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One half is the irreducible fraction resulting from dividing one by two (1⁄2), or the fraction resulting from dividing …

Postal stamp, Ireland, 1940: one halfpenny postage due.

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1. One half – One half is the irreducible fraction resulting from dividing one by two, or the fraction resulting from dividing any number by its double. Multiplication by one half is equivalent to division by two, or halving, conversely, division by one half is equivalent to multiplication by two, or doubling, one half appears often in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts, for instance, the area S of a triangle is computed S = 1⁄2 × base × perpendicular height. The Riemann hypothesis states that every nontrivial complex root of the Riemann zeta function has a part equal to 1⁄2. One half has two different decimal expansions, the familiar 0.5 and the recurring 0.49999999 and it has a similar pair of expansions in any even base. It is a trap to believe these expressions represent distinct numbers. Equals 1 for detailed discussion of a related case, in odd bases, one half has no terminating representation, only a single representation with a repeating fractional component, such as 0.11111111. in ternary. 1⁄2 is also one of the few fractions to usually have a key of its own on typewriters and it also has its own code point in some early extensions of ASCII at 171. In Unicode, it has its own unit at U+00BD in the C1 Controls and Latin-1 Supplement block. List of numbers Division by two

2. Decimal – This article aims to be an accessible introduction. For the mathematical definition, see Decimal representation, the decimal numeral system has ten as its base, which, in decimal, is written 10, as is the base in every positional numeral system. It is the base most widely used by modern civilizations. Decimal fractions have terminating decimal representations and other fractions have repeating decimal representations, Decimal notation is the writing of numbers in a base-ten numeral system. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, Roman numerals have symbols for the decimal powers and secondary symbols for half these values. Brahmi numerals have symbols for the nine numbers 1–9, the nine decades 10–90, plus a symbol for 100, Chinese numerals have symbols for 1–9, and additional symbols for powers of ten, which in modern usage reach 1072. Positional decimal systems include a zero and use symbols for the ten values to represent any number, positional notation uses positions for each power of ten, units, tens, hundreds, thousands, etc. The position of each digit within a number denotes the multiplier multiplied with that position has a value ten times that of the position to its right. There were at least two independent sources of positional decimal systems in ancient civilization, the Chinese counting rod system. Ten is the number which is the count of fingers and thumbs on both hands, the English word digit as well as its translation in many languages is also the anatomical term for fingers and toes. In English, decimal means tenth, decimate means reduce by a tenth, however, the symbols used in different areas are not identical, for instance, Western Arabic numerals differ from the forms used by other Arab cultures. A decimal fraction is a fraction the denominator of which is a power of ten. g, Decimal fractions 8/10, 1489/100, 24/100000, and 58900/10000 are expressed in decimal notation as 0.8,14.89,0.00024,5.8900 respectively. In English-speaking, some Latin American and many Asian countries, a period or raised period is used as the separator, in many other countries, particularly in Europe. The integer part, or integral part of a number is the part to the left of the decimal separator. The part from the separator to the right is the fractional part. It is usual for a number that consists only of a fractional part to have a leading zero in its notation. Any rational number with a denominator whose only prime factors are 2 and/or 5 may be expressed as a decimal fraction and has a finite decimal expansion. 1/2 =0.5 1/20 =0.05 1/5 =0.2 1/50 =0.02 1/4 =0.25 1/40 =0.025 1/25 =0.04 1/8 =0.125 1/125 =0.008 1/10 =0

3. Magic square – In recreational mathematics, a magic square is a n × n square grid filled with distinct positive integers in the range 1,2. N2 such that each contains a different integer and the sum of the integers in each row, column. The sum is called the constant or magic sum of the magic square. A square grid with n cells on each side is said to have order n. In regard to magic sum, the problem of magic squares only requires the sum of row, column and diagonal to be equal. Thus, although magic squares may contain negative integers, they are just variations by adding or multiplying a number to every positive integer in the original square. Magic squares are called normal magic squares, in the sense that there are non-normal magic squares which integers are not restricted in 1,2. However, in places, magic squares is used as a general term to cover both the normal and non-normal ones, especially when non-normal ones are under discussion. Moreover, the term magic squares is also used to refer to various types of word squares. Magic squares have a history, dating back to at least 650 BC in China. At various times they have acquired magical or mythical significance, and have appeared as symbols in works of art, the constant that is the sum of every row, column and diagonal is called the magic constant or magic sum, M. Every normal magic square has a constant dependent on the n, calculated by the formula M = n /2. N2 is n 2 /2 which when divided by the n is the magic constant. For normal magic squares of orders n =3,4,5,6,7, and 8, the constants are, respectively,15,34,65,111,175. Normal magic squares of all sizes can be constructed except 2×2, any magic square can be rotated and reflected to produce 8 trivially distinct squares. In magic square theory, all of these are deemed equivalent. Excluding rotations and reflections, there is exactly one 3×3 magic square, exactly 880 4×4 magic squares, for the 6×6 case, there are estimated to be approximately 1.8 ×1019 squares. Then all magic squares of an order have the same moment of inertia as each other

4. Typewriter – A typewriter is a mechanical or electromechanical machine for writing characters similar to those produced by printers movable type. A typewriter operates by means of keys that strike a ribbon to transmit ink or carbon impressions onto paper, typically, a single character is printed on each key press. The machine prints characters by making ink impressions of type elements similar to the used in movable type letterpress printing. At the end of the century, the term typewriter was also applied to a person who used a typing machine. After its invention in the 1860s, the quickly became an indispensable tool for practically all writing other than personal handwritten correspondence. It was widely used by writers, in offices. As with the automobile, telephone, and telegraph, a number of people contributed insights, historians have estimated that some form of typewriter was invented 52 times as thinkers tried to come up with a workable design. Some of the early typing instruments, In 1575 an Italian printmaker, Francesco Rampazzetto, invented the scrittura tattile, in 1714, Henry Mill obtained a patent in Britain for a machine that, from the patent, appears to have been similar to a typewriter. In 1802 Italian Agostino Fantoni developed a particular typewriter to enable his blind sister to write, in 1808 Italian Pellegrino Turri invented a typewriter. He also invented carbon paper to provide the ink for his machine, in 1823 Italian Pietro Conti di Cilavegna invented a new model of typewriter, the tachigrafo, also known as tachitipo. In 1829, William Austin Burt patented a machine called the Typographer which, the Science Museum describes it merely as the first writing mechanism whose invention was documented, but even that claim may be excessive, since Turris invention pre-dates it. Even in the hands of its inventor, this machine was slower than handwriting, Burt and his promoter John D. Sheldon never found a buyer for the patent, so the invention was never commercially produced, because the typographer used a dial, rather than keys, to select each character, it was called an index typewriter rather than a keyboard typewriter. Index typewriters of that era resemble the squeeze-style embosser from the 1960s more than they resemble the modern keyboard typewriter, by the mid-19th century, the increasing pace of business communication had created a need for mechanization of the writing process. Stenographers and telegraphers could take down information at rates up to 130 words per minute, from 1829 to 1870, many printing or typing machines were patented by inventors in Europe and America, but none went into commercial production. Charles Thurber developed multiple patents, of which his first in 1843 was developed as an aid to the blind, in 1855, the Italian Giuseppe Ravizza created a prototype typewriter called Cembalo scrivano o macchina da scrivere a tasti. It was a machine that let the user see the writing as it was typed. In 1861, Father Francisco João de Azevedo, a Brazilian priest, made his own typewriter with basic materials and tools, such as wood, in that same year the Brazilian emperor D