Arithmetic, Geometry and Algebra

Introduction

Mathematics means "knowledge, study, learning". It includes the study of topics such as arithmetic, algebra, geometry and mathematical analysis. It has no generally accepted definition.

Several civilizations in China, India, Egypt, Central America and Mesopotamia equally contributed to mathematics. Counting system was first developed by the Sumerians. Mathematicians developed arithmetic, which includes basic operations, like addition, subtraction, multiplication, fractions and square roots.

As civilizations developed, mathematicians began to work with geometry, which deals with the areas and volumes to make angular measurements. Geometry is used everywhere from home construction to fashion and interior design.

Algebra was invented in the ninth century by a Persian mathematician, Mohammed ibn-Musa al-Khowarizmi. He also developed quick methods for multiplying and dividing numbers, which are known as algorithms. The study of algebra meant mathematicians were solving linear equations and systems, as well as quadratics solutions. 

Arithmetics – Numbers and Operations

Arithmetic is one of the first few subjects that you learned at lower grades. It deals with numbers and basic operations on them. It is the foundation for studying other branches of mathematics.

Arithmetic originated from the Greek word arithmos, is a branch of mathematics that consists of the study of counting numbers and the properties of the traditional operations on them such as addition(+), subtraction(-), multiplication(x) and division(). Arithmetic is an elementary part of number theory.

In addition to basic operations, this subject also includes more advanced operations, such as percentage, square roots, exponentiation, logarithmic functions, trigonometric functions and many more.

The four basic operations addition, subtraction, multiplication and division are commonly referred to as the four arithmetic operations.

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The four main properties of operations are:

  1. Commutative Property

  2. Associative Property

  3. Distributive Property

  4. Additive Identity

The BODMAS or PEMDAS rule is followed for order of operation involved +, −,×, and ÷. The order of operation is:

B:- Brackets

O: -Order

D: -Division

M:- Multiplication

A: -Addition

S: -Subtraction

Geometry-Shapes

Geometry is a study of shapes. It is broadly classified into two types: plane geometry and solid geometry. Plane geometry deals with two-dimensional figures like square, circle, rectangle, triangle and many more. Whereas Solid geometry deals with the study of three- dimensional shapes like cube, cuboid, cylinder, cone, sphere, and many more.

The study of this shape is needed to find lengths, widths, area, volume, perimeter, and many more terms. 

In mathematics, we need specific terms again and again to solve problems. It becomes difficult to write the full terms repeatedly, hence the shortcuts for these terms are discovered and it is called a symbol.

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Algebra

Algebra is one of the branches of Mathematics which deals with variables and numbers.A combination of constants and variables connected by the signs of the fundamental operation of addition, subtraction, multiplication, and division is called an algebraic expression. Various parts of an algebraic expression that are separated by the signs of + or - are called the terms of the expression. An algebraic expression is defined as a sum, difference, product or quotient of constants and variables. 

Consider,

 12x + 50

Here this expression is called an algebraic expression where x varies in values so it is a variable and 50 is constant. 12x and 50 are the terms and they are separated by the sign +. We can write anything a, b, c ….z in place of variables.

Algebra consist of different methods of solving a pair of linear equations:

1.Elimination method

2. Substitution method

3.Cross multiplication method

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Let us understand the difference between Arithmetic and Algebra. 

Difference Between Arithmetic and Algebra

Arithmetic

Algebra

Arithmetic, being the most basic of all branches of mathematics, deals with the basic counting of numbers and by using operations like addition, multiplication, division and subtraction on them.

Algebraic a branch of mathematics which deals with variables and numbers for solving problems. It uses generalized rules for problem solving.

Generally, associated with elementary school mathematics

Generally, associated with high school mathematics

Computation with specific numbers

Introduces generality and abstraction related concepts

Four operations (adding, subtracting, multiplication and division)

Algebra uses numbers and variables for solving problems. It is based on application of generalized rules for problem solving

Based on the information provided in the problem (memorized results for small values of numbers)

Based on the standard moves of elementary algebra

Number related

Variable related


Difference between arithmetic and algebra will make the arithmetic and algebra concepts more clear.

Let us understand the difference between Algebra and Geometry

Difference Between Algebra and Geometry

Algebra

Geometry

Algebra is a branch of mathematics that uses variables, in the forms of letters and symbols, to act as numbers or quantities in equations and formulas. 

Geometry is a branch of mathematics that studies points, lines, varied-dimensional objects and shapes, surfaces, and solids.

The main focuses in algebra are arithmetic, equations and understanding relationships between variables or ratios. 

Geometry focuses on understanding the geometric shapes and using their formulas. Most formulas convey how to find missing numbers, degrees and radians. 

Algebra does not use angles or degrees. 

Measurements consist of determining the degrees or radians o.f angles, areas, perimeters and points. 

Algebra has to do with equations and formulas

Geometry has to do with objects and shapes.



Differences between algebra and geometry will make the algebra and geometry concepts more clear.

Fun Facts:

  •  It was Babylonians who came up with Algebra in 1900 BC.

  • The use of signs addition(+) and subtraction(-) prove to be beneficial in performing algebraic equations. Before that, people use written words to express the functions of addition and subtraction which was a time-consuming process.

FAQ (Frequently Asked Questions)

1. What are the Branches of Algebra?

Answer: The branches of algebra are:

  1. Pre-algebra

  2. Elementary algebra

  3. Abstract algebra

  4. Linear algebra

  5. Universal algebra

2. Who is the Father of Arithmetic?

Answer: The 7th Century Great Indian mathematician and astronomer Brahmagupta is the father of arithmetic.He was from the state of Rajasthan of northwest India. He is also referred to as Bhillamalacarya, the teacher from Bhillamala. He became the head of the astronomical observatory at Ujjain in central India.

3. What are the Geometry Applications?

Answer: Geometry is widely used in day to day life. It has many practical uses in our daily life. Geometry is used by architects to design blueprints of their sites. They used different terms like angles, length, width, height, area, and many more. Geometry is also used in CAD computer-aided design. It is widely used in designing computer games. The way in which the characters move through their virtual worlds requires geometric computations. A technique that simulates a 3-D world using a 2-D map is used. Geometry is also used in GPS for locating the exact position. Everything around us is in the form of a particular shape.