Arithmetic is a branch of mathematics.
Arithmetic is the area of mathematics focused on numbers and the operations performed with them. It should be remembered that numbers are the signs that allow a quantity to be expressed.
Before entering fully into clarifying the meaning of the term, we are going to analyze its etymological origin. We can say that it is a word that comes from the Latin noun arithmetica , which in turn derives from the Greek aritmetikos . This last word is the result of the sum of two different parts:
- The name arithmos , which can be translated as "number" .
- The suffix – tikos , which is used to indicate “relating to” .
Origin of arithmetic
The formal emergence of arithmetic took place in Ancient Greece from an increase in the rigor of mathematics and the development of proofs. This is how the four elementary operations of this branch were established: addition , subtraction , multiplication and division .
Advancing in the complexity of arithmetic, you can go from elementary operations to others such as the extraction of roots and the calculation of powers . In addition, it is possible to include letters next to the numbers in order to achieve the representation of different variables.
Personalities who promoted it
Among the most important figures in arithmetic in Ancient Greece we can highlight the following:
- Euclid , who is considered the father of geometry. He produced numerous works that have become pillars of arithmetic, such as "The Elements" .
- Nicomachus of Gerasa , who is listed as a Neopythagorean mathematician. One of his most important and recognized works was "Introduction to Arithmetic" , where, among other issues, he explains number theory. This work was so important that it became manual in the Platonic schools.
The abacus helps solve arithmetic calculations.
Arithmetic calculations
Arithmetic calculations can be carried out in different ways. If they are simple operations, they can be performed mentally or with the help of the fingers of the hand. In ancient times, the abacus was also used, a device with small balls that move to make calculations . Currently, arithmetic operations are usually carried out with a calculator , whether physical or virtual.
Although it is true that the abacus is one of the best-known instruments that have been used to carry out calculations within arithmetic, in history many others have existed and still exist with the same objective. We are referring to the counting sticks , the Babylonian tablet , the adding machine ...
Other uses of the concept
The study of the properties and functions of numbers is known as high arithmetic . In this framework we can talk about binary arithmetic (which uses zero and one to represent values ), modular arithmetic (which works with modules) and ordinal arithmetic (oriented to ordinal numbers), among others.
Second-order arithmetic , on the other hand, is composed of different axiomatic systems that allow the formalization of natural numbers and the subsets formed by them.