# The Evolution Of The Topic

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Subject Topic Create a written narrative of the evolution of the topic. Include significant contributions from cultures and individuals. Describe important current applications of the topic that would be of particular interest for students.
Number Systems Complex Numbers The earliest reference to complex numbers is from Hero of Alexandria’s work Stereometrica in the 1st century AD, where he contemplates the volume of a frustum of a pyramid.

The proper study first came about in the 16th century when algebraic answers for roots of cubics and quartics were revealed by Italian mathematicians Tartaglia and Cardano. For example, Tartaglia’s formula for a cubic equation x^3=x gives the solution as 1/√3 ((√(-1))^(1/3)+1/(√(-1))^(1/3) ).
For example, the treatment of resistors, capacitors, and inductors are unified by combining them in a single complex number called the impedance, which is the measure of the opposition that a circuit presents to a current when a certain voltage is applied.
Algebra The Quadratic Formula Early methods for solving quadratic equations were purely geometric.

Babylonian tablets contained problems which could be reduced to solving quadratic equations. The Egyptian Berlin Papyrus (2050-1650 BC) contains the solution to a two-term quadratic equation.

Euclid (300 BC) used geometric methods to solve quadratic equations in his book Elements.

In Arithmetica, Diophantus (250 BC) solved quadratic equations with methods which more closely resembled algebra. However, his solution only gave one root, even when both roots are positive.

Brahmagupta (597-668 AD) explicitly described the quadratic formula in words instead of symbols in Brahmasphutasiddhanta in 628 AD. His solution of ax^2+bx=c equated to the formula: x=(√(4ac+b^2 )-b)/2a
In the 9th century, Persian mathematician al-Khwarizmi solved quadratic equations algebraically.

The quadratic formula which covered all cases was first described by Simon Stevin in 1594.

The quadratic formula that we know today was published by Rene Descartes in La Geometrie in 1637.

The first appearance of the general solution in modern mathematical literature was in an 1896 paper by Henry