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Arithmetic ARITHMETIC (from the Greek ἀριθμός arithmos, "number ") is a branch of mathematics that consists of the study of numbers , especially the properties of the traditional operations between them—addition , subtraction , multiplication and division . Arithmetic Arithmetic is an elementary part of number theory , and number theory is considered to be one of the toplevel divisions of modern mathematics , along with algebra , geometry , and analysis . The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory [...More...]  "Arithmetic" on: Wikipedia Yahoo 

Roman Abacus The Ancient Romans developed the ROMAN HAND ABACUS , a portable, but less capable, base10 version of the previous Babylonian abacus. It was the first portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals Roman numerals . As Karl Menninger says on page 315 of his book, "For more extensive and complicated calculations, such as those involved in Roman land surveys , there was, in addition to the hand abacus, a true reckoning board with unattached counters or pebbles. The Etruscan cameo and the Greek predecessors, such as the Salamis Tablet and the Darius Vase , give us a good idea of what it must have been like, although no actual specimens of the true Roman counting board are known to be extant. But language, the most reliable and conservative guardian of a past culture, has come to our rescue once more [...More...]  "Roman Abacus" on: Wikipedia Yahoo 

Vigesimal The VIGESIMAL or BASE 20 numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten ). CONTENTS* 1 Places * 1.1 Converting table * 2 Fractions * 3 Cyclic numbers * 4 Real numbers * 5 Use * 5.1 Africa * 5.2 Americas * 5.3 Asia * 5.4 In Europe Europe * 5.4.1 Origins * 5.4.2 Examples * 5.5 Related observations * 6 Examples in Mesoamerican languages * 6.1 Powers of twenty in Yucatec Maya and Nahuatl * 6.2 Counting in units of twenty * 7 Further reading * 8 Notes PLACESIn a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system [...More...]  "Vigesimal" on: Wikipedia Yahoo 

Tally Marks TALLY MARKS, also called HASH MARKS, are a unary numeral system . They are a form of numeral used for counting . They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded. However, because of the length of large numbers, tallies are not commonly used for static text. Notched sticks, known as tally sticks , were also historically used for this purpose. CONTENTS * 1 Early history * 2 Clustering * 3 Writing systems * 4 See also * 5 References EARLY HISTORY Main article: Prehistoric numerals Counting Counting aids other than body parts appear in the Upper Paleolithic . The oldest tally sticks date to between 35,000 and 25,000 years ago, in the form of notched bones found in the context of the European Aurignacian to Gravettian and in Africa's Late Stone Age [...More...]  "Tally Marks" on: Wikipedia Yahoo 

Egyptian Numerals The system of ancient EGYPTIAN NUMERALS was used in Ancient Egypt from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs . The Egyptians had no concept of a placevalued system such as the decimal system . The hieratic form of numerals stressed an exact finite series notation, ciphered one to one onto the Egyptian alphabet [...More...]  "Egyptian Numerals" on: Wikipedia Yahoo 

Democratic Republic Of The Congo Coordinates : 2°52′48″S 23°39′22″E / 2.88°S 23.656°E / 2.88; 23.656 Democratic Republic of the Congo République démocratique du Congo (French ) Repubilika ya Kôngo ya Dimokalasi (Kongo ) Republíki ya Kongó Demokratíki ( Lingala ) Jamhuri ya Kidemokrasia ya Kongo (Swahili ) Ditunga dia Kongu wa Mungalaata (LubaKatanga ) Flag Coat of arms MOTTO: "Justice – Paix – Travail" (French) "Justice – Peace – Work" ANTHEM: Debout Congolais (French) "Arise, Congolese" Location of Democratic [...More...]  "Democratic Republic Of The Congo" on: Wikipedia Yahoo 

Maya Numerals The MAYA NUMERAL SYSTEM is a vigesimal (base20) positional notation used in the Maya civilization to represent numbers. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal lines stacked above each other. 400s 20s 1s 33 429 5125 Numbers after 19 were written vertically in powers of twenty. For example, thirtythree would be written as one dot above three dots, which are in turn atop two lines. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33. Upon reaching 202 or 400, another row is started (203 or 8000, then 204 or 160,000, and so on). The number 429 would be written as one dot above one dot above four dots and a bar, or (1×202) + (1×201) + 9 = 429 [...More...]  "Maya Numerals" on: Wikipedia Yahoo 

Hellenistic Civilization The HELLENISTIC PERIOD covers the period of ancient Greek (Hellenic) history and Mediterranean history between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire Roman Empire as signified by the Battle of Actium Battle of Actium in 31 BC and the subsequent conquest of Ptolemaic Egypt Egypt the following year. At this time, Greek cultural influence and power was at its peak in Europe Europe , Africa Africa and Asia Asia , experiencing prosperity and progress in the arts , exploration , literature , theatre , architecture , music , mathematics , philosophy , and science . It is often considered a period of transition, sometimes even of decadence or degeneration , compared to the enlightenment of the Greek Classical era [...More...]  "Hellenistic Civilization" on: Wikipedia Yahoo 

Syriac Christianity SYRIAC CHRISTIANITY (Syriac : ܡܫܝܚܝܘܬܐ ܣܘܪܝܝܬܐ / mšiḥāiūṯā suryāiṯā) refers to Eastern Christian traditions that employs Syriac in their liturgical rites . The Syriac language Syriac language is a dialect of Middle Aramaic Aramaic that emerged in Edessa Edessa , Assyria Assyria Upper Mesopotamia , in the early 1st century AD, and is considered closely related to the Aramaic of Jesus Aramaic of Jesus [...More...]  "Syriac Christianity" on: Wikipedia Yahoo 

Counting Rods COUNTING RODS (traditional Chinese : 籌; simplified Chinese : 筹; pinyin : chóu; Japanese : 算木; rōmaji : sangi) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China China , Japan Japan , Korea Korea , and Vietnam Vietnam . They are placed either horizontally or vertically to represent any integer or rational number . The written forms based on them are called ROD NUMERALS [...More...]  "Counting Rods" on: Wikipedia Yahoo 

Greek Numerals GREEK NUMERALS, also known as IONIC, IONIAN, MILESIAN, or ALEXANDRIAN NUMERALS, are a system of writing numbers using the letters of the Greek alphabet . In modern Greece Greece , they are still used for ordinal numbers and in contexts similar to those in which Roman numerals Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers , however, Greece Greece uses Arabic numerals Arabic numerals . CONTENTS * 1 History * 2 Description * 3 Table * 4 Higher numbers * 5 Zero * 6 See also * 7 References * 8 External links HISTORYThe Minoan and Mycenaean civilizations ' Linear A and Linear B alphabets used a different system, called Aegean numerals Aegean numerals , which included specialized symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000 [...More...]  "Greek Numerals" on: Wikipedia Yahoo 

Pythagoreanism PYTHAGOREANISM originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism . Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism or Neoplatonism . Pythagorean ideas exercised a marked influence on Aristotle Aristotle , and Plato Plato , and through them, all of Western philosophy Western philosophy . Historians from the Stanford Encyclopedia of Philosophy Philosophy pointed out Aristotle Aristotle makes clear that there are several groups of people included under the heading "socalled Pythagoreans," by explicitly distinguishing those Pythagoreans who posited the table of opposites from the main Pythagorean system [...More...]  "Pythagoreanism" on: Wikipedia Yahoo 

Ishango Bone The ISHANGO BONE is a bone tool , dated to the Upper Paleolithic Upper Paleolithic era. It is a dark brown length of bone, the fibula of a baboon , with a sharp piece of quartz affixed to one end, perhaps for engraving. It was first thought to be a tally stick , as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool. It has also been suggested that the scratches might have been to create a better grip on the handle or for some other nonmathematical reason. The Ishango bone was found in 1960 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo . It was discovered in the area of Ishango near the Semliki River [...More...]  "Ishango Bone" on: Wikipedia Yahoo 

Counting Board The COUNTING BOARD is the precursor of the abacus , and the earliest known form of a counting device (excluding fingers and other very simple methods). Counting boards were made of stone or wood, and the counting was done on the board with beads, or pebbles etc. Not many boards survive because of the perishable materials used in their construction. The oldest known counting board, the Salamis Tablet (c. 300 BC) was discovered on the Greek island of Salamis in 1899. It is thought to have been used by the Babylonians in about 300 BC and is more of a gaming board than a calculating device. It is marble, about 150 x 75 x 4.5 cm, and is in the Greek National museum in Athens Athens . It has carved Greek letters and parallel grooves. The German mathematicican Adam Ries described the use of counting boards in Rechenbuch auf Linien und Ziphren in allerlei Handthierung / geschäfften und Kaufmanschafft [...More...]  "Counting Board" on: Wikipedia Yahoo 

Ancient Greek The ANCIENT GREEK language includes the forms of Greek used in ancient Greece Greece and the ancient world from around the 9th century BC to the 6th century AD. It is often roughly divided into the Archaic period (9th to 6th centuries BC), Classical period (5th and 4th centuries BC), and Hellenistic period Hellenistic period ( Koine Greek Koine Greek , 3rd century BC to the 4th century AD). It is antedated in the second millennium BC by Mycenaean Greek and succeeded by medieval Greek . The language of the Hellenistic phase is known as Koine (common). Koine is regarded as a separate historical stage of its own, although in its earliest form it closely resembled Attic Greek and in its latest form it approaches Medieval Greek Medieval Greek . Prior to the Koine period, Greek of the classic and earlier periods included several regional dialects [...More...]  "Ancient Greek" on: Wikipedia Yahoo 

Hindu–Arabic Numerals ARABIC NUMERALS, also called HINDU–ARABIC NUMERALS are the ten digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system , the most common system for the symbolic representation of numbers in the world today. In this numeral system , a sequence of digits such as "975" is read as a single number, using the position of the digit in the sequence to interpret its value. The symbol for zero is the key to the effectiveness of the system, which was developed by ancient mathematicians in the Indian subcontinent around AD 500. The system was adopted by Arabic Arabic mathematicians in Baghdad Baghdad and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from Arabic Arabic letters in the Maghreb Maghreb , the western region of the Arab world Arab world [...More...]  "Hindu–Arabic Numerals" on: Wikipedia Yahoo 