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Arithmetic Of Quadratic Forms
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but the ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tables Generales Aritmetique MG 2108
Table may refer to: * Table (furniture), a piece of furniture with a flat surface and one or more legs * Table (landform), a flat area of land * Table (information), a data arrangement with rows and columns * Table (database), how the table data arrangement is used within databases * Calligra Tables, a spreadsheet application * Mathematical table * Table (parliamentary procedure) * Tables (board game) * Table, surface of the sound board (music) of a string instrument * ''Al-Ma'ida'', the fifth ''surah'' of the Qur'an, usually translated as “The Table” * Water table See also * Spreadsheet, a computer application * Table cut, a type of diamond cut * The Table (other) * Table Mountain (other) * Table Rock (other) * Tabler (other) * Tablet (other) Tablet may refer to: Medicine * Tablet (pharmacy), a mixture of pharmacological substances pressed into a small cake or bar, colloquially called a "pill" Computing * Tablet computer, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using Numerical digit, digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal numeral system (used in common life), the number ''three'' in the binary numeral system (used in computers), and the number ''two'' in the unary numeral system (e.g. used in Tally marks, tallying scores). The number the numeral represents is called its value. Not all number systems can represent all numbers that are considered in the modern days; for example, Roman numerals have no zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at least a standard representation) *Reflec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus (mathematician), Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hellenistic Civilization
In Classical antiquity, the Hellenistic period covers the time in History of the Mediterranean region, Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in 31 BC and the conquest of Ptolemaic Kingdom, Ptolemaic Egypt the following year. The Ancient Greek word ''Hellas'' (, ''Hellás'') was gradually recognized as the name of Greece, name for Greece, from which the word ''Hellenistic'' was derived. "Hellenistic" is distinguished from "Hellenic" in that the latter refers to Greece itself, while the former encompasses all ancient territories under Greek influence, in particular the East after the conquests of Alexander the Great. After the Macedonian invasion of the Achaemenid Empire in 330 BC and its disintegration shortly after, the Hellenistic kingdoms were established throughout Southwest Asia, south-west Asia (Seleucid Empire, Attalid dynasty, Kingdom of Pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maya Numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (a shell), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal bars; sometimes it is also written as three vertical dots to the left of two vertical bars. With these three symbols, each of the twenty vigesimal digits could be written. Numbers after 19 were written vertically in powers of twenty. The Maya used powers of twenty, just as the Hindu–Arabic numeral system uses powers of ten. For example, thirty-three would be written as one dot, above three dots atop two bars. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vigesimal
vigesimal () or base-20 (base-score) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). '' Vigesimal'' is derived from the Latin adjective '' vicesimus'', meaning 'twentieth'. Places In a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system. One modern method of finding the extra needed symbols is to write ten as the letter (the 20 means base ), to write nineteen as , and the numbers between with the corresponding letters of the alphabet. This is similar to the common computer-science practice of writing hexadecimal numerals over 9 with the letters "A–F". Another less common method skips over the letter "I", in order to avoid confusion between I20 as eighteen and one, so that the number eighteen is written as J20, and nineteen is written as K20. The number twenty is written as . According to this notation: : is equivalent to forty in decimal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonian Numerals
Assyro-Chaldean Babylonian cuneiform numerals were written in cuneiform (script), cuneiform, using a wedge-tipped Phragmites, reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians, who were famous for their astronomical observations, as well as their calculations (aided by their invention of the abacus), used a sexagesimal (base-60) Positional notation, positional numeral system inherited from either the Sumerian or the Akkadian civilizations. Neither of the predecessors was a positional system (having a convention for which 'end' of the numeral represented the units). Origin This system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages rather than Sumerian lexical numbers. However, the use of a special Sumerian sign for 60 (beside two Semitic signs for the same number) attests to a relation with the Sumerian system. Characters The Babyloni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sexagesimal
Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates. The number 60, a superior highly composite number, has twelve factors, 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 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 e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Abacus
The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of earlier abacuses like those that were used by the Greeks and Babylonians. Origin The Roman abacus 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. Karl Menninger said: 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. Above all, it has preserved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Epigraphical Museum in Athens. It has carved Greek letters and parallel grooves. The German mathematician Adam Ries described the use of counting boards in . In the novel ''Wolf Hall'', Hilary Mantel refers to Thomas Cromwell using a counting board in 16th-century England. References See also * Abacus * Calculator An electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the value may be negated if placed before another digit). In modern positional systems, such as the decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian numeral system, base 60, was the first positional system to be developed, and its influence is present today ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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