World Book Trivia Challenge Advanced-6/11-numbers

The most famous irrational number is the number pi (π). Pi is the ratio of a circle’s circumference to its diameter. No fraction of integers describes this quantity.
Unlike a rational number, an irrational number can be represented by a nonterminating, nonrepeating decimal. No group of digits in such a number repeats itself in exactly the same order. For example, the first eight decimal digits of π are 3.1415927. But the digits go on forever after that, with no pattern.

During the late 1600's, the German mathematician and philosopher Gottfried Wilhelm Leibniz developed the binary numeral system. However, mathematicians found no practical use for the system until the 1940's, when computers were developed. Computers and other electronic devices used the binary system because they could represent any number with circuits that were in one of two states, on or off.

The Hindus gradually developed a way of eliminating place names. They invented the symbol sunya (meaning empty), which we call zero. With this symbol, they could write "105" instead of "1 sata, 5."

In advanced mathematics, there is a still larger set of numbers, the complex numbers. Complex numbers take the form a + bi. In this formula, a and b are real numbers. The quantity i equals the square root of –1 . No real number, when multiplied by itself, results in a negative number. Thus, the quantity i is called the imaginary unit. The word “imaginary” does not mean the number is made-up or fictional. Nor does the word “real” mean that real numbers are more real than other numbers.

Ratio, «RAY shee oh or RAY shoh», is an ordered pair or set that represents a relationship between numbers or quantities. The numbers in a ratio are called the terms of the ratio.

Natural numbers are also called counting numbers or positive integers. They are the numbers 1, 2, 3, and so on. The set of whole numbers is often said to include the natural numbers, plus zero. Some mathematicians include zero with the natural numbers.

Most ancient people used calculating objects, such as pebbles and sticks, rather than written numbers. An individual manipulated the objects on a board, a cloth, or some other surface. Lines drawn on the surface helped the individual distinguish columns or rows that had different numerical values.
People living in western Africa used a type of small seashell called a cowrie shell for their calculations. The Inca of South America calculated with kernels of wheat on a board. The ancient Greeks and Romans used stones on wood or marble tables. The Chinese and Japanese used small bamboo or wooden reckoning sticks on a board divided into columns.

Complex number is a number with two components: a real part and an imaginary part. Complex numbers are usually written in the form a + bi or a + ib. In this expression, a and b represent real numbers.

The English scientist Sir Isaac Newton invented calculus in the mid-1660's. His discovery was published in 1687. Working independently, the German philosopher and mathematician Gottfried Wilhelm Leibniz also invented calculus in the mid-1670's. He published his findings in 1684 and 1686.

By themselves, numbers are just ideas. But we can write or discuss numbers using symbols called numerals. For example, several different numerals can represent the number we think of as twelve. They include the decimal numeral 12, the Roman numeral XII, and the binary numeral 1100.