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125-460: An abacus ( pl. : abaci or abacuses ), also called a counting frame , is a hand -operated calculating tool which was used from ancient times in the ancient Near East , Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system . An abacus consists of a two-dimensional array of slidable beads (or similar objects). In their earliest designs, the beads could be loose on

250-611: A unit square , was approximated by the Babylonians of the Old Babylonian Period ( 1900 BC – 1650 BC ) as Because √ 2  ≈  1.414 213 56 ... is an irrational number , it cannot be expressed exactly in sexagesimal (or indeed any integer-base system), but its sexagesimal expansion does begin 1;24,51,10,7,46,6,4,44... ( OEIS :  A070197 ) The value of π as used by the Greek mathematician and scientist Ptolemy

375-405: A writing implement and paper (needed for algorism ) or an electric power source . 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. The abacus is still used to teach

500-533: A 5-digit base-20 system. The word Nepōhualtzintzin Nahuatl pronunciation: [nepoːwaɬˈt͡sint͡sin] comes from Nahuatl , formed by the roots; Ne – personal -; pōhual or pōhualli Nahuatl pronunciation: [ˈpoːwalːi] – the account -; and tzintzin Nahuatl pronunciation: [ˈt͡sint͡sin] – small similar elements. Its complete meaning was taken as: counting with small similar elements. Its use

625-481: A bead frame similar to the Russian abacus but with straight wires and a vertical frame is common (see image). 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

750-578: A calculation as quickly as with a physical instrument. 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. Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture. This Mesoamerican abacus used

875-829: A compact fist, presumably for fighting purposes. The fist is compact and thus effective as a weapon. It also provides protection for the fingers. However, this is not widely accepted to be one of the primary selective pressures acting on hand morphology throughout human evolution, with tool use and production being thought to be far more influential. Sexagesimal The number 60, a superior highly composite number , has twelve divisors , namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers . With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60

1000-579: 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 manipulating counters on a table with the other. The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles ( Latin : calculi ) were used. Marked lines indicated units, fives, tens, etc. as in

1125-560: A diversity of forms and materials in other cultures. 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. The quipu of

1250-416: A flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Each rod typically represents one digit of a multi-digit number laid out using a positional numeral system such as base ten (though some cultures used different numerical bases ). Roman and East Asian abacuses use a system resembling bi-quinary coded decimal , with

1375-415: A group of wide, wedge-shaped marks representing up to five tens ( [REDACTED] , [REDACTED] , [REDACTED] , [REDACTED] , [REDACTED] ). The value of the digit was the sum of the values of its component parts: Numbers larger than 59 were indicated by multiple symbol blocks of this form in place value notation . Because there was no symbol for zero it is not always immediately obvious how

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1500-399: A higher degree, the hands of other primates are anatomically similar and the dexterity of the human hand can not be explained solely on anatomical factors. The neural machinery underlying hand movements is a major contributing factor; primates have evolved direct connections between neurons in cortical motor areas and spinal motoneurons , giving the cerebral cortex monosynaptic control over

1625-501: A number should be interpreted, and its true value must sometimes have been determined by its context. For example, the symbols for 1 and 60 are identical. Later Babylonian texts used a placeholder ( [REDACTED] ) to represent zero, but only in the medial positions, and not on the right-hand side of the number, as in numbers like 13 200 . In the Chinese calendar , a system is commonly used in which days or years are named by positions in

1750-455: A number, then are manipulated to perform a mathematical operation with another number, and their final position can be read as the result (or can be used as the starting number for subsequent operations). In the ancient world, abacuses were a practical calculating tool. Although calculators and computers are commonly used today instead of abacuses, abacuses remain in everyday use in some countries. The abacus has an advantage of not requiring

1875-523: A pencil—reflects individual brain functioning. Among humans, the hands play an important function in body language and sign language . Likewise, the ten digits of two hands and the twelve phalanges of four fingers (touchable by the thumb) have given rise to number systems and calculation techniques. Many mammals and other animals have grasping appendages similar in form to a hand such as paws , claws , and talons, but these are not scientifically considered to be grasping hands. The scientific use of

2000-403: A period of one or two sexagesimal digits can only have regular number multiples of 59 or 61 as their denominators, and that other non-regular numbers have fractions that repeat with a longer period. The representations of irrational numbers in any positional number system (including decimal and sexagesimal) neither terminate nor repeat . The square root of 2 , the length of the diagonal of

2125-399: A primitive trait, while the palms of other extant higher primates are elongated to the extent that some of the thumb's original function has been lost (most notably in highly arboreal primates such as the spider monkey ). In humans, the big toe is thus more derived than the thumb. There is a hypothesis suggesting the form of the modern human hand is especially conducive to the formation of

2250-506: A representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "seem to have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations". Greek historian Herodotus mentioned the abacus in Ancient Egypt . He wrote that the Egyptians manipulated

2375-535: 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 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

2500-457: A semicolon (;) to separate the integer and fractional portions of the number and using a comma (,) to separate the positions within each portion. For example, the mean synodic month used by both Babylonian and Hellenistic astronomers and still used in the Hebrew calendar is 29;31,50,8,20 days. This notation is used in this article. In the sexagesimal system, any fraction in which the denominator

2625-482: A sequence of ten stems and in another sequence of 12 branches. The same stem and branch repeat every 60 steps through this cycle. Book VIII of Plato 's Republic involves an allegory of marriage centered on the number 60 = 12 960 000 and its divisors. This number has the particularly simple sexagesimal representation 1,0,0,0,0. Later scholars have invoked both Babylonian mathematics and music theory in an attempt to explain this passage. Ptolemy 's Almagest ,

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2750-404: A sexagesimal system where the maximum value in any position is 59. The Greeks limited their use of sexagesimal numbers to the fractional part of a number. In medieval Latin texts, sexagesimal numbers were written using Arabic numerals ; the different levels of fractions were denoted minuta (i.e., fraction), minuta secunda , minuta tertia , etc. By the 17th century it became common to denote

2875-407: A single slanted deck, with ten beads on each wire (except one wire with four beads for quarter- ruble fractions). 4-bead wire was introduced for quarter- kopeks , which were minted until 1916. The Russian abacus is 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

3000-450: A strong undercurrent of decimal notation, such as in how sexagesimal digits are written. Their use has also always included (and continues to include) inconsistencies in where and how various bases are to represent numbers even within a single text. The most powerful driver for rigorous, fully self-consistent use of sexagesimal has always been its mathematical advantages for writing and calculating fractions. In ancient texts this shows up in

3125-505: A switch on the computer in either an "on" or "off" position. 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. Although blind students have benefited from talking calculators,

3250-631: A top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally used, but some allow simple fractional components (e.g. 1 ⁄ 2 , 1 ⁄ 4 , and 1 ⁄ 12 in Roman abacus ), and a decimal point can be imagined for fixed-point arithmetic . Any particular abacus design supports multiple methods to perform calculations, including addition , subtraction , multiplication , division , and square and cube roots . The beads are first arranged to represent

3375-427: A transitional element to the fifth metacarpal. Together with the thumb, the four fingers form four oblique arches, of which the arch of the index finger functionally is the most important, especially for precision grip, while the arch of the little finger contribute an important locking mechanism for power grip. The thumb is undoubtedly the "master digit" of the hand, giving value to all the other fingers. Together with

3500-491: A treatise on mathematical astronomy written in the second century AD, uses base 60 to express the fractional parts of numbers. In particular, his table of chords , which was essentially the only extensive trigonometric table for more than a millennium, has fractional parts of a degree in base 60, and was practically equivalent to a modern-day table of values of the sine function. Medieval astronomers also used sexagesimal numbers to note time. Al-Biruni first subdivided

3625-470: A useful tool throughout life. Hand A hand is a prehensile , multi- fingered appendage located at the end of the forearm or forelimb of primates such as humans , chimpanzees , monkeys , and lemurs . A few other vertebrates such as the koala (which has two opposable thumbs on each "hand" and fingerprints extremely similar to human fingerprints ) are often described as having "hands" instead of paws on their front limbs. The raccoon

3750-436: 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. 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

3875-430: Is a regular number (having only 2, 3, and 5 in its prime factorization ) may be expressed exactly. Shown here are all fractions of this type in which the denominator is less than or equal to 60: However numbers that are not regular form more complicated repeating fractions . For example: The fact that the two numbers that are adjacent to sixty, 59 and 61, are both prime numbers implies that fractions that repeat with

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4000-405: 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 contents of the abacus. Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus. In Japan,

4125-474: Is located on one of the sides, parallel to the arm. A reliable way of identifying human hands is from the presence of opposable thumbs. Opposable thumbs are identified by the ability to be brought opposite to the fingers, a muscle action known as opposition. The skeleton of the human hand consists of 27 bones: the eight short carpal bones of the wrist are organized into a proximal row ( scaphoid , lunate , triquetral and pisiform ) which articulates with

4250-569: Is next to the four beads, and pressing the "clearing" button puts the upper bead in the upper position, and the lower bead in the lower position. The abacus is still manufactured in Japan, despite 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, one can complete

4375-472: Is often used, either on a string of beads or on a rigid framework. 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

4500-408: Is supplemented by the precision grip between the thumb and the distal finger pads made possible by the opposable thumbs. Hominidae (great apes including humans) acquired an erect bipedal posture about 3.6  million years ago , which freed the hands from the task of locomotion and paved the way for the precision and range of motion in human hands. Functional analyses of the features unique to

4625-629: Is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted. For example, the largest sexagesimal digit is "59". According to Otto Neugebauer , the origins of sexagesimal are not as simple, consistent, or singular in time as they are often portrayed. Throughout their many centuries of use, which continues today for specialized topics such as time, angles, and astronomical coordinate systems, sexagesimal notations have always contained

4750-497: Is to the neck of a metacarpal. One can also have a broken finger . The prehensile hands and feet of primates evolved from the mobile hands of semi- arboreal tree shrews that lived about 60  million years ago . This development has been accompanied by important changes in the brain and the relocation of the eyes to the front of the face, together allowing the muscle control and stereoscopic vision necessary for controlled grasping. This grasping, also known as power grip,

4875-505: Is usually described as having "hands" though opposable thumbs are lacking. Some evolutionary anatomists use the term hand to refer to the appendage of digits on the forelimb more generally—for example, in the context of whether the three digits of the bird hand involved the same homologous loss of two digits as in the dinosaur hand. The human hand usually has five digits: four fingers plus one thumb ; these are often referred to collectively as five fingers , however, whereby

5000-540: The Ekari people of Western New Guinea . Modern uses for the sexagesimal system include measuring angles , geographic coordinates , electronic navigation, and time . One hour of time is divided into 60 minutes , and one minute is divided into 60 seconds. Thus, a measurement of time such as 3:23:17 (3 hours, 23 minutes, and 17 seconds) can be interpreted as a whole sexagesimal number (no sexagesimal point), meaning 3 × 60 + 23 × 60 + 17 × 60 seconds . However, each of

5125-521: The French Revolution . The Salamis Tablet , found on the Greek island Salamis in 1846 AD, dates to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) in length, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In the tablet's center is a set of 5 parallel lines equally divided by

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5250-468: 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

5375-469: 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. 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

5500-513: 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 1:4 device. The beads are always in the shape of a diamond. The quotient division is generally used instead of the division method; at

5625-638: 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 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

5750-538: The Roman numeral system. 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. 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

5875-634: The Soviet Union . The Russian abacus began to lose popularity only after the mass production of domestic microcalculators in 1974. 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

6000-470: The carpal tunnel and contribute to the deep and superficial palmar arches . Several muscle tendons attaching to the TCL and the distal carpals also contribute to maintaining the carpal arch. Compared to the carpal arches, the arch formed by the distal ends of the metacarpal bones is flexible due to the mobility of the peripheral metacarpals (thumb and little finger). As these two metacarpals approach each other,

6125-600: The chimpanzee–human last common ancestor (CHLCA) and absent in modern humans are still present in the hands of Australopithecus , Paranthropus , and Homo floresiensis . This suggests that the derived changes in modern humans and Neanderthals did not evolve until 2.5 to 1.5 million years ago or after the appearance of the earliest Acheulian stone tools, and that these changes are associated with tool-related tasks beyond those observed in other hominins. The thumbs of Ardipithecus ramidus , an early hominin, are almost as robust as in humans, so this may be

6250-419: The dermis of palmoplantar skin inhibit melanin production and thus the ability to tan , and promote the thickening of the stratum lucidum and stratum corneum layers of the epidermis . All parts of the skin involved in grasping are covered by papillary ridges ( fingerprints ) acting as friction pads. In contrast, the hairy skin on the dorsal side is thin, soft, and pliable, so that the skin can recoil when

6375-523: The ulnar nerve may result in a condition in which some of the fingers cannot be flexed. A common fracture of the hand is a scaphoid fracture —a fracture of the scaphoid bone , one of the carpal bones. This is the commonest carpal bone fracture and can be slow to heal due to a limited blood flow to the bone. There are various types of fracture to the base of the thumb; these are known as Rolando fractures , Bennet's fracture , and Gamekeeper's thumb . Another common fracture, known as Boxer's fracture ,

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6500-535: 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. 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. In

6625-505: The Chinese, Korean, and Japanese models, the Roman model used grooves, presumably making arithmetic calculations much slower.) 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

6750-571: 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 or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus was used in Achaemenid Persia, the Etruscan civilization , Ancient Rome, and the Western Christian world until

6875-445: The abacus is called soroban ( 算盤, そろばん , 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. Today's Japanese abacus is a 1:4 type, four-bead abacus, introduced from China in

7000-488: 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 blind people find this number machine

7125-500: The abacus was used for more complex operations, i.e. cube roots, Feynman won easily. However, the number chosen at random was close to a number Feynman happened to know was an exact cube, allowing him to use approximate methods. 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

7250-517: The abacus with modifications, it became widely used in Europe again during the 11th century It used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster and was more easily moved. The earliest known written documentation of the Chinese abacus dates to the 2nd century BC. The Chinese abacus, also known as the suanpan (算盤/算盘, lit. "calculating tray"), comes in various lengths and widths, depending on

7375-402: The back of the hand), the deep palmar arch , and the superficial palmar arch . Together these three arches and their anastomoses provide oxygenated blood to the palm, the fingers, and the thumb. The hand is drained by the dorsal venous network of the hand with deoxygenated blood leaving the hand via the cephalic vein and the basilic vein . The glabrous (hairless) skin on the front of

7500-459: 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, e.g. 6 times 7, may be represented by shifting 7 beads on 6 wires. 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"),

7625-418: The bones of the forearm, and a distal row ( trapezium , trapezoid , capitate and hamate ), which articulates with the bases of the five metacarpal bones of the hand. The heads of the metacarpals will each in turn articulate with the bases of the proximal phalanx of the fingers and thumb. These articulations with the fingers are the metacarpophalangeal joints known as the knuckles. At the palmar aspect of

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7750-465: The countries around them – India, China, and the Roman Empire – which is how the abacus may have been exported to other countries. The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. Demosthenes (384–322 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

7875-437: The densest areas of nerve endings in the body, and are the richest source of tactile feedback. They also have the greatest positioning capability of the body; thus, the sense of touch is intimately associated with hands. Like other paired organs (eyes, feet, legs) each hand is dominantly controlled by the opposing brain hemisphere , so that handedness —the preferred hand choice for single-handed activities such as writing with

8000-519: The disorders that can cause this is Catel-Manzke syndrome . The fingers may be fused in a disorder known as syndactyly . Or there may be an absence of one or more central fingers—a condition known as ectrodactyly . Additionally, some people are born without one or both hands ( amelia ). Hereditary multiple exostoses of the forearm—also known as hereditary multiple osteochondromas—is another cause of hand and forearm deformity in children and adults. There are several cutaneous conditions that can affect

8125-447: The exact number varies between people: whereas a pair of sesamoid bones are found at virtually all thumb metacarpophalangeal joints, sesamoid bones are also common at the interphalangeal joint of the thumb (72.9%) and at the metacarpophalangeal joints of the little finger (82.5%) and the index finger (48%). In rare cases, sesamoid bones have been found in all the metacarpophalangeal joints and all distal interphalangeal joints except that of

8250-414: The fact that sexagesimal is used most uniformly and consistently in mathematical tables of data. Another practical factor that helped expand the use of sexagesimal in the past even if less consistently than in mathematical tables, was its decided advantages to merchants and buyers for making everyday financial transactions easier when they involved bargaining for and dividing up larger quantities of goods. In

8375-426: The fingers and toes". The ratio of the length of the index finger to the length of the ring finger in adults is affected by the level of exposure to male sex hormones of the embryo in utero . This digit ratio is below 1 for both sexes but it is lower in males than in females on average. A number of genetic disorders affect the hand. Polydactyly is the presence of more than the usual number of fingers. One of

8500-434: The fingers are stretched. On the dorsal side, the skin can be moved across the hand up to 3 cm (1.2 in); an important input the cutaneous mechanoreceptors . The web of the hand is a "fold of skin which connects the digits". These webs, located between each set of digits, are known as skin folds (interdigital folds or plica interdigitalis). They are defined as "one of the folds of skin, or rudimentary web, between

8625-417: The first metacarpophalangeal joints are small, almost spherical bones called the sesamoid bones. The fourteen phalanges make up the fingers and thumb, and are numbered I-V (thumb to little finger) when the hand is viewed from an anatomical position (palm up). The four fingers each consist of three phalanx bones: proximal, middle, and distal. The thumb only consists of a proximal and distal phalanx. Together with

8750-518: The form of several yupanas, researchers 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. The Russian abacus, the schoty ( Russian : счёты , plural from Russian : счёт , counting), usually has

8875-546: The fundamentals of mathematics to children in most countries. The word abacus dates to at least 1387 AD when a Middle English work borrowed the word from Latin that described a sandboard abacus. The Latin word is derived from ancient Greek ἄβαξ ( 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

9000-418: The groove on the dorsum of inferior side of ulna. The hand is innervated by the radial , median , and ulnar nerves . The radial nerve supplies the finger extensors and the thumb abductor , thus the muscles that extends at the wrist and metacarpophalangeal joints (knuckles); and that abducts and extends the thumb. The median nerve supplies the flexors of the wrist and digits, the abductors and opponens of

9125-456: The hand including the nails . The autoimmune disease rheumatoid arthritis can affect the hand, particularly the joints of the fingers. Some conditions can be treated by hand surgery . These include carpal tunnel syndrome , a painful condition of the hand and fingers caused by compression of the median nerve , and Dupuytren's contracture , a condition in which fingers bend towards the palm and cannot be straightened. Similarly, injury to

9250-457: The hand of modern humans have shown that they are consistent with the stresses and requirements associated with the effective use of paleolithic stone tools. It is possible that the refinement of the bipedal posture in the earliest hominids evolved to facilitate the use of the trunk as leverage in accelerating the hand. While the human hand has unique anatomical features, including a longer thumb and fingers that can be controlled individually to

9375-448: The hand, that of the thumb is the most mobile (and the least longitudinal). While the ray formed by the little finger and its associated metacarpal bone still offers some mobility, the remaining rays are firmly rigid. The phalangeal joints of the index finger, however, offer some independence to its finger, due to the arrangement of its flexor and extension tendons. The carpal bones form two transversal rows, each forming an arch concave on

9500-400: The hand, the palm, is relatively thick and can be bent along the hand's flexure lines where the skin is tightly bound to the underlying tissue and bones. Compared to the rest of the body's skin, the hands' palms (as well as the soles of the feet ) are usually lighter—and even much lighter in dark-skinned individuals, compared to the other side of the hand. Indeed, genes specifically expressed in

9625-934: The hour sexagesimally into minutes , seconds , thirds and fourths in 1000 while discussing Jewish months. Around 1235 John of Sacrobosco continued this tradition, although Nothaft thought Sacrobosco was the first to do so. The Parisian version of the Alfonsine tables (ca. 1320) used the day as the basic unit of time, recording multiples and fractions of a day in base-60 notation. The sexagesimal number system continued to be frequently used by European astronomers for performing calculations as late as 1671. For instance, Jost Bürgi in Fundamentum Astronomiae (presented to Emperor Rudolf II in 1592), his colleague Ursus in Fundamentum Astronomicum , and possibly also Henry Briggs , used multiplication tables based on

9750-461: The human hand are plesiomorphic (shared by both ancestors and extant primate species); the elongated thumbs and short hands more closely resemble the hand proportions of Miocene apes than those of extant primates. Humans did not evolve from knuckle-walking apes, and chimpanzees and gorillas independently acquired elongated metacarpals as part of their adaptation to their modes of locomotion. Several primitive hand features most likely present in

9875-413: The human hand include: There are five digits attached to the hand, notably with a nail fixed to the end in place of the normal claw . The four fingers can be folded over the palm which allows the grasping of objects. Each finger, starting with the one closest to the thumb, has a colloquial name to distinguish it from the others: The thumb (connected to the first metacarpal bone and trapezium )

10000-413: The human hand, including pentadactyly (having five fingers), the hairless skin of the palm and fingers, and the os centrale found in human embryos, prosimians, and apes. Furthermore, the precursors of the intrinsic muscles of the hand are present in the earliest fishes, reflecting that the hand evolved from the pectoral fin and thus is much older than the arm in evolutionary terms. The proportions of

10125-425: The inconsistencies in how numbers were represented within most texts extended all the way down to the most basic cuneiform symbols used to represent numeric quantities. For example, the cuneiform symbol for 1 was an ellipse made by applying the rounded end of the stylus at an angle to the clay, while the sexagesimal symbol for 60 was a larger oval or "big 1". But within the same texts in which these symbols were used,

10250-450: The index and middle finger, it forms the dynamic tridactyl configuration responsible for most grips not requiring force. The ring and little fingers are more static, a reserve ready to interact with the palm when great force is needed. The muscles acting on the hand can be subdivided into two groups: the extrinsic and intrinsic muscle groups. The extrinsic muscle groups are the long flexors and extensors . They are called extrinsic because

10375-421: The index finger. For example, in some individuals, the ulnar nerve supplies the entire ring finger and the ulnar side of the middle finger, whilst, in others, the median nerve supplies the entire ring finger. The hand is supplied with blood from two arteries, the ulnar artery and the radial artery . These arteries form three arches over the dorsal and palmar aspects of the hand, the dorsal carpal arch (across

10500-427: The integer part of sexagesimal numbers by a superscripted zero, and the various fractional parts by one or more accent marks. John Wallis , in his Mathesis universalis , generalized this notation to include higher multiples of 60; giving as an example the number 49‵‵‵‵36‵‵‵25‵‵15‵1°15′2″36‴49⁗ ; where the numbers to the left are multiplied by higher powers of 60, the numbers to the right are divided by powers of 60, and

10625-477: The interlocking shapes of the carpal bones, and the wrist is therefore more stable in flexion than in extension. The distal carpal arch affects the function of the CMC joints and the hands, but not the function of the wrist or the proximal carpal arch. The ligaments that maintain the distal carpal arches are the transverse carpal ligament and the intercarpal ligaments (also oriented transversally). These ligaments also form

10750-476: The late 3rd millennium BC, Sumerian/Akkadian units of weight included the kakkaru ( talent , approximately 30 kg) divided into 60 manû ( mina ), which was further subdivided into 60 šiqlu ( shekel ); the descendants of these units persisted for millennia, though the Greeks later coerced this relationship into the more base-10 compatible ratio of a shekel being one 50th of a mina . Apart from mathematical tables,

10875-420: The long finger. The articulations are: The fixed and mobile parts of the hand adapt to various everyday tasks by forming bony arches: longitudinal arches (the rays formed by the finger bones and their associated metacarpal bones), transverse arches (formed by the carpal bones and distal ends of the metacarpal bones), and oblique arches (between the thumb and four fingers): Of the longitudinal arches or rays of

11000-570: 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). 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

11125-402: 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 connected neural pathways. They are able to retrieve memory to deal with complex processes. AMC involves both visuospatial and visuomotor processing that generate

11250-456: The motoneurons of the hand muscles; placing the hands "closer" to the brain. The recent evolution of the human hand is thus a direct result of the development of the central nervous system , and the hand, therefore, is a direct tool of our consciousness—the main source of differentiated tactile sensations—and a precise working organ enabling gestures—the expressions of our personalities. There are nevertheless several primitive features left in

11375-455: The muscle belly is located on the forearm. The intrinsic muscle groups are the thenar (thumb) and hypothenar (little finger) muscles; the interosseous muscles ( four dorsally and three volarly ) originating between the metacarpal bones; and the lumbrical muscles arising from the deep flexor (and are special because they have no bony origin) to insert on the dorsal extensor hood mechanism. The fingers have two long flexors, located on

11500-399: The number 10 was represented as a circle made by applying the round end of the style perpendicular to the clay, and a larger circle or "big 10" was used to represent 100. Such multi-base numeric quantity symbols could be mixed with each other and with abbreviations, even within a single number. The details and even the magnitudes implied (since zero was not used consistently ) were idiomatic to

11625-436: The number marked with the superscripted zero is multiplied by 1. This notation leads to the modern signs for degrees, minutes, and seconds. The same minute and second nomenclature is also used for units of time, and the modern notation for time with hours, minutes, and seconds written in decimal and separated from each other by colons may be interpreted as a form of sexagesimal notation. In some usage systems, each position past

11750-413: 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, to represent numbers in a bi-quinary coded decimal -like system. 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

11875-403: The palmar gutter deepens. The central-most metacarpal (middle finger) is the most rigid. It and its two neighbors are tied to the carpus by the interlocking shapes of the metacarpal bones. The thumb metacarpal only articulates with the trapezium and is therefore completely independent, while the fifth metacarpal (little finger) is semi-independent with the fourth metacarpal (ring finger) which forms

12000-407: The palmar side of the thumb, index, middle, and half ring fingers. Dorsal branches innervates the distal phalanges of the index, middle, and half ring fingers. The ulnar nerve supplies the ulnar third of the hand, both at the palm and the back of the hand, and the little and half ring fingers. There is a considerable variation to this general pattern, except for the little finger and volar surface of

12125-410: The palmar side. Because the proximal arch simultaneously has to adapt to the articular surface of the radius and to the distal carpal row, it is by necessity flexible. In contrast, the capitate, the "keystone" of the distal arch, moves together with the metacarpal bones and the distal arch is therefore rigid. The stability of these arches is more dependent of the ligaments and capsules of the wrist than of

12250-442: The particular time periods, cultures, and quantities or concepts being represented. While such context-dependent representations of numeric quantities are easy to critique in retrospect, in modern times we still have dozens of regularly used examples of topic-dependent base mixing, including the recent innovation of adding decimal fractions to sexagesimal astronomical coordinates. The sexagesimal system as used in ancient Mesopotamia

12375-593: 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. 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

12500-415: The phalanges of the fingers and thumb these metacarpal bones form five rays or poly-articulated chains. Because supination and pronation (rotation about the axis of the forearm) are added to the two axes of movements of the wrist, the ulna and radius are sometimes considered part of the skeleton of the hand. There are numerous sesamoid bones in the hand, small ossified nodes embedded in tendons;

12625-503: The post-Biblical sense "sand used as a writing surface"). Both abacuses and abaci are used as plurals. The user of an abacus is called an abacist . The Sumerian abacus appeared between 2700 and 2300 BC. It held a table of successive columns which delimited the successive orders of magnitude of their sexagesimal (base 60) number system. Some scholars point to a character in Babylonian cuneiform that may have been derived from

12750-402: 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. The Russian abacus was in use in shops and markets throughout the former Soviet Union , and its usage

12875-597: 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. The four-bead abacus spread, and became common around the world. Improvements to the Japanese abacus arose in various places. In China, an abacus with an aluminium frame and plastic beads has been used. The file

13000-536: The sexagesimal point was numbered, using Latin or French roots: prime or primus , seconde or secundus , tierce , quatre , quinte , etc. To this day we call the second-order part of an hour or of a degree a "second". Until at least the 18th century, ⁠ 1 / 60 ⁠ of a second was called a "tierce" or "third". In the 1930s, Otto Neugebauer introduced a modern notational system for Babylonian and Hellenistic numbers that substitutes modern decimal notation from 0 to 59 in each position, while using

13125-468: The sexagesimal system in the late 16th century, to calculate sines. In the late 18th and early 19th centuries, Tamil astronomers were found to make astronomical calculations, reckoning with shells using a mixture of decimal and sexagesimal notations developed by Hellenistic astronomers. Base-60 number systems have also been used in some other cultures that are unrelated to the Sumerians, for example by

13250-487: The shorter grooves denote fives (five units, five tens, etc.) resembling a bi-quinary coded decimal system related to the Roman numerals . The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions). The Roman system of 'counter casting' was used widely in medieval Europe, and persisted in limited use into the nineteenth century. Wealthy abacists used decorative minted counters, called jetons . Due to Pope Sylvester II 's reintroduction of

13375-403: The tendons of these form the anatomical snuff box . Also, the index finger and the little finger have an extra extensor used, for instance, for pointing. The extensors are situated within 6 separate compartments. The first four compartments are located in the grooves present on the dorsum of inferior side of radius while the 5th compartment is in between radius and ulna. The 6th compartment is in

13500-410: The term hand in this sense to distinguish the terminations of the front paws from the hind ones is an example of anthropomorphism . The only true grasping hands appear in the mammalian order of primates . Hands must also have opposable thumbs , as described later in the text. The hand is located at the distal end of each arm. Apes and monkeys are sometimes described as having four hands, because

13625-718: The three sexagesimal digits in this number (3, 23, and 17) is written using the decimal system. Similarly, the practical unit of angular measure is the degree , of which there are 360 (six sixties) in a circle. There are 60 minutes of arc in a degree, and 60 arcseconds in a minute. In version 1.1 of the YAML data storage format, sexagesimals are supported for plain scalars, and formally specified both for integers and floating point numbers. This has led to confusion, as e.g. some MAC addresses would be recognised as sexagesimals and loaded as integers, where others were not and loaded as strings. In YAML 1.2 support for sexagesimals

13750-405: The thumb in opposition, making grasping possible. The extensors are located on the back of the forearm and are connected in a more complex way than the flexors to the dorsum of the fingers. The tendons unite with the interosseous and lumbrical muscles to form the extensorhood mechanism. The primary function of the extensors is to straighten out the digits. The thumb has two extensors in the forearm;

13875-415: The thumb is included as one of the fingers . It has 27 bones, not including the sesamoid bone , the number of which varies among people, 14 of which are the phalanges ( proximal , intermediate and distal ) of the fingers and thumb. The metacarpal bones connect the fingers and the carpal bones of the wrist . Each human hand has five metacarpals and eight carpal bones. Fingers contain some of

14000-461: The thumb, the first and second lumbrical. The ulnar nerve supplies the remaining intrinsic muscles of the hand. All muscles of the hand are innervated by the brachial plexus (C5–T1) and can be classified by innervation: The radial nerve supplies the skin on the back of the hand from the thumb to the ring finger and the dorsal aspects of the index, middle, and half ring fingers as far as the proximal interphalangeal joints. The median nerve supplies

14125-410: The toes are long and the hallux is opposable and looks more like a thumb , thus enabling the feet to be used as hands. The word "hand" is sometimes used by evolutionary anatomists to refer to the appendage of digits on the forelimb such as when researching the homology between the three digits of the bird hand and the dinosaur hand. An adult human male's hand weighs about a pound. Areas of

14250-465: 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. The prototype of the Chinese abacus appeared during the Han dynasty , and the beads are oval. The Song dynasty and earlier used

14375-435: The underside of the forearm. They insert by tendons to the phalanges of the fingers. The deep flexor attaches to the distal phalanx, and the superficial flexor attaches to the middle phalanx. The flexors allow for the actual bending of the fingers. The thumb has one long flexor and a short flexor in the thenar muscle group. The human thumb also has other muscles in the thenar group ( opponens and abductor brevis muscle ), moving

14500-471: The use of mathematics)" (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ἄβακoς ( abakos )). While the table strewn with dust definition is popular, some argue evidence is insufficient for that conclusion. Greek ἄβαξ probably borrowed from a Northwest Semitic language like Phoenician , evidenced by a cognate with the Hebrew word ʾābāq ( אבק ‎), or "dust" (in

14625-407: 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. 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

14750-465: 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. 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

14875-418: Was 3;8,30 = 3 + ⁠ 8 / 60 ⁠ + ⁠ 30 / 60 ⁠ = ⁠ 377 / 120 ⁠ ≈ 3.141 666 .... Jamshīd al-Kāshī , a 15th-century Persian mathematician, calculated 2 π as a sexagesimal expression to its correct value when rounded to nine subdigits (thus to ⁠ 1 / 60 ⁠ ); his value for 2 π was 6;16,59,28,1,34,51,46,14,50. Like √ 2 above, 2 π

15000-420: Was dropped. In Hellenistic Greek astronomical texts, such as the writings of Ptolemy , sexagesimal numbers were written using Greek alphabetic numerals , with each sexagesimal digit being treated as a distinct number. Hellenistic astronomers adopted a new symbol for zero, — ° , which morphed over the centuries into other forms, including the Greek letter omicron, ο, normally meaning 70, but permissible in

15125-405: Was not a pure base-60 system, in the sense that it did not use 60 distinct symbols for its digits . Instead, the cuneiform digits used ten as a sub-base in the fashion of a sign-value notation : a sexagesimal digit was composed of a group of narrow, wedge-shaped marks representing units up to nine ( [REDACTED] , [REDACTED] , [REDACTED] , [REDACTED] , ..., [REDACTED] ) and

15250-497: Was not allowed. 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

15375-576: 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 Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians. 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,

15500-496: 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 reduce abacus use in

15625-520: Was taught in the Calmecac to the temalpouhqueh Nahuatl pronunciation: [temaɬˈpoʍkeʔ] , who were students dedicated to taking the accounts of skies, from childhood. 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

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