Quadratic Equations, Completing the Square and Two Algorithms to Find the Quadratic Extremum (The New Mathematics for the Millions Book 8)

In school most high students wonder why quadratics are taught and wonder why they must learn to “complete the square”.

The examples in this book apply to a wide cross section of the types of Quadratic Extremum questions that most professionals come across in their work. It should be self-evident why quadratics are taught, as well as the technique of “completing the square.”

It is said by many Historians of Mathematics that the mathematician who developed the “completing the square” technique used in solving quadratic equations was the 9th century Muslim mathematician Abu Ja’far Muhammad ibn Musa Al- Khwarismi, also know as Alkarismi.

Much like the ancient mathematicians Pythagoras and Euclid, very little is known for certain about Alkarismi except that he was born circa 780 A.D., most likely south of the Aral Sea and east of the Caspian Sea. Alkarismi was an Arab intellectual who worked translating scholarly works from Ancient Greece, and from sources in India and Persia contemporary to his life-time, at the House of Wisdom in Baghdad.

One of Alkarismi’s important treatise was Algoritmi de Numero. It is from the title of this Latin translation of this treatise that we get the word Algorithm.

Alkarismi also wrote a treatise titled Hisab Al-Jabar w’Al-Muqabala. Drawing from the Oxford English Dictionary definition the title translated means “the science of restoring what is missing and equating like with like.” It is said that the term Algebra draws from Al-Jabar in the title of Alkarismi’s treatise.

The term Quadratic draws its meaning from the Latin word Quadratum, which is a four-sided figure. The name Quadratic is meant to remind us how we can solve the equations by “completing the square” – by drawing or completing the Quadratum.