1.
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
2.
Greek alphabet
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It is the ancestor of the Latin and Cyrillic scripts. In its classical and modern forms, the alphabet has 24 letters, Modern and Ancient Greek use different diacritics. In standard Modern Greek spelling, orthography has been simplified to the monotonic system, examples In both Ancient and Modern Greek, the letters of the Greek alphabet have fairly stable and consistent symbol-to-sound mappings, making pronunciation of words largely predictable. Ancient Greek spelling was generally near-phonemic, among consonant letters, all letters that denoted voiced plosive consonants and aspirated plosives in Ancient Greek stand for corresponding fricative sounds in Modern Greek. This leads to groups of vowel letters denoting identical sounds today. Modern Greek orthography remains true to the spellings in most of these cases. The following vowel letters and digraphs are involved in the mergers, Modern Greek speakers typically use the same, modern, in other countries, students of Ancient Greek may use a variety of conventional approximations of the historical sound system in pronouncing Ancient Greek. Several letter combinations have special conventional sound values different from those of their single components, among them are several digraphs of vowel letters that formerly represented diphthongs but are now monophthongized. In addition to the three mentioned above, there is also ⟨ου⟩, pronounced /u/, the Ancient Greek diphthongs ⟨αυ⟩, ⟨ευ⟩ and ⟨ηυ⟩ are pronounced, and respectively in voicing environments in Modern Greek. The Modern Greek consonant combinations ⟨μπ⟩ and ⟨ντ⟩ stand for and respectively, ⟨τζ⟩ stands for, in addition, both in Ancient and Modern Greek, the letter ⟨γ⟩, before another velar consonant, stands for the velar nasal, thus ⟨γγ⟩ and ⟨γκ⟩ are pronounced like English ⟨ng⟩. There are also the combinations ⟨γχ⟩ and ⟨γξ⟩ and these signs were originally designed to mark different forms of the phonological pitch accent in Ancient Greek. The letter rho, although not a vowel, also carries a rough breathing in word-initial position, if a rho was geminated within a word, the first ρ always had the smooth breathing and the second the rough breathing leading to the transiliteration rrh. The vowel letters ⟨α, η, ω⟩ carry an additional diacritic in certain words, the iota subscript. This iota represents the former offglide of what were originally long diphthongs, ⟨ᾱι, ηι, ωι⟩, another diacritic used in Greek is the diaeresis, indicating a hiatus. In 1982, a new, simplified orthography, known as monotonic, was adopted for use in Modern Greek by the Greek state. Although it is not a diacritic, the comma has a function as a silent letter in a handful of Greek words, principally distinguishing ό. There are many different methods of rendering Greek text or Greek names in the Latin script, the form in which classical Greek names are conventionally rendered in English goes back to the way Greek loanwords were incorporated into Latin in antiquity. In this system, ⟨κ⟩ is replaced with ⟨c⟩, the diphthongs ⟨αι⟩ and ⟨οι⟩ are rendered as ⟨ae⟩ and ⟨oe⟩ respectively, and ⟨ει⟩ and ⟨ου⟩ are simplified to ⟨i⟩ and ⟨u⟩ respectively
3.
Pi
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The number π is a mathematical constant, the ratio of a circles circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter π since the mid-18th century, being an irrational number, π cannot be expressed exactly as a fraction. Still, fractions such as 22/7 and other numbers are commonly used to approximate π. The digits appear to be randomly distributed, in particular, the digit sequence of π is conjectured to satisfy a specific kind of statistical randomness, but to date no proof of this has been discovered. Also, π is a number, i. e. a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass, ancient civilizations required fairly accurate computed values for π for practical reasons. It was calculated to seven digits, using techniques, in Chinese mathematics. The extensive calculations involved have also used to test supercomputers. Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres. Because of its role as an eigenvalue, π appears in areas of mathematics. It is also found in cosmology, thermodynamics, mechanics, attempts to memorize the value of π with increasing precision have led to records of over 70,000 digits. In English, π is pronounced as pie, in mathematical use, the lowercase letter π is distinguished from its capitalized and enlarged counterpart ∏, which denotes a product of a sequence, analogous to how ∑ denotes summation. The choice of the symbol π is discussed in the section Adoption of the symbol π, π is commonly defined as the ratio of a circles circumference C to its diameter d, π = C d The ratio C/d is constant, regardless of the circles size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π implicitly makes use of geometry, although the notion of a circle can be extended to any curved geometry. Here, the circumference of a circle is the arc length around the perimeter of the circle, a quantity which can be defined independently of geometry using limits. An integral such as this was adopted as the definition of π by Karl Weierstrass, definitions of π such as these that rely on a notion of circumference, and hence implicitly on concepts of the integral calculus, are no longer common in the literature. One such definition, due to Richard Baltzer, and popularized by Edmund Landau, is the following, the cosine can be defined independently of geometry as a power series, or as the solution of a differential equation
4.
Epsilon
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Epsilon is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel /e/. In the system of Greek numerals it has the value five and it was derived from the Phoenician letter He. Letters that arose from epsilon include the Roman E, Ë and Ɛ, in essence, the uppercase form of epsilon looks identical to Latin E. The lowercase version has two variants, both inherited from medieval Greek handwriting. One, the most common in typography and inherited from medieval minuscule. The other, also known as lunate or uncial epsilon and inherited from earlier uncial writing, while in normal typography these are just alternative font variants, they may have different meanings as mathematical symbols. Computer systems therefore offer distinct encodings for them, in Unicode, the character U+0一3F5 Greek lunate epsilon symbol is provided specifically for the lunate form. In TeX, \epsilon denotes the lunate form, while \varepsilon denotes the reversed-3 form, there is also a Latin epsilon or open e, which looks similar to the Greek lowercase epsilon. It is encoded in Unicode as U+025B and U+0190 and is used as an IPA phonetic symbol, the lunate or uncial epsilon has also provided inspiration for the euro sign. The lunate epsilon is not to be confused with the set membership symbol, in addition, mathematicians have read the symbol ∈ as element of, as in 1 is an element of the natural numbers for 1 ∈ N, for example. As late as 1960, ϵ itself was used for set membership, Only gradually did a fully separate stylized symbol take the place of epsilon. In a related context, Peano also introduced the use of a backwards epsilon, ∍, for the phrase such that, the letter Ε was taken over from the Phoenician letter He when Greeks first adopted alphabetic writing. In archaic Greek writing, its shape is often identical to that of the Phoenician letter. Archaic writing often preserves the Phoenician form with a stem extending slightly below the lowest horizontal bar. In the classical era, through the influence of cursive writing styles. Besides its classical Greek sound value, the short /e/ phoneme, for instance, in early Attic before c.500 B. C. it was used also both for the long, open /ɛː/, and for the long close /eː/. In the former role, it was replaced in the classic Greek alphabet by Eta. Some dialects used yet other ways of distinguishing between various e-like sounds, in Corinth, the normal function of Ε to denote /e/ and /ɛː/ was taken by a glyph resembling a pointed B, while Ε was used only for long close /eː/
5.
Theta
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Theta is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth. In the system of Greek numerals it has a value of 9, in Ancient Greek, θ represented the aspirated voiceless dental plosive /t̪ʰ/, but in Modern Greek it represents the voiceless dental fricative /θ/. In its archaic form, θ was written as a cross within a circle, archaic crossed forms of theta are seen in the wheel letters of Linear A and Linear B. The cursive form ϑ was retained by Unicode as U+03D1 ϑ GREEK THETA SYMBOL, for the purpose of writing Greek text, the two can be font variants of a single character, but θ and ϑ are also used as distinct symbols in technical and mathematical contexts. In the Latin script used for the Gaulish language, theta developed into the tau gallicum, conventionally transliterated as Ð, the phonetic value of the tau gallicum is thought to have been. The early Cyrillic letter fita developed from θ and this letter existed in the Russian alphabet until the 1918 Russian orthography reform. In the International Phonetic Alphabet, represents the voiceless dental fricative and it does not represent the consonant in the, which is the voiced dental fricative. The lower-case letter θ is used as a symbol for, A plane angle in geometry, a Variable in trigonometry A special function of several complex variables. One of the Chebyshev functions in prime number theory, the score of a test taker in item response theory. Theta Type Replication, a type of bacterial DNA replication specific to circular chromosomes, threshold value of an artificial neuron. A Bayer designation letter applied to a star in a constellation, usually the star so labelled. The parameter frequently used in writing the likelihood function, the Watterson estimator for the population mutation rate in population genetics. Indicates a minimum optimum integration level determined by the intersection of GG, the GG-LL schedules are a tool used in analyzing the potential benefits of a country pegging their domestic currency to a foreign currency. The reserve ratio of banks in economic models, the ordinal collapsing function developed by Solomon Feferman The upper-case letter Θ is used as a symbol for, Quantity or temperature, by SI standard. An asymptotically tight bound in the analysis of algorithms, a certain ordinal number in set theory. Pentaquarks, exotic baryons in particle physics, a brain signal frequency ranging from 4–8 Hz. One of the known as Greeks in finance, representing time decay of options or the change in the intrinsic value of an option divided by the number of days until the option expires. A variable indicating temperature difference in heat transfer, according to Porphyry of Tyros, the Egyptians used an X within a circle as a symbol of the soul, having a value of nine, it was used as a symbol for Ennead
6.
Eta
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Eta is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its value in the classical Attic dialect of Ancient Greek was a long vowel, raised to in hellenistic Greek. In the system of Greek numerals it has a value of 8 and it was derived from the Phoenician letter heth. Letters that arose from eta include the Latin H and the Cyrillic letter И, the letter shape H was originally used in most Greek dialects to represent the sound /h/, a voiceless glottal fricative. In this function, it was borrowed in the 8th century BC by the Etruscan and other Old Italic alphabets and this also gave rise to the Latin alphabet with its letter H. Other regional variants of the Greek alphabet, in dialects that still preserved the sound /h/, in the southern Italian colonies of Heracleia and Tarentum, the letter shape was reduced to a half-heta lacking the right vertical stem. From this sign later developed the sign for rough breathing or spiritus asper, in 403 BC, Athens took over the Ionian spelling system and with it the vocalic use of H. This later became the standard orthography in all of Greece, itacism is continued into Modern Greek, where the letter name is pronounced and represents the sound /i/. It shares this function with other letters and digraphs, which are all pronounced alike. This phenomenon at large is called iotacism, Eta was also borrowed with the sound value of into the Cyrillic script, where it gave rise to the Cyrillic letter И. In Modern Greek the letter, pronounced, represents a close front unrounded vowel, in Classical Greek, it represented a long open-mid front unrounded vowel, /ɛː/. The upper-case letter Η is used as a symbol in textual criticism for the Alexandrian text-type, the lower-case letter η is used as a symbol in, Thermodynamics, the efficiency of a Carnot heat engine, or packing fraction. Chemistry, the hapticity, or the number of atoms of an attached to one coordination site of the metal in a coordination compound. For example, a group can coordinate to palladium in the η¹ mode or the η³ mode. Optics, the impedance of a medium, or the quantum efficiency of detectors. Particle physics, to represent the η mesons, experimental particle physics, η stands for pseudorapidity. Cosmology, η represents conformal time, dt = adη, relativity and Quantum field theory, η represents the metric tensor of Minkowski space. Statistics, η2 is the regression coefficient