Algebra as Pattern: Relation Between Algebra and Patterns

Algebra is a disciple in mathematics that deals with different Symbols and also manipulates those symbols. It describes the various patterns which are around us. Algebra is a very important part of mathematics and also our lives. If we see any repetitive pattern where we can use algebra for its simplification, a general expression can be created to describe that specific pattern. Illustration of any sort of expression makes the problem easier and also helps in a better understanding of the topic. Algebraic thinking helps in recognizing patterns, representing the relationships, making generalizations, and also analyzing how things change. Algebraic patterns support critical thinking, reasoning, and dealing with problems mathematically. Here, we will discuss more on the topic along with some important questions.

Key Takeaways: Algebra, Algebraic Patterns, Matchstick Patterns.

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Algebra and Patterns

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The whole process involves the events of the knowledge, the procedure, and the different techniques which are divided into two parts:

1. Functions and Patterns:? These helps in the development of the understanding of the consistent change and the relationships.
2. Equivalence and the Equations: These helps in the development of the understanding of the balance and the methods which are related to problem-solving equations.

Algebraic Notations help in the representation of the problem which is in sort of numeric sentences and also involves unknown quantities.

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Algebra

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Algebra is a branch of mathematics that is very useful for the expression of any type of mathematical expression by the development of various relationships using alphabets or any other type of symbols. The objects in algebra are donated as different variables in algebra. Equations, terms, and expressions are used in a different type of arithmetic statements and operations which helps in drawing the link between the items which does not change over the period i.e., they have a non-constant value.

We use algebra and algebraic formulas in our day-to-day life, algebra is the exponents, polynomials, quadratic equations, etc.

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Arithmetic Algebraic Pattern

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Different patterns can be created using different objects like pencils, match sticks, etc. you can just arrange a few pencils in a given space and then add on different layers above it, just like the figure given below. The figure follows a certain pattern where two pencils are kept in every layer which makes a certain pattern. You can increase as many layers as you want, it could be 10 or 100?

If you make 10 layers then the number of pencils will be double the amount of the layers in it that is 20.

This means if you want 'x' number of layers/ levels then you need to multiply that 'x' by two to get the total number of pencils being used that making the number of pencils equal to '2x'. In this way, many algebraic patterns can be created based on different algebraic expressions.

All the patterns have their predefined pattern, given below are the patterns made up of match sticks.

Also Read: Algebra

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Algebraic matchsticks Patterns

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We can make many different patterns using matchsticks, Take a look at the following square pattern, squares can not get separated easily and the neighboring squares have common matchsticks. We can also use other basic things that we use in our daily life to make different patterns. Observe the following pattern:

In the given pattern the number of match sticks is increasing in a series of three (4, 7, 10, and 13 ) which makes the pattern one more than thrice the number of squares in the given pattern.

So, the pattern can be simply defined by using the algebraic expression '3x + 1'; (where x refers to the number of squares)

Now, we will look at how a triangle pattern can be made by using matchsticks as shown in the below figure. Here, the triangles are connected with each other.

In this matchstick pattern, the number of matchsticks is 3, 5, 7, and 9, which is more than twice the number of triangles in the given pattern. Therefore, the pattern is 2x + 1, where x is the number of triangles.

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Relation between Algebra and Algebra Patterns

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Let's consider an example to understand the relationship between algebra and algebra Patterns.

The pattern goes on likewise;

The simple rules are given below to determine the position of each element, it will make the process look very easy.

• The Letter 'C' is on the positions which are the multiples of three. then the given algebraic expression will be 3x. (where the x=1,2,3...)
• The Letter 'B' and the letter 'A' have different starting points but they also follow the same pattern which is '+3' at every step. 
• The Letter 'A' is on position 1, 4, 7, 10, 13, … and ‘B’ has 2, 5, 8, 11, …; these positions are mainly the growth of algebraic patterns that helps the students to analyze them and helps them to interpret the whole pattern.

Also Read: Section Formula in Coordinate Geometry

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Things to Remember

• Functions and patterns help in the development of the understanding of the consistent change and the relationships.
• Equivalence and the Equations help in the development of the understanding of the balance and the methods which are related to problem-solving equations.
• Algebra is a branch of mathematics that is very useful for the expression of any type of mathematical expression by the development of various relationships using alphabets or any other type of symbols.
• The objects in algebra are donated as different variables in algebra. 
• Equations, terms, and expressions are used in a different type of arithmetic statements and operations which helps in drawing the link between the items which does not change over the period i.e., they have a non-constant value.

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