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The town of Babylon, located in modern-day Iraq, was founded by ancient Akkadian-speaking people of southern Mesopotamia.
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Using a geometric method of completing the square, Babylonians moved pieces of rectangles and squares to solve. They needed a method of finding how much to increase the size of their fields to pay the tax collector.
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Egyptian engineers, scribes, and priests kept tables for all possible sides and shapes of squares and rectangles. Evidence that ancient Egyptians could solve some quadratic equations was recorded on the Berlin Papyrus.
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1792-1750 BCE
King Hammurabi brought central and southern Mesopotamia under Babylonian rule.
After his death, the Babylonian empire reverted to several small kingdoms. -
Arab invasion led by ʿAmr ibn al-ʿĀṣ in AD 639–642
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Cyrus the Great (Persian king) conquered Babylon
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Pythagoras used geometry, and refused to allow that ratios of the area of squares and the length of their sides could be anything other than rational.
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Using a strictly geometric approach, Euclid found a general procedure to solving quadratics. He concluded that irrational numbers exist.
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Indian mathematician Brahmagupta's understanding of negative numbers allowed for solving quadratic equations with two solutions, one possibly negative.
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Mathematicians of al-Khwārīzmī’s time did not employ the concept of negative numbers, so Muhammad ibn Mūsa al-Khwārīzmī did not use negative coefficients or accept negative solutions.
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We know about Sridhara through the writings of Bhaskara II, also an Indian mathematician. He was one of the first to give a formula for solving quadratic equations. His formula was very close to the derivation of the quadratic formula that we use.
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Bhaskara II demonstrated that the quadratic equation has two roots by discovering that any positive number (the discriminant of the quadratic formula) has two square roots.
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"Abraham bar Hiyya's book, Treatise on Measurement and Calculation, is the earliest Arab algebra book in Europe. It contains the complete solution of the general quadratic. 1145 was also the year that al-Khwarizmi's book was translated." O'Connor, JJ, and EF Robertson. “Abraham Bar Hiyya - Biography.” Maths History, Nov. 1999, mathshistory.st-andrews.ac.uk/Biographies/Abraham/.
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People embraced education, classical arts, science, mathematics, and literature.
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He combined Al-Khwarismi's solution with Euclid's geometric solution. He also acknowledged the existence of imaginary numbers (roots of negative numbers).
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Shakespeare is often considered "the greatest dramatist" of all time" (Biography.com, 2019)
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Viete used vowels to represent unknowns in equations and consonants to represent known quantities. By using letters to represent known and unknown quantities, he was able to write general forms of equations, rather than relying on specific examples.
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Descartes wrote La Gèometrie, which introduced the convention where letters near the beginning of the alphabet represent known quantities and letters near the end represent unknowns. The quadratic formula adopted the form as we know it today.
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On July 4, 1776, the Continental Congress voted to adopt the Declaration of Independence
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Loh, a mathematician at Carnegie Mellon University, discovered a simple method for solving quadratic equations without using the quadratic formula.
