The Quadratic Equation History

HISTORY OF THE QUADRATIC EQUATION

Chapter 1 The original problem 2000 (or so)BC

Egyptian, Chinese and Babylonian engineers were really smart people. They knew that it's possible to store nine times more bales of hay if the side of the square loft is tripled.

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They also found out how to calculate the area of more complex shapes like rectangles, T-shapes. . . However, they didn't know how to calculate the sides of the shapes if the area was given- which was often what their clients really needed. And so, this is the original problem: a certain shape must be scaled with a total area, and what are the lengths of the sides to make a floor plan.

HISTORY OF THE QUADRATIC EQUATION

Chapter 2 1500BC The Beginnings – Egypt

Egyptian mathematics did not know equations and numbers like we do nowadays. Egyptian wise men (engineers, scribes and priests) calculated the area for all possible sides and shapes of squares and rectangles and made a look-up table.

So, if someone wanted a loft with a certain shape and a certain capacity to store bales of papyrus, the engineer would go to his table and find the most fitting design. The engineers did not have time to calculate so the table they used was a reproduction of a master look-up table. The copyists didn't know anything about maths so sometimes they made mistakes, and copies of the copies were not very clear.

These tables still exist, and it is possible to see the errors!

HISTORY OF THE QUADRATIC EQUATION

Chapter 3 400 BCE The Next Step - Babylon and China

The Egyptian have a good method to solve quadratic equations, but Babylonian found a more general solution. They used a numbersystem that was similar to the one we use today with time and degrees: the hexagesimal system. By 400 BC they found a method called 'completing the square' to solve generic problems involving areas. Around the same time, or a bit later, this method also appears in Chinese documents.

The Chinese, like the Egyptians, also did not use a numeric system, but they calculate areas with simple mathematical operations, using the abacus.

HISTORY OF THE QUADRATIC EQUATION

Chapter 4 300BC Geometry - Hellenistic Mediterranean Area

Pythagoras (500 BC in Croton, Italy) and Euclid (300 BC in Alexandria, Egypt) found a general procedure to solve the quadratic equation based on geometry.

Pythagoras noted that the ratios between the area of a square and the length of the side were not always integer, but he refused to accept irrational numbers.

Euclid went even further and concluded that irrational numbers exist.

Many wars occurring in Europe, and also the early Middle Ages turned the mathematical world in Europe silent until the 13th Century.

HISTORY OF THE QUADRATIC EQUATION Chapter 5 700AD All Numbers – India

Hindu mathematics has used the decimal system (the one we use) since 600AD. Hindu people used mathematics in commerce. If someone had a debt the numbers would be negative, if someone had a credit the numbers would be positive.

Around 700AD Brahmagupta used irrational numbers and found a general solution for the quadratic equation; he also recognised two roots in the solution.

The final, complete solution as we know it today came around 1100AD, by another Hindu mathematician called Baskhara, who was the first to recognise that any positive number has two square roots.

HISTORY OF THE QUADRATIC EQUATION Chapter 6 820AD Powerful Islamic Science - Persia Around 820AD, near Baghdad, Mohammad bin Musa Al-Khwarismi, a famous Islamic mathematician who knew Hindu mathematics, also studied the quadratic equation. He didn’t like negative solutions so he gave a positive solution to the quadratic equation. This particular solution was brought to Europe by Jewish mathematician/astronomer Abraham bar Hiyya (Savasorda in Latin) who lived in Barcelona around 1100.

Chapter 7 1500AD Renaissance - Europe By 1545 Girolamo Cardano, one of the best algebraists of his time, compiled the works related to the quadratic equations. He blended AlKhwarismi's solution with the Euclidean geometry.

At the end of the 16th Century the mathematical notation and symbolism was introduced by François Viète, in France.

In 1637, when René Descartes published La Géométrie, modern Mathematics was born, and the quadratic formula has adopted the form we know today.