1.
Night writing
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It was designed in 1808 by Charles Barbier in response to Napoleons demand for a code that soldiers could use to communicate silently and without light at night. Called sonography, each grid of dots stands for a character or phoneme, barbiers system was related to the Polybius square, in which a two-digit code represents a character. g. 4–2 for t represented by As many as twelve dots would be needed to represent one symbol, barbiers system was found to be too difficult for soldiers to learn and was rejected by the military. In 1821, Barbier visited the National Institute for the Blind in Paris, France, Braille identified the major failing of the code, which was that the human finger could not encompass the whole symbol without moving and so could not move rapidly from one symbol to another. His modification was to use a 6-dot cell, the Braille system that revolutionized written communication for the visually impaired
2.
French Braille
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French Braille is the original braille alphabet, and the basis of all others. The alphabetic order of French has become the basis of the international braille convention, punctuation is as follows, The lower values are readings within numbers. Formatting and mode-changing marks are, As in English Braille, the sign is doubled for all caps. ⟨⠢⟩ and ⟨⠔⟩ are used to begin. This is the internationally recognized number system, however, in French Braille a new system, the Antoine braille digits, is used for mathematics and is recommended for all academic publications. This uses ⠠ combined with the first nine letters of the decade, from ⠠⠡ for ⟨1⟩ to ⠠⠪ for ⟨9⟩. The period/decimal and fraction bar also change, the Antoine numbers are being promoted in France and Luxembourg, but are not much used in with French Braille in Quebec. See the punctuation section above for Antoine mathematical notation, readings have changed slightly since modern braille was first published in 1837. The greatest change has been various secondary readings which were added to the alphabet, in general, only the assignments of the basic 26 letters of the French alphabet are retained in other braille alphabets. For example, among the additional letters, in German Braille only ü and ö coincide with French Braille, however, there are several alphabets which are much more closely related. Flemish Dutch uses the French Braille alphabet, in contrast to the German-derived Netherlands Dutch Braille, Italian Braille is identical to the French apart from doubling up French Braille ò to Italian ó and ò, since French has no ó. Indeed, a difference of these alphabets is the remapping of French vowels with a grave accent to an acute accent. Spanish changes all five of these vowels, as well as taking ü, the continental Scandinavian languages took the extended French letters â, ä/æ, and ö/ø. Vietnamese Braille is also similar, though it has added tone letters, and according uses French ⠵ z for d. Catalan Braille adds ⠇⠐⠇ for print ⟨l·l⟩, and Spanish Braille uses ⠻ for the non-French consonant ñ, luxembourgish Braille has since switch to eight-point braille, adding a dot at point 8 for the three vowels with accents. Punctuation and formatting are in general similar as well, though changes in French punctuation over time means that languages use older French conventions. For example, French parentheses and quotation marks originally had the values they do today. Other changes have accrued over time, and in some cases vary from country to country
3.
Universal Character Set characters
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The Unicode Consortium and the International Organisation for Standardisation collaborate on the Universal Character Set. The UCS is a standard to map characters used in natural language, mathematics, music. By creating this mapping, the UCS enables computer software vendors to interoperate, because it is a universal map, it can be used to represent multiple languages at the same time. UCS has a capacity to encode over 1 million characters. Each UCS character is represented by a code point, which is an integer between 0 and 1,114,111, used to represent each character within the internal logic of text processing software. The number of encoded characters is made up as follows,128,019 graphical characters 218 special purpose characters for control, ISO maintains the basic mapping of characters from character name to code point. Often the terms character and code point will get used interchangeably, however, when a distinction is made, a code point refers to the integer of the character, what one might think of as its address. Input methods can be through keyboard or a character palette. The UCS can be divided in various ways, such as by plane, block, character category, the x must be lowercase in XML documents. The nnnn or hhhh may be any number of digits and may include leading zeros, the hhhh may mix uppercase and lowercase, though uppercase is the usual style. In contrast, an entity reference refers to a character by the name of an entity which has the desired character as its replacement text. The entity must either be predefined or explicitly declared in a Document Type Definition, the format is the same as for any entity reference, &name, where name is the case-sensitive name of the entity. Unicode and ISO divide the set of points into 17 planes. As of 2016 ISO and the Unicode Consortium has only allocated characters, the others remain empty and reserved for future use. Most characters are assigned to the first plane, the Basic Multilingual Plane. This is to ease the transition for legacy software since the Basic Multilingual Plane is addressable with just two octets. The characters outside the first plane usually have very specialized or rare use. Each plane corresponds with the value of the one or two hexadecimal digits preceding the four ones, hence U+24321 is in Plane 2, U+4321 is in Plane 0
4.
Louis Braille
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Louis Braille was a French educator and inventor of a system of reading and writing for use by the blind or visually impaired. His system remains known worldwide simply as braille, blinded in both eyes as a result of an early childhood accident, Braille mastered his disability while still a boy. He excelled in his education and received scholarship to Frances Royal Institute for Blind Youth, while still a student there, he began developing a system of tactile code that could allow blind people to read and write quickly and efficiently. Inspired by the cryptography of Charles Barbier, Braille constructed a new method built specifically for the needs of the blind. He presented his work to his peers for the first time in 1824, in adulthood, Braille served as a professor at the Institute and had an avocation as a musician, but he largely spent the remainder of his life refining and extending his system. It went unused by most educators for years after his death, but posterity has recognized braille as a revolutionary invention. Louis Braille was born in Coupvray, France, a town about twenty miles east of Paris. He and his three elder siblings – Monique Catherine, Louis-Simon, and Marie Céline – lived with their parents, Simon-René and Monique, Simon-René maintained a successful enterprise as a leatherer and maker of horse tack. As soon as he could walk, Braille spent time playing in his fathers workshop, at the age of three, the child was toying with some of the tools, trying to make holes in a piece of leather with an awl. Squinting closely at the surface, he pressed down hard to drive the point in, a local physician bound and patched the affected eye and even arranged for Braille to be met the next day in Paris by a surgeon, but no treatment could save the damaged organ. Due to his age, Braille did not realize at first that he had lost his sight. His parents made many efforts – quite uncommon for the era – to raise their youngest child in a normal fashion and he learned to navigate the village and country paths with canes his father hewed for him, and he grew up seemingly at peace with his disability. Brailles bright and creative mind impressed the teachers and priests. Braille studied in Coupvray until the age of ten, Braille, the last of the familys children to leave the household, departed for the school in February 1819. At that time the Royal Institute was an underfunded, ramshackle affair, the children were taught how to read by a system devised by the schools founder, Valentin Haüy. Not blind himself, Haüy was a philanthropist who devoted his life to helping the blind and he designed and manufactured a small library of books for the children using a technique of embossing heavy paper with the raised imprints of Latin letters. Readers would trace their fingers over the text, comprehending slowly, Braille was helped by the Haüy books, but he also despaired over their lack of depth, the amount of information kept in such books was necessarily small. Because the raised letters were made in a complex artisanal process using wet paper pressed against copper wire, so that the young Louis could send letters back home, Simon-René provided him with an alphabet made from bits of thick leather
5.
Braille
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Braille /ˈbreɪl/ is a tactile writing system used by people who are blind or visually impaired. It is traditionally written with embossed paper, braille-users can read computer screens and other electronic supports thanks to refreshable braille displays. They can write braille with the slate and stylus or type it on a braille writer, such as a portable braille note-taker. Braille is named after its creator, Frenchman Louis Braille, who lost his eyesight due to a childhood accident, in 1824, at the age of 15, Braille developed his code for the French alphabet as an improvement on night writing. He published his system, which included musical notation, in 1829. The second revision, published in 1837, was the first binary form of writing developed in the modern era, Braille characters are small rectangular blocks called cells that contain tiny palpable bumps called raised dots. The number and arrangement of these dots distinguish one character from another, since the various braille alphabets originated as transcription codes of printed writing systems, the mappings vary from language to language. Braille cells are not the thing to appear in braille text. There may be embossed illustrations and graphs, with the lines either solid or made of series of dots, arrows, bullets that are larger than braille dots, a full Braille cell includes six raised dots arranged in two lateral rows each having three dots. The dot positions are identified by numbers from one through six,64 solutions are possible from using one or more dots. A single cell can be used to represent a letter, number, punctuation mark. In the face of screen-reader software, braille usage has declined, in Barbiers system, sets of 12 embossed dots encoded 36 different sounds. It proved to be too difficult for soldiers to recognize by touch, in 1821 Barbier visited the Royal Institute for the Blind in Paris, where he met Louis Braille. Brailles solution was to use 6-dot cells and to assign a specific pattern to each letter of the alphabet. At first, braille was a transliteration of French orthography, but soon various abbreviations, contractions. The expanded English system, called Grade-2 Braille, was complete by 1905, for blind readers, Braille is an independent writing system, rather than a code of printed orthography. Braille is derived from the Latin alphabet, albeit indirectly, in Brailles original system, the dot patterns were assigned to letters according to their position within the alphabetic order of the French alphabet, with accented letters and w sorted at the end. The first ten letters of the alphabet, a–j, use the upper four dot positions and these stand for the ten digits 1–9 and 0 in a system parallel to Hebrew gematria and Greek isopsephy
6.
Decimal mark
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A decimal mark is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for the decimal mark, the choice of symbol for the decimal mark also affects the choice of symbol for the thousands separator used in digit grouping, so the latter is also treated in this article. In mathematics the decimal mark is a type of radix point, in the Middle Ages, before printing, a bar over the units digit was used to separate the integral part of a number from its fractional part, e. g.9995. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear, a similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal mark, e. g.9995. Later, a separatrix between the units and tenths position became the norm among Arab mathematicians, e. g. 99ˌ95, when this character was typeset, it was convenient to use the existing comma or full stop instead. The separatrix was also used in England as an L-shaped or vertical bar before the popularization of the period, gerbert of Aurillac marked triples of columns with an arc when using his Hindu–Arabic numeral-based abacus in the 10th century. Fibonacci followed this convention when writing numbers such as in his influential work Liber Abaci in the 13th century, in France, the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries, such as Italy, also chose to use the comma to mark the decimal units position and it has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits, in some countries, a raised dot or dash may be used for grouping or decimal mark, this is particularly common in handwriting. In the United States, the stop or period was used as the standard decimal mark. g. However, as the mid dot was already in use in the mathematics world to indicate multiplication. In the event, the point was decided on by the Ministry of Technology in 1968, the three most spoken international auxiliary languages, Ido, Esperanto, and Interlingua, all use the comma as the decimal mark. Interlingua has used the comma as its decimal mark since the publication of the Interlingua Grammar in 1951, Esperanto also uses the comma as its official decimal mark, while thousands are separated by non-breaking spaces,12345678,9. Idos Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido officially states that commas are used for the mark while full stops are used to separate thousands, millions. So the number 12,345,678.90123 for instance, the 1931 grammar of Volapük by Arie de Jong uses the comma as its decimal mark, and uses the middle dot as the thousands separator. In 1958, disputes between European and American delegates over the representation of the decimal mark nearly stalled the development of the ALGOL computer programming language. ALGOL ended up allowing different decimal marks, but most computer languages, the 22nd General Conference on Weights and Measures declared in 2003 that the symbol for the decimal marker shall be either the point on the line or the comma on the line. It further reaffirmed that numbers may be divided in groups of three in order to facilitate reading, neither dots nor commas are ever inserted in the spaces between groups
7.
Ratio
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In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, thus, a ratio can be a fraction as opposed to a whole number. Also, in example the ratio of lemons to oranges is 6,8. The numbers compared in a ratio can be any quantities of a kind, such as objects, persons, lengths. A ratio is written a to b or a, b, when the two quantities have the same units, as is often the case, their ratio is a dimensionless number. A rate is a quotient of variables having different units, but in many applications, the word ratio is often used instead for this more general notion as well. The numbers A and B are sometimes called terms with A being the antecedent, the proportion expressing the equality of the ratios A, B and C, D is written A, B = C, D or A, B, C, D. This latter form, when spoken or written in the English language, is expressed as A is to B as C is to D. A, B, C and D are called the terms of the proportion. A and D are called the extremes, and B and C are called the means, the equality of three or more proportions is called a continued proportion. Ratios are sometimes used three or more terms. The ratio of the dimensions of a two by four that is ten inches long is 2,4,10, a good concrete mix is sometimes quoted as 1,2,4 for the ratio of cement to sand to gravel. It is impossible to trace the origin of the concept of ratio because the ideas from which it developed would have been familiar to preliterate cultures. For example, the idea of one village being twice as large as another is so basic that it would have been understood in prehistoric society, however, it is possible to trace the origin of the word ratio to the Ancient Greek λόγος. Early translators rendered this into Latin as ratio, a more modern interpretation of Euclids meaning is more akin to computation or reckoning. Medieval writers used the word to indicate ratio and proportionalitas for the equality of ratios, Euclid collected the results appearing in the Elements from earlier sources. The Pythagoreans developed a theory of ratio and proportion as applied to numbers, the discovery of a theory of ratios that does not assume commensurability is probably due to Eudoxus of Cnidus. The exposition of the theory of proportions that appears in Book VII of The Elements reflects the earlier theory of ratios of commensurables, the existence of multiple theories seems unnecessarily complex to modern sensibility since ratios are, to a large extent, identified with quotients. This is a recent development however, as can be seen from the fact that modern geometry textbooks still use distinct terminology and notation for ratios
8.
Proportionality (mathematics)
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In mathematics, two variables are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant multiplier. The constant is called the coefficient of proportionality or proportionality constant, if one variable is always the product of the other and a constant, the two are said to be directly proportional. X and y are directly proportional if the ratio y/x is constant, if the product of the two variables is always a constant, the two are said to be inversely proportional. X and y are inversely proportional if the product xy is constant, to express the statement y is directly proportional to x mathematically, we write an equation y = cx, where c is the proportionality constant. Symbolically, this is written as y ∝ x, to express the statement y is inversely proportional to x mathematically, we write an equation y = c/x. We can equivalently write y is proportional to 1/x. An equality of two ratios is called a proportion, for example, a/c = b/d, where no term is zero. Given two variables x and y, y is proportional to x if there is a non-zero constant k such that y = k x. The relation is denoted, using the ∝ or ~ symbol, as y ∝ x. If an object travels at a constant speed, then the distance traveled is directly proportional to the time spent traveling, the circumference of a circle is directly proportional to its diameter, with the constant of proportionality equal to π. Since y = k x is equivalent to x = y, it follows that if y is proportional to x, with proportionality constant k. The concept of inverse proportionality can be contrasted against direct proportionality, consider two variables said to be inversely proportional to each other. If all other variables are constant, the magnitude or absolute value of one inversely proportional variable decreases if the other variable increases. Formally, two variables are proportional if each of the variables is directly proportional to the multiplicative inverse of the other. As an example, the time taken for a journey is inversely proportional to the speed of travel, the graph of two variables varying inversely on the Cartesian coordinate plane is a rectangular hyperbola. The product of the x and y values of each point on the curve equals the constant of proportionality, since neither x nor y can equal zero, the graph never crosses either axis. A variable y is proportional to a variable x, if y is directly proportional to the exponential function of x, that is if there exist non-zero constants k. Likewise, a y is logarithmically proportional to a variable x, if y is directly proportional to the logarithm of x, that is if there exist non-zero constants k
9.
Obelus
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An obelus is a symbol consisting of a short horizontal line with a dot above and below, and in other uses it is a symbol resembling a small dagger. In mathematics it is used to represent the mathematical operation of division. It is therefore called the division sign. Division may also be indicated by a line or a slash. In ISO 80000-2-9.6 it says, The symbol ÷ should not be used. In editing texts an obelus takes the form of a mark and is used as a reference mark, or to indicate that a person is deceased. In mathematics, the symbol has also been used to represent subtraction in Northern Europe. The word obelus comes from ὀβελός, the Ancient Greek word for a stick, spit. This is the root as that of the word obelisk. Originally this sign was used in ancient manuscripts to mark passages that were suspected of being corrupted or spurious, the dagger symbol, also called an obelisk, is derived from the obelus and continues to be used for this purpose. The incident of the Bloody Sweat in Gethsemane and the saying Father forgive them, although previously used for subtraction, the obelus was first used as a symbol for division in 1659 in the algebra book Teutsche Algebra by Johann Rahn. Some think that John Pell, who edited the book, may have been responsible for use of the symbol. The usage of the obelus to represent subtraction continued in parts of Europe. Other symbols for division include the slash or solidus, and the fraction bar, in Microsoft Windows, the obelus is produced with Alt+0247 on the number pad or by pressing Alt Gr+⇧ Shift++ when an appropriate keyboard layout is in use. In classic Mac OS and macOS, it is produced with ⌥ Option+/, on UNIX-based systems using Screen or X with a Compose key enabled, it can be produced by composing, and -, though this is locale- and setting-dependent. It may also be input by Unicode code-point on GTK-based applications by pressing Control+⇧ Shift+U, followed by the codepoint in hexadecimal, in the Unicode character set, the obelus is known as the division sign and has the code point U+00F7. In HTML, it can be encoded as ÷, or ÷, in LaTeX, the obelus is obtained by \div. Commercial minus sign, ⁒, which resembles a tilted obelus Jeff Miller, Earliest Uses of Various Mathematical Symbols Michael Quinion