Rules of Algebra' by Girolamo Cardano, translated and edited bt T. Richard Witmer, MIT 1968. When he says to complete the square, he really means to complete a geometric square. Cardano gives the proper credit to Euclid in II, 4 of the elements. Euclid solved quadratic equations geometrically and x^2 ( x square ) really was a square evan though we use a 2. Peace, Don Cook