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Alginates Alginic acid, or alginate, is extracted from brown algae. Its uses range from gelling agents in food, to medical dressings. Alginic acid also has been used in the field of biotechnology as a biocompatible medium for cell encapsulation and cell immobilization. Molecular cuisine is also a user of the substance for its gelling properties, by which it becomes a delivery vehicle for flavours.	Algae
Between 100,000 and 170,000 wet tons of Macrocystis are harvested annually in New Mexico for alginate extraction and abalone feed. Energy source	Algae
Energy source To be competitive and independent from fluctuating support from (local) policy on the long run, biofuels should equal or beat the cost level of fossil fuels. Here, algae-based fuels hold great promise, directly related to the potential to produce more biomass per unit area in a year than any other form of biomass. The break-even point for algae-based biofuels is estimated to occur by 2025. Fertilizer	Algae
Fertilizer For centuries, seaweed has been used as a fertilizer; George Owen of Henllys writing in the 16th century referring to drift weed in South Wales:	Algae
Today, algae are used by humans in many ways; for example, as fertilizers, soil conditioners, and livestock feed. Aquatic and microscopic species are cultured in clear tanks or ponds and are either harvested or used to treat effluents pumped through the ponds. Algaculture on a large scale is an important type of aquaculture in some places. Maerl is commonly used as a soil conditioner. Nutrition	Algae
Nutrition Naturally growing seaweeds are an important source of food, especially in Asia, leading some to label them as superfoods. They provide many vitamins including: A, B1, B2, B6, niacin, and C, and are rich in iodine, potassium, iron, magnesium, and calcium. In addition, commercially cultivated microalgae, including both algae and cyanobacteria, are marketed as nutritional supplements, such as spirulina, Chlorella and the vitamin-C supplement from Dunaliella, high in beta-carotene.	Algae
Algae are national foods of many nations: China consumes more than 70 species, including fat choy, a cyanobacterium considered a vegetable; Japan, over 20 species such as nori and aonori; Ireland, dulse; Chile, cochayuyo. Laver is used to make laver bread in Wales, where it is known as ; in Korea, . It is also used along the west coast of North America from California to British Columbia, in Hawaii and by the Māori of New Zealand. Sea lettuce and badderlocks are salad ingredients in Scotland, Ireland,	Algae
are salad ingredients in Scotland, Ireland, Greenland, and Iceland. Algae is being considered a potential solution for world hunger problem.	Algae
Two popular forms of algae are used in cuisine: Chlorella: This form of alga is found in freshwater and contains photosynthetic pigments in its chloroplast. It is high in iron, zinc, magnesium, vitamin B2 and Omega-3 Fatty acids. Furthermore, it contains all nine of the essential amino acids the body does not produce on its own	Algae
Spirulina: Known otherwise as a cyanobacterium (a prokaryote, incorrectly referred to as a "blue-green alga"), contains 10% more protein than Chlorella as well as more thiamine and copper.	Algae
The oils from some algae have high levels of unsaturated fatty acids. For example, Parietochloris incisa is very high in arachidonic acid, where it reaches up to 47% of the triglyceride pool. Some varieties of algae favored by vegetarianism and veganism contain the long-chain, essential omega-3 fatty acids, docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA). Fish oil contains the omega-3 fatty acids, but the original source is algae (microalgae in particular), which are eaten by marine life such as	Algae
which are eaten by marine life such as copepods and are passed up the food chain. Algae have emerged in recent years as a popular source of omega-3 fatty acids for vegetarians who cannot get long-chain EPA and DHA from other vegetarian sources such as flaxseed oil, which only contains the short-chain alpha-linolenic acid (ALA).	Algae
Pollution control Sewage can be treated with algae, reducing the use of large amounts of toxic chemicals that would otherwise be needed. Algae can be used to capture fertilizers in runoff from farms. When subsequently harvested, the enriched algae can be used as fertilizer. Aquaria and ponds can be filtered using algae, which absorb nutrients from the water in a device called an algae scrubber, also known as an algae turf scrubber.	Algae
Agricultural Research Service scientists found that 60–90% of nitrogen runoff and 70–100% of phosphorus runoff can be captured from manure effluents using a horizontal algae scrubber, also called an algal turf scrubber (ATS). Scientists developed the ATS, which consists of shallow, 100-foot raceways of nylon netting where algae colonies can form, and studied its efficacy for three years. They found that algae can readily be used to reduce the nutrient runoff from agricultural fields and increase the	Algae
runoff from agricultural fields and increase the quality of water flowing into rivers, streams, and oceans. Researchers collected and dried the nutrient-rich algae from the ATS and studied its potential as an organic fertilizer. They found that cucumber and corn seedlings grew just as well using ATS organic fertilizer as they did with commercial fertilizers. Algae scrubbers, using bubbling upflow or vertical waterfall versions, are now also being used to filter aquaria and ponds.	Algae
Polymers Various polymers can be created from algae, which can be especially useful in the creation of bioplastics. These include hybrid plastics, cellulose-based plastics, poly-lactic acid, and bio-polyethylene. Several companies have begun to produce algae polymers commercially, including for use in flip-flops and in surf boards. Bioremediation The alga Stichococcus bacillaris has been seen to colonize silicone resins used at archaeological sites; biodegrading the synthetic substance.	Algae
Pigments The natural pigments (carotenoids and chlorophylls) produced by algae can be used as alternatives to chemical dyes and coloring agents.	Algae
The presence of some individual algal pigments, together with specific pigment concentration ratios, are taxon-specific: analysis of their concentrations with various analytical methods, particularly high-performance liquid chromatography, can therefore offer deep insight into the taxonomic composition and relative abundance of natural algae populations in sea water samples.	Algae
Stabilizing substances Carrageenan, from the red alga Chondrus crispus, is used as a stabilizer in milk products. Additional images See also AlgaeBase AlgaePARC Eutrophication Iron fertilization Marimo algae Microbiofuels Microphyte Photobioreactor Phycotechnology Plant Toxoid – anatoxin References Bibliography General . Regional Britain and Ireland Australia New Zealand Europe Arctic Greenland Faroe Islands . Canary Islands Morocco South Africa North America	Algae
Morocco South Africa North America External links – a database of all algal names including images, nomenclature, taxonomy, distribution, bibliography, uses, extracts EnAlgae Endosymbiotic events Polyphyletic groups	Algae
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hindu-Arabic numeral system. The exact origin of the abacus has not yet emerged. It consists of rows of movable beads, or similar objects, strung on a wire. They represent digits. One of the two numbers is set up, and the beads are manipulated to perform an operation such as	Abacus
are manipulated to perform an operation such as addition, or even a square or cubic root.	Abacus
In their earliest designs, the rows of beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Abacuses are still made, often as a bamboo frame with beads sliding on wires. In the ancient world, particularly before the introduction of positional notation, abacuses were a practical calculating tool. The abacus is still used to teach the fundamentals of mathematics to some children, e.g., in post-Soviet	Abacus
to some children, e.g., in post-Soviet states.	Abacus
Designs such as the Japanese soroban have been used for practical calculations of up to multi-digit numbers. Any particular abacus design supports multiple methods to perform calculations, including the four basic operations and square and cube roots. Some of these methods work with non-natural numbers (numbers such as and ).	Abacus
Although calculators and computers are commonly used today instead of abacuses, abacuses remain in everyday use in some countries. Merchants, traders, and clerks in some parts of Eastern Europe, Russia, China, and Africa use abacuses. The abacus remains in common use as a scoring system in non-electronic table games. Others may use an abacus due to visual impairment that prevents the use of a calculator.	Abacus
Etymology	Abacus
The word abacus dates to at least AD 1387 when a Middle English work borrowed the word from Latin that described a sandboard abacus. The Latin word is derived from ancient Greek (abax) which means something without a base, and colloquially, any piece of rectangular material. Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust", or "drawing-board covered with dust (for the use of mathematics)" (the exact shape of the Latin	Abacus
of mathematics)" (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, (abakos). While the table strewn with dust definition is popular, some argue evidence is insufficient for that conclusion. Greek probably borrowed from a Northwest Semitic language like Phoenician, evidenced by a cognate with the Hebrew word ʾābāq (), or “dust” (in the post-Biblical sense "sand used as a writing surface").	Abacus
Both abacuses and abaci (soft or hard "c") are used as plurals. The user of an abacus is called an abacist. History Mesopotamia The Sumerian abacus appeared between 2700–2300 BC. It held a table of successive columns which delimited the successive orders of magnitude of their sexagesimal (base 60) number system.	Abacus
Some scholars point to a character in Babylonian cuneiform that may have been derived from a representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".	Abacus
Egypt Greek historian Herodotus mentioned the abacus in Ancient Egypt. He wrote that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument are yet to be discovered.	Abacus
Persia At around 600 BC, Persians first began to use the abacus, during the Achaemenid Empire. Under the Parthian, Sassanian, and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire- which is how the abacus may have been exported to other countries. Greece	Abacus
The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. Demosthenes (384 BC–322 BC) complained that the need to use pebbles for calculations was too difficult. A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius use the abacus as a metaphor for human behavior, stating "that men that sometimes stood for more and sometimes for less" like the pebbles on an abacus. The Greek abacus was a table of wood	Abacus
an abacus. The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome, and the Western Christian world until the French Revolution.	Abacus
A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet) dates to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble in length, wide, and thick, on which are 5 groups of markings. In the tablet's center is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it.	Abacus
a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line. Also from this time frame, the Darius Vase was unearthed in 1851. It was covered with pictures, including a "treasurer" holding a wax tablet in one hand while	Abacus
holding a wax tablet in one hand while manipulating counters on a table with the other.	Abacus
China The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.	Abacus
The Chinese abacus, also known as the suanpan (算盤/算盘, lit. "calculating tray"), is typically tall and comes in various widths, depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom one. The beads are usually rounded and made of hardwood. The beads are counted by moving them up or down towards the beam; beads moved toward the beam are counted, while those moved away from it are not. One of the top beads is 5,	Abacus
away from it are not. One of the top beads is 5, while one of the bottom beads is 1. Each rod has a number under it, showing the place value. The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.	Abacus
The prototype of the Chinese abacus appeared during the Han Dynasty, and the beads are oval. The Song Dynasty and earlier used the 1:4 type or four-beads abacus similar to the modern abacus including the shape of the beads commonly known as Japanese-style abacus.	Abacus
In the early Ming Dynasty, the abacus began to appear in a 1:5 ratio. The upper deck had one bead and the bottom had five beads. In the late Ming Dynasty, the abacus styles appeared in a 2:5 ratio. The upper deck had two beads, and the bottom had five. Various calculation techniques were devised for Suanpan enabling efficient calculations. Some schools teach students how to use it.	Abacus
In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).	Abacus
The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, given evidence of a trade relationship between the Roman Empire and China. However, no direct connection has been demonstrated, and the similarity of the abacuses may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. Incidentally, this allows	Abacus
suanpan has 5 plus 2. Incidentally, this allows use with a hexadecimal numeral system (or any base up to 18) which may have been used for traditional Chinese measures of weight. (Instead of running on wires as in the Chinese, Korean, and Japanese models, the Roman model used grooves, presumably making arithmetic calculations much slower.)	Abacus
Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a placeholder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians. Rome	Abacus
The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens, etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe and persisted in limited use into the nineteenth century. Due to Pope Sylvester II's reintroduction of the abacus with modifications,	Abacus
reintroduction of the abacus with modifications, it became widely used in Europe again during the 11th century This abacus used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster and was more easily moved.	Abacus
Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.	Abacus
One example of archaeological evidence of the Roman abacus, shown nearby in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives –five units, five tens, etc., essentially in a bi-quinary coded decimal system, related to the Roman numerals. The short grooves on the right may	Abacus
numerals. The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions).	Abacus
India	Abacus
The Abhidharmakośabhāṣya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartikā) on the number one (ekāṅka) means it is a one while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand". It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the	Abacus
were already finding new ways of recording the contents of the abacus. Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus.	Abacus
Japan In Japan, the abacus is called soroban (, lit. "counting tray"). It was imported from China in the 14th century. It was probably in use by the working class a century or more before the ruling class adopted it, as the class structure obstructed such changes. The 1:4 abacus, which removes the seldom-used second and fifth bead became popular in the 1940s.	Abacus
Today's Japanese abacus is a 1:4 type, four-bead abacus, introduced from China in the Muromachi era. It adopts the form of the upper deck one bead and the bottom four beads. The top bead on the upper deck was equal to five and the bottom one is similar to the Chinese or Korean abacus, and the decimal number can be expressed, so the abacus is designed as a one:four device. The beads are always in the shape of a diamond. The quotient division is generally used instead of the division method; at the same	Abacus
used instead of the division method; at the same time, in order to make the multiplication and division digits consistently use the division multiplication. Later, Japan had a 3:5 abacus called 天三算盤, which is now in the Ize Rongji collection of Shansi Village in Yamagata City. Japan also used a 2:5 type abacus.	Abacus
The four-bead abacus spread, and became common around the world. Improvements to the Japanese abacus arose in various places. In China an aluminium frame plastic bead abacus was used. The file is next to the four beads, and pressing the "clearing" button put the upper bead in the upper position, and the lower bead in the lower position.	Abacus
The abacus is still manufactured in Japan even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation. Using visual imagery can complete a calculation as quickly as a physical instrument.	Abacus
Korea The Chinese abacus migrated from China to Korea around 1400 AD. Koreans call it jupan (주판), supan (수판) or jusan (주산). The four-beads abacus (1:4) was introduced during the Goryeo Dynasty. The 5:1 abacus was introduced to Korea from China during the Ming Dynasty. Native America	Abacus
Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture. This Mesoamerican abacus used a 5-digit base-20 system. The word Nepōhualtzintzin comes from Nahuatl, formed by the roots; Ne – personal -; pōhual or pōhualli – the account -; and tzintzin – small similar elements. Its complete meaning was taken as: counting with small similar elements. Its use was taught in the Calmecac to the temalpouhqueh , who were students dedicated to taking the accounts of skies, from	Abacus
dedicated to taking the accounts of skies, from childhood.	Abacus
The Nepōhualtzintzin was divided into two main parts separated by a bar or intermediate cord. In the left part were four beads. Beads in the first row have unitary values (1, 2, 3, and 4), and on the right side, three beads had values of 5, 10, and 15, respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding count in the first row.	Abacus
The device featured 13 rows with 7 beads, 91 in total. This was a basic number for this culture. It had a close relation to natural phenomena, the underworld, and the cycles of the heavens. One Nepōhualtzintzin (91) represented the number of days that a season of the year lasts, two Nepōhualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin (273) is the number of days of a baby's gestation, and four Nepōhualtzintzin (364) completed a cycle and	Abacus
four Nepōhualtzintzin (364) completed a cycle and approximated one year. When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to 18 in floating point, which precisely calculated large and small amounts, although round off was not allowed.	Abacus
The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo, who in his travels throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them in gold, jade, encrustations of shell, etc. Very old Nepōhualtzintzin are attributed to the Olmec culture, and some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures.	Abacus
Sanchez wrote in Arithmetic in Maya that another base 5, base 4 abacus had been found in the Yucatán Peninsula that also computed calendar data. This was a finger abacus, on one hand, 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2, and 3 were used. Note the use of zero at the beginning and end of the two cycles.	Abacus
The quipu of the Incas was a system of colored knotted cords used to record numerical data, like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana (Quechua for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 Italian mathematician De Pasquale proposed an explanation. By comparing the form of several yupanas, researchers found that calculations were based using	Abacus
found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20, and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum.	Abacus
Russia	Abacus
The Russian abacus, the schoty (, plural from , counting), usually has a single slanted deck, with ten beads on each wire (except one wire with four beads for quarter-ruble fractions). Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916. The Russian abacus is often used vertically, with each wire running horizontally. The wires are usually bowed upward in the center, to keep the beads pinned to either side. It is cleared when all the beads are moved to the right. During	Abacus
when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually are of a different color from the other eight. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.	Abacus
The Russian abacus was in use in shops and markets throughout the former Soviet Union, and its usage was taught in most schools until the 1990s. Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia; according to Yakov Perelman. Some businessmen attempting to import calculators into the Russian Empire were known to leave in despair after watching a skilled abacus operator. Likewise, the mass production of Felix arithmometers since 1924 did not significantly	Abacus
arithmometers since 1924 did not significantly reduce abacus use in the Soviet Union. The Russian abacus began to lose popularity only after the mass production of domestic microcalculators in 1974.	Abacus
The Russian abacus was brought to France around 1820 by mathematician Jean-Victor Poncelet, who had served in Napoleon's army and had been a prisoner of war in Russia. The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid. The Turks and the Armenian people used abacuses similar to the	Abacus
the Armenian people used abacuses similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians.	Abacus
School abacus Around the world, abacuses have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic. In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame is common (see image).	Abacus
The wireframe may be used either with positional notation like other abacuses (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use. Teaching multiplication,	Abacus
suggests the latter use. Teaching multiplication, e.g. 6 times 7, may be represented by shifting 7 beads on 6 wires.	Abacus
The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ("calculating frame"), is often used, either on a string of beads or on a rigid framework. Feynman vs the abacus	Abacus
Physicist Richard Feynman was noted for facility in mathematical calculations. He wrote about an encounter in Brazil with a Japanese abacus expert, who challenged him to speed contests between Feynman's pen and paper, and the abacus. The abacus was much faster for addition, somewhat faster for multiplication, but Feynman was faster at division. When the abacus was used for a really difficult challenge, i.e. cube roots, Feynman won easily. However, the number chosen at random was close to a number Feynman	Abacus
chosen at random was close to a number Feynman happened to know was an exact cube, allowing him to use approximate methods.	Abacus
Neurological analysis	Abacus
Learning how to calculate with the abacus may improve capacity for mental calculation. Abacus-based mental calculation (AMC), which was derived from the abacus, is the act of performing calculations, including addition, subtraction, multiplication, and division, in the mind by manipulating an imagined abacus. It is a high-level cognitive skill that runs calculations with an effective algorithm. People doing long-term AMC training show higher numerical memory capacity and experience more effectively	Abacus
memory capacity and experience more effectively connected neural pathways. They are able to retrieve memory to deal with complex processes. AMC involves both visuospatial and visuomotor processing that generate the visual abacus and move the imaginary beads. Since it only requires that the final position of beads be remembered, it takes less memory and less computation time.	Abacus
Renaissance abacuses Binary abacus The binary abacus is used to explain how computers manipulate numbers. The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII. The device consists of a series of beads on parallel wires arranged in three separate rows. The beads represent a switch on the computer in either an "on" or "off" position.	Abacus
Visually impaired users An adapted abacus, invented by Tim Cranmer, and called a Cranmer abacus is commonly used by visually impaired users. A piece of soft fabric or rubber is placed behind the beads, keeping them in place while the users manipulate them. The device is then used to perform the mathematical functions of multiplication, division, addition, subtraction, square root, and cube root.	Abacus
Although blind students have benefited from talking calculators, the abacus is often taught to these students in early grades. Blind students can also complete mathematical assignments using a braille-writer and Nemeth code (a type of braille code for mathematics) but large multiplication and long division problems are tedious. The abacus gives these students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many	Abacus
their sighted peers using pencil and paper. Many blind people find this number machine a useful tool throughout life.	Abacus
See also Chinese Zhusuan Chisanbop Logical abacus Mental abacus Napier's bones Sand table Slide rule Soroban Suanpan Notes Footnotes References Reading External links Tutorials Min Multimedia Abacus curiosities Abacus in Various Number Systems at cut-the-knot Java applet of Chinese, Japanese and Russian abaci An atomic-scale abacus Examples of Abaci Aztex Abacus Indian Abacus	Abacus
Mathematical tools Chinese mathematics Egyptian mathematics Greek mathematics Indian mathematics Japanese mathematics Roman mathematics	Abacus
An acid is a molecule or ion capable of either donating a proton (i.e., hydrogen ion, H+), known as a Brønsted–Lowry acid, or, capable of forming a covalent bond with an electron pair, known as a Lewis acid.	Acid
The first category of acids are the proton donors, or Brønsted–Lowry acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents. A Brønsted or Arrhenius acid usually contains a hydrogen atom bonded to a chemical structure that is still energetically favorable after loss of H+.	Acid
Aqueous Arrhenius acids have characteristic properties which provide a practical description of an acid. Acids form aqueous solutions with a sour taste, can turn blue litmus red, and react with bases and certain metals (like calcium) to form salts. The word acid is derived from the Latin acidus/acēre, meaning 'sour'. An aqueous solution of an acid has a pH less than 7 and is colloquially also referred to as "acid" (as in "dissolved in acid"), while the strict definition refers only to the solute. A lower	Acid
definition refers only to the solute. A lower pH means a higher acidity, and thus a higher concentration of positive hydrogen ions in the solution. Chemicals or substances having the property of an acid are said to be acidic.	Acid
Common aqueous acids include hydrochloric acid (a solution of hydrogen chloride which is found in gastric acid in the stomach and activates digestive enzymes), acetic acid (vinegar is a dilute aqueous solution of this liquid), sulfuric acid (used in car batteries), and citric acid (found in citrus fruits). As these examples show, acids (in the colloquial sense) can be solutions or pure substances, and can be derived from acids (in the strict sense) that are solids, liquids, or gases. Strong acids and some	Acid
solids, liquids, or gases. Strong acids and some concentrated weak acids are corrosive, but there are exceptions such as carboranes and boric acid.	Acid
The second category of acids are Lewis acids, which form a covalent bond with an electron pair. An example is boron trifluoride (BF3), whose boron atom has a vacant orbital which can form a covalent bond by sharing a lone pair of electrons on an atom in a base, for example the nitrogen atom in ammonia (NH3). Lewis considered this as a generalization of the Brønsted definition, so that an acid is a chemical species that accepts electron pairs either directly or by releasing protons (H+) into the solution,	Acid
or by releasing protons (H+) into the solution, which then accept electron pairs. However, hydrogen chloride, acetic acid, and most other Brønsted–Lowry acids cannot form a covalent bond with an electron pair and are therefore not Lewis acids. Conversely, many Lewis acids are not Arrhenius or Brønsted–Lowry acids. In modern terminology, an acid is implicitly a Brønsted acid and not a Lewis acid, since chemists almost always refer to a Lewis acid explicitly as a Lewis acid.	Acid

Alginates Alginic acid, or alginate, is extracted from brown algae. Its uses range from gelling agents in food, to medical dressings. Alginic acid also has been used in the field of biotechnology as a biocompatible medium for cell encapsulation and cell immobilization. Molecular cuisine is also a user of the substance for its gelling properties, by which it becomes a delivery vehicle for flavours.

Algae

Between 100,000 and 170,000 wet tons of Macrocystis are harvested annually in New Mexico for alginate extraction and abalone feed. Energy source

Algae

Energy source To be competitive and independent from fluctuating support from (local) policy on the long run, biofuels should equal or beat the cost level of fossil fuels. Here, algae-based fuels hold great promise, directly related to the potential to produce more biomass per unit area in a year than any other form of biomass. The break-even point for algae-based biofuels is estimated to occur by 2025. Fertilizer

Algae

Fertilizer For centuries, seaweed has been used as a fertilizer; George Owen of Henllys writing in the 16th century referring to drift weed in South Wales:

Algae

Today, algae are used by humans in many ways; for example, as fertilizers, soil conditioners, and livestock feed. Aquatic and microscopic species are cultured in clear tanks or ponds and are either harvested or used to treat effluents pumped through the ponds. Algaculture on a large scale is an important type of aquaculture in some places. Maerl is commonly used as a soil conditioner. Nutrition

Algae

Nutrition Naturally growing seaweeds are an important source of food, especially in Asia, leading some to label them as superfoods. They provide many vitamins including: A, B1, B2, B6, niacin, and C, and are rich in iodine, potassium, iron, magnesium, and calcium. In addition, commercially cultivated microalgae, including both algae and cyanobacteria, are marketed as nutritional supplements, such as spirulina, Chlorella and the vitamin-C supplement from Dunaliella, high in beta-carotene.

Algae

Algae are national foods of many nations: China consumes more than 70 species, including fat choy, a cyanobacterium considered a vegetable; Japan, over 20 species such as nori and aonori; Ireland, dulse; Chile, cochayuyo. Laver is used to make laver bread in Wales, where it is known as ; in Korea, . It is also used along the west coast of North America from California to British Columbia, in Hawaii and by the Māori of New Zealand. Sea lettuce and badderlocks are salad ingredients in Scotland, Ireland,

Algae

are salad ingredients in Scotland, Ireland, Greenland, and Iceland. Algae is being considered a potential solution for world hunger problem.

Algae

Two popular forms of algae are used in cuisine: Chlorella: This form of alga is found in freshwater and contains photosynthetic pigments in its chloroplast. It is high in iron, zinc, magnesium, vitamin B2 and Omega-3 Fatty acids. Furthermore, it contains all nine of the essential amino acids the body does not produce on its own

Algae

Spirulina: Known otherwise as a cyanobacterium (a prokaryote, incorrectly referred to as a "blue-green alga"), contains 10% more protein than Chlorella as well as more thiamine and copper.

Algae

The oils from some algae have high levels of unsaturated fatty acids. For example, Parietochloris incisa is very high in arachidonic acid, where it reaches up to 47% of the triglyceride pool. Some varieties of algae favored by vegetarianism and veganism contain the long-chain, essential omega-3 fatty acids, docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA). Fish oil contains the omega-3 fatty acids, but the original source is algae (microalgae in particular), which are eaten by marine life such as

Algae

which are eaten by marine life such as copepods and are passed up the food chain. Algae have emerged in recent years as a popular source of omega-3 fatty acids for vegetarians who cannot get long-chain EPA and DHA from other vegetarian sources such as flaxseed oil, which only contains the short-chain alpha-linolenic acid (ALA).

Algae

Pollution control Sewage can be treated with algae, reducing the use of large amounts of toxic chemicals that would otherwise be needed. Algae can be used to capture fertilizers in runoff from farms. When subsequently harvested, the enriched algae can be used as fertilizer. Aquaria and ponds can be filtered using algae, which absorb nutrients from the water in a device called an algae scrubber, also known as an algae turf scrubber.

Algae

Agricultural Research Service scientists found that 60–90% of nitrogen runoff and 70–100% of phosphorus runoff can be captured from manure effluents using a horizontal algae scrubber, also called an algal turf scrubber (ATS). Scientists developed the ATS, which consists of shallow, 100-foot raceways of nylon netting where algae colonies can form, and studied its efficacy for three years. They found that algae can readily be used to reduce the nutrient runoff from agricultural fields and increase the

Algae

runoff from agricultural fields and increase the quality of water flowing into rivers, streams, and oceans. Researchers collected and dried the nutrient-rich algae from the ATS and studied its potential as an organic fertilizer. They found that cucumber and corn seedlings grew just as well using ATS organic fertilizer as they did with commercial fertilizers. Algae scrubbers, using bubbling upflow or vertical waterfall versions, are now also being used to filter aquaria and ponds.

Algae

Polymers Various polymers can be created from algae, which can be especially useful in the creation of bioplastics. These include hybrid plastics, cellulose-based plastics, poly-lactic acid, and bio-polyethylene. Several companies have begun to produce algae polymers commercially, including for use in flip-flops and in surf boards. Bioremediation The alga Stichococcus bacillaris has been seen to colonize silicone resins used at archaeological sites; biodegrading the synthetic substance.

Algae

Pigments The natural pigments (carotenoids and chlorophylls) produced by algae can be used as alternatives to chemical dyes and coloring agents.

Algae

The presence of some individual algal pigments, together with specific pigment concentration ratios, are taxon-specific: analysis of their concentrations with various analytical methods, particularly high-performance liquid chromatography, can therefore offer deep insight into the taxonomic composition and relative abundance of natural algae populations in sea water samples.

Algae

Stabilizing substances Carrageenan, from the red alga Chondrus crispus, is used as a stabilizer in milk products. Additional images See also AlgaeBase AlgaePARC Eutrophication Iron fertilization Marimo algae Microbiofuels Microphyte Photobioreactor Phycotechnology Plant Toxoid – anatoxin References Bibliography General . Regional Britain and Ireland Australia New Zealand Europe Arctic Greenland Faroe Islands . Canary Islands Morocco South Africa North America

Algae

Morocco South Africa North America External links – a database of all algal names including images, nomenclature, taxonomy, distribution, bibliography, uses, extracts EnAlgae Endosymbiotic events Polyphyletic groups

Algae

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hindu-Arabic numeral system. The exact origin of the abacus has not yet emerged. It consists of rows of movable beads, or similar objects, strung on a wire. They represent digits. One of the two numbers is set up, and the beads are manipulated to perform an operation such as

Abacus

are manipulated to perform an operation such as addition, or even a square or cubic root.

Abacus

In their earliest designs, the rows of beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Abacuses are still made, often as a bamboo frame with beads sliding on wires. In the ancient world, particularly before the introduction of positional notation, abacuses were a practical calculating tool. The abacus is still used to teach the fundamentals of mathematics to some children, e.g., in post-Soviet

Abacus

to some children, e.g., in post-Soviet states.

Abacus

Designs such as the Japanese soroban have been used for practical calculations of up to multi-digit numbers. Any particular abacus design supports multiple methods to perform calculations, including the four basic operations and square and cube roots. Some of these methods work with non-natural numbers (numbers such as and ).

Abacus

Although calculators and computers are commonly used today instead of abacuses, abacuses remain in everyday use in some countries. Merchants, traders, and clerks in some parts of Eastern Europe, Russia, China, and Africa use abacuses. The abacus remains in common use as a scoring system in non-electronic table games. Others may use an abacus due to visual impairment that prevents the use of a calculator.

Abacus

Etymology

Abacus

The word abacus dates to at least AD 1387 when a Middle English work borrowed the word from Latin that described a sandboard abacus. The Latin word is derived from ancient Greek (abax) which means something without a base, and colloquially, any piece of rectangular material. Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust", or "drawing-board covered with dust (for the use of mathematics)" (the exact shape of the Latin

Abacus

of mathematics)" (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, (abakos). While the table strewn with dust definition is popular, some argue evidence is insufficient for that conclusion. Greek probably borrowed from a Northwest Semitic language like Phoenician, evidenced by a cognate with the Hebrew word ʾābāq (), or “dust” (in the post-Biblical sense "sand used as a writing surface").

Abacus

Both abacuses and abaci (soft or hard "c") are used as plurals. The user of an abacus is called an abacist. History Mesopotamia The Sumerian abacus appeared between 2700–2300 BC. It held a table of successive columns which delimited the successive orders of magnitude of their sexagesimal (base 60) number system.

Abacus

Some scholars point to a character in Babylonian cuneiform that may have been derived from a representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".

Abacus

Egypt Greek historian Herodotus mentioned the abacus in Ancient Egypt. He wrote that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument are yet to be discovered.

Abacus

Persia At around 600 BC, Persians first began to use the abacus, during the Achaemenid Empire. Under the Parthian, Sassanian, and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire- which is how the abacus may have been exported to other countries. Greece

Abacus

The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. Demosthenes (384 BC–322 BC) complained that the need to use pebbles for calculations was too difficult. A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius use the abacus as a metaphor for human behavior, stating "that men that sometimes stood for more and sometimes for less" like the pebbles on an abacus. The Greek abacus was a table of wood

Abacus

an abacus. The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome, and the Western Christian world until the French Revolution.

Abacus

A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet) dates to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble in length, wide, and thick, on which are 5 groups of markings. In the tablet's center is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it.

Abacus

a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line. Also from this time frame, the Darius Vase was unearthed in 1851. It was covered with pictures, including a "treasurer" holding a wax tablet in one hand while

Abacus

holding a wax tablet in one hand while manipulating counters on a table with the other.

Abacus

China The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.

Abacus

The Chinese abacus, also known as the suanpan (算盤/算盘, lit. "calculating tray"), is typically tall and comes in various widths, depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom one. The beads are usually rounded and made of hardwood. The beads are counted by moving them up or down towards the beam; beads moved toward the beam are counted, while those moved away from it are not. One of the top beads is 5,

Abacus

away from it are not. One of the top beads is 5, while one of the bottom beads is 1. Each rod has a number under it, showing the place value. The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.

Abacus

The prototype of the Chinese abacus appeared during the Han Dynasty, and the beads are oval. The Song Dynasty and earlier used the 1:4 type or four-beads abacus similar to the modern abacus including the shape of the beads commonly known as Japanese-style abacus.

Abacus

In the early Ming Dynasty, the abacus began to appear in a 1:5 ratio. The upper deck had one bead and the bottom had five beads. In the late Ming Dynasty, the abacus styles appeared in a 2:5 ratio. The upper deck had two beads, and the bottom had five. Various calculation techniques were devised for Suanpan enabling efficient calculations. Some schools teach students how to use it.

Abacus

In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).

Abacus

The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, given evidence of a trade relationship between the Roman Empire and China. However, no direct connection has been demonstrated, and the similarity of the abacuses may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. Incidentally, this allows

Abacus

suanpan has 5 plus 2. Incidentally, this allows use with a hexadecimal numeral system (or any base up to 18) which may have been used for traditional Chinese measures of weight. (Instead of running on wires as in the Chinese, Korean, and Japanese models, the Roman model used grooves, presumably making arithmetic calculations much slower.)

Abacus

Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a placeholder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians. Rome

Abacus

The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens, etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe and persisted in limited use into the nineteenth century. Due to Pope Sylvester II's reintroduction of the abacus with modifications,

Abacus

reintroduction of the abacus with modifications, it became widely used in Europe again during the 11th century This abacus used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster and was more easily moved.

Abacus

Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.

Abacus

One example of archaeological evidence of the Roman abacus, shown nearby in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives –five units, five tens, etc., essentially in a bi-quinary coded decimal system, related to the Roman numerals. The short grooves on the right may

Abacus

numerals. The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions).

Abacus

India

Abacus

The Abhidharmakośabhāṣya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartikā) on the number one (ekāṅka) means it is a one while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand". It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the

Abacus

were already finding new ways of recording the contents of the abacus. Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus.

Abacus

Japan In Japan, the abacus is called soroban (, lit. "counting tray"). It was imported from China in the 14th century. It was probably in use by the working class a century or more before the ruling class adopted it, as the class structure obstructed such changes. The 1:4 abacus, which removes the seldom-used second and fifth bead became popular in the 1940s.

Abacus

Today's Japanese abacus is a 1:4 type, four-bead abacus, introduced from China in the Muromachi era. It adopts the form of the upper deck one bead and the bottom four beads. The top bead on the upper deck was equal to five and the bottom one is similar to the Chinese or Korean abacus, and the decimal number can be expressed, so the abacus is designed as a one:four device. The beads are always in the shape of a diamond. The quotient division is generally used instead of the division method; at the same

Abacus

used instead of the division method; at the same time, in order to make the multiplication and division digits consistently use the division multiplication. Later, Japan had a 3:5 abacus called 天三算盤, which is now in the Ize Rongji collection of Shansi Village in Yamagata City. Japan also used a 2:5 type abacus.

Abacus

The four-bead abacus spread, and became common around the world. Improvements to the Japanese abacus arose in various places. In China an aluminium frame plastic bead abacus was used. The file is next to the four beads, and pressing the "clearing" button put the upper bead in the upper position, and the lower bead in the lower position.

Abacus

The abacus is still manufactured in Japan even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation. Using visual imagery can complete a calculation as quickly as a physical instrument.

Abacus

Korea The Chinese abacus migrated from China to Korea around 1400 AD. Koreans call it jupan (주판), supan (수판) or jusan (주산). The four-beads abacus (1:4) was introduced during the Goryeo Dynasty. The 5:1 abacus was introduced to Korea from China during the Ming Dynasty. Native America

Abacus

Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture. This Mesoamerican abacus used a 5-digit base-20 system. The word Nepōhualtzintzin comes from Nahuatl, formed by the roots; Ne – personal -; pōhual or pōhualli – the account -; and tzintzin – small similar elements. Its complete meaning was taken as: counting with small similar elements. Its use was taught in the Calmecac to the temalpouhqueh , who were students dedicated to taking the accounts of skies, from

Abacus

dedicated to taking the accounts of skies, from childhood.

Abacus

The Nepōhualtzintzin was divided into two main parts separated by a bar or intermediate cord. In the left part were four beads. Beads in the first row have unitary values (1, 2, 3, and 4), and on the right side, three beads had values of 5, 10, and 15, respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding count in the first row.

Abacus

The device featured 13 rows with 7 beads, 91 in total. This was a basic number for this culture. It had a close relation to natural phenomena, the underworld, and the cycles of the heavens. One Nepōhualtzintzin (91) represented the number of days that a season of the year lasts, two Nepōhualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin (273) is the number of days of a baby's gestation, and four Nepōhualtzintzin (364) completed a cycle and

Abacus

four Nepōhualtzintzin (364) completed a cycle and approximated one year. When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to 18 in floating point, which precisely calculated large and small amounts, although round off was not allowed.

Abacus

The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo, who in his travels throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them in gold, jade, encrustations of shell, etc. Very old Nepōhualtzintzin are attributed to the Olmec culture, and some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures.

Abacus

Sanchez wrote in Arithmetic in Maya that another base 5, base 4 abacus had been found in the Yucatán Peninsula that also computed calendar data. This was a finger abacus, on one hand, 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2, and 3 were used. Note the use of zero at the beginning and end of the two cycles.

Abacus

The quipu of the Incas was a system of colored knotted cords used to record numerical data, like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana (Quechua for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 Italian mathematician De Pasquale proposed an explanation. By comparing the form of several yupanas, researchers found that calculations were based using

Abacus

found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20, and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum.

Abacus

Russia

Abacus

The Russian abacus, the schoty (, plural from , counting), usually has a single slanted deck, with ten beads on each wire (except one wire with four beads for quarter-ruble fractions). Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916. The Russian abacus is often used vertically, with each wire running horizontally. The wires are usually bowed upward in the center, to keep the beads pinned to either side. It is cleared when all the beads are moved to the right. During

Abacus

when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually are of a different color from the other eight. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.

Abacus

The Russian abacus was in use in shops and markets throughout the former Soviet Union, and its usage was taught in most schools until the 1990s. Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia; according to Yakov Perelman. Some businessmen attempting to import calculators into the Russian Empire were known to leave in despair after watching a skilled abacus operator. Likewise, the mass production of Felix arithmometers since 1924 did not significantly

Abacus

arithmometers since 1924 did not significantly reduce abacus use in the Soviet Union. The Russian abacus began to lose popularity only after the mass production of domestic microcalculators in 1974.

Abacus

The Russian abacus was brought to France around 1820 by mathematician Jean-Victor Poncelet, who had served in Napoleon's army and had been a prisoner of war in Russia. The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid. The Turks and the Armenian people used abacuses similar to the

Abacus

the Armenian people used abacuses similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians.

Abacus

School abacus Around the world, abacuses have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic. In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame is common (see image).

Abacus

The wireframe may be used either with positional notation like other abacuses (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use. Teaching multiplication,

Abacus

suggests the latter use. Teaching multiplication, e.g. 6 times 7, may be represented by shifting 7 beads on 6 wires.

Abacus

The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ("calculating frame"), is often used, either on a string of beads or on a rigid framework. Feynman vs the abacus

Abacus

Physicist Richard Feynman was noted for facility in mathematical calculations. He wrote about an encounter in Brazil with a Japanese abacus expert, who challenged him to speed contests between Feynman's pen and paper, and the abacus. The abacus was much faster for addition, somewhat faster for multiplication, but Feynman was faster at division. When the abacus was used for a really difficult challenge, i.e. cube roots, Feynman won easily. However, the number chosen at random was close to a number Feynman

Abacus

chosen at random was close to a number Feynman happened to know was an exact cube, allowing him to use approximate methods.

Abacus

Neurological analysis

Abacus

Learning how to calculate with the abacus may improve capacity for mental calculation. Abacus-based mental calculation (AMC), which was derived from the abacus, is the act of performing calculations, including addition, subtraction, multiplication, and division, in the mind by manipulating an imagined abacus. It is a high-level cognitive skill that runs calculations with an effective algorithm. People doing long-term AMC training show higher numerical memory capacity and experience more effectively

Abacus

memory capacity and experience more effectively connected neural pathways. They are able to retrieve memory to deal with complex processes. AMC involves both visuospatial and visuomotor processing that generate the visual abacus and move the imaginary beads. Since it only requires that the final position of beads be remembered, it takes less memory and less computation time.

Abacus

Renaissance abacuses Binary abacus The binary abacus is used to explain how computers manipulate numbers. The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII. The device consists of a series of beads on parallel wires arranged in three separate rows. The beads represent a switch on the computer in either an "on" or "off" position.

Abacus

Visually impaired users An adapted abacus, invented by Tim Cranmer, and called a Cranmer abacus is commonly used by visually impaired users. A piece of soft fabric or rubber is placed behind the beads, keeping them in place while the users manipulate them. The device is then used to perform the mathematical functions of multiplication, division, addition, subtraction, square root, and cube root.

Abacus

Although blind students have benefited from talking calculators, the abacus is often taught to these students in early grades. Blind students can also complete mathematical assignments using a braille-writer and Nemeth code (a type of braille code for mathematics) but large multiplication and long division problems are tedious. The abacus gives these students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many

Abacus

their sighted peers using pencil and paper. Many blind people find this number machine a useful tool throughout life.

Abacus

See also Chinese Zhusuan Chisanbop Logical abacus Mental abacus Napier's bones Sand table Slide rule Soroban Suanpan Notes Footnotes References Reading External links Tutorials Min Multimedia Abacus curiosities Abacus in Various Number Systems at cut-the-knot Java applet of Chinese, Japanese and Russian abaci An atomic-scale abacus Examples of Abaci Aztex Abacus Indian Abacus

Abacus

Mathematical tools Chinese mathematics Egyptian mathematics Greek mathematics Indian mathematics Japanese mathematics Roman mathematics

Abacus

An acid is a molecule or ion capable of either donating a proton (i.e., hydrogen ion, H+), known as a Brønsted–Lowry acid, or, capable of forming a covalent bond with an electron pair, known as a Lewis acid.

Acid

The first category of acids are the proton donors, or Brønsted–Lowry acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents. A Brønsted or Arrhenius acid usually contains a hydrogen atom bonded to a chemical structure that is still energetically favorable after loss of H+.

Acid

Aqueous Arrhenius acids have characteristic properties which provide a practical description of an acid. Acids form aqueous solutions with a sour taste, can turn blue litmus red, and react with bases and certain metals (like calcium) to form salts. The word acid is derived from the Latin acidus/acēre, meaning 'sour'. An aqueous solution of an acid has a pH less than 7 and is colloquially also referred to as "acid" (as in "dissolved in acid"), while the strict definition refers only to the solute. A lower

Acid

definition refers only to the solute. A lower pH means a higher acidity, and thus a higher concentration of positive hydrogen ions in the solution. Chemicals or substances having the property of an acid are said to be acidic.

Acid

Common aqueous acids include hydrochloric acid (a solution of hydrogen chloride which is found in gastric acid in the stomach and activates digestive enzymes), acetic acid (vinegar is a dilute aqueous solution of this liquid), sulfuric acid (used in car batteries), and citric acid (found in citrus fruits). As these examples show, acids (in the colloquial sense) can be solutions or pure substances, and can be derived from acids (in the strict sense) that are solids, liquids, or gases. Strong acids and some

Acid

solids, liquids, or gases. Strong acids and some concentrated weak acids are corrosive, but there are exceptions such as carboranes and boric acid.

Acid

The second category of acids are Lewis acids, which form a covalent bond with an electron pair. An example is boron trifluoride (BF3), whose boron atom has a vacant orbital which can form a covalent bond by sharing a lone pair of electrons on an atom in a base, for example the nitrogen atom in ammonia (NH3). Lewis considered this as a generalization of the Brønsted definition, so that an acid is a chemical species that accepts electron pairs either directly or by releasing protons (H+) into the solution,

Acid

or by releasing protons (H+) into the solution, which then accept electron pairs. However, hydrogen chloride, acetic acid, and most other Brønsted–Lowry acids cannot form a covalent bond with an electron pair and are therefore not Lewis acids. Conversely, many Lewis acids are not Arrhenius or Brønsted–Lowry acids. In modern terminology, an acid is implicitly a Brønsted acid and not a Lewis acid, since chemists almost always refer to a Lewis acid explicitly as a Lewis acid.

Acid