arithmetic

词源: count, number, art, craft

Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them - addition, subtraction, multiplication, division, exponentiation and extraction of roots. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level 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.

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.

Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals, and the vigesimal (base 20) system that defined Maya numerals. Because of this place-value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation.

Greek numerals were used by Archimedes, Diophantus and others in a positional notation not very different from the modern notation. The ancient Greeks lacked a symbol for zero until the Hellenistic period, and they used three separate sets of symbols as digits: one set for the units place, one for the tens place, and one for the hundreds. For the thousands place, they would reuse the symbols for the units place, and so on. Their addition algorithm was identical to the modern method, and their multiplication algorithm was only slightly different. Their long division algorithm was the same, and the digit-by-digit square root algorithm, popularly used as recently as the 20th century, was known to Archimedes (who may have invented it).

The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra. The ancient Chinese used a positional notation similar to that of the Greeks. Since they also lacked a symbol for zero, they had one set of symbols for the units place, and a second set for the tens place. For the hundreds place, they then reused the symbols for the units place, and so on. Their symbols were based on the ancient counting rods [算筹]. The exact time where the Chinese started calculating with positional representation is unknown, though it is known that the adoption started before 400 BC. The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers. This is explained in the Nine Chapters on the Mathematical Art (Jiuzhang Suanshu), which was written by Liu Hui dated back to 2nd century BC.

《九章算术》是中国古代的一部数学书，作者已不可考。其《方程》章在数学史上首次阐述了负数及其加减运算法则。西汉(约公元前200~8年)的张苍和耿寿昌曾对它做过增补和整理——“汉北平侯张苍、大司农中丞耿寿昌，皆以善算名世”。现今流传的大多是263年(魏晋时期)刘徽所注的《九章算术注》(原文+注解)。刘徽还写了《海岛算经》。

《数书九章》是秦九韶的唯一著作。秦九韶(1208年－1268年)，南宋著名数学家，与李冶、杨辉、朱世杰并称宋元数学四大家。

杨辉三角形是二项式系数(a+b)ⁿ的一种排列方式，在他1261年所著的《详解九章算法》中出现。帕斯卡在1654年发现同一规律。

《算经十书》指汉、唐一千多年间的十部著名数学著作，它们曾是隋唐时代国子监算学科的教科书。它们是：《周髀算经》、《九章算术》、《海岛算经》、《张丘建算经》、《夏侯阳算经》、《五经算术》、《缉古算经》、《缀术》、《五曹算经》、《孙子算经》。

Leibniz's Stepped Reckoner was the first calculator that could perform all four arithmetic operations.

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs).

Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry [三角学].

六级/考研单词: arithmetic, mathematics, subtract, extract, elementary, algebra, geometry, synonym, artefact, interpret, decimal, digit, nil, lately, dynasty, ongoing, rod, reckon, compute, logic, float

标签：used,number,place,numbers,was,arithmetic
来源： https://www.cnblogs.com/funwithwords/p/15834225.html