### MATH HOMEWORK

What is Mathematics?

Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports.

Since the beginning of recorded history, mathematic discovery has been at the forefront of every civilized society, and in use in even the most primitive of cultures. The needs of math arose based on the wants of society. The more complex a society, the more complex the mathematical needs. Primitive tribes needed little more than the ability to count, but also relied on math to calculate the position of the sun and the physics of hunting.

Several civilizations — in China, India, Egypt, Central America and Mesopotamia — contributed to mathematics as we know it today. The Sumerians were the first people to develop a counting system. Mathematicians developed arithmetic, which includes basic operations, multiplication, fractions and square roots. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in America, the Mayans developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed.

As civilizations developed, mathematicians began to work with geometry, which computes areas and volumes to make angular measurements and has many practical applications. Geometry is used in everything from home construction to fashion and interior design.

Geometry went hand in hand with algebra, invented in the ninth century by a Persian mathematician, Mohammed ibn-Musa al-Khowarizmi. He also developed quick methods for multiplying and diving numbers, which are known as algorithms — a corruption of his name.

Algebra offered civilizations a way to divide inheritances and allocate resources. The study of algebra meant mathematicians were solving linear equations and systems, as well as quadratics, and delving into positive and negative solutions. Mathematicians in ancient times also began to look at number theory. With origins in the construction of shape, number theory looks at figurate numbers, the characterization of numbers, and theorems.

Math and the Greeks

The study of math within early civilizations was the building blocks for the math of the Greeks, who developed the model of abstract mathematics through geometry. Greece, with its incredible architecture and complex system of government, was the model of mathematic achievement until modern times. Greek mathematicians were divided into several schools:

The Ionian School, founded by Thales, who is often credited for having given the first deductive proofs and developing five basic theorems in plane geometry.

The Pythagorean School, founded by Pythagoras, who studied proportion, plane and solid geometry, and number theory.

The Eleatic School, which included Zeno of Elea, famous for his four paradoxes.

The Sophist School, which is credited for offering higher education in the advanced Greek cities. Sophists provided instruction on public debate using abstract reasoning.

The Platonic School, founded by Plato, who encouraged research in mathematics in a setting much like a modern university.

The School of Eudoxus, founded by Eudoxus, who developed the theory of proportion and magnitude and produced many theorems in plane geometry

The School of Aristotle, also known as the Lyceum, was founded by Aristotle and followed the Platonic school.