Mathematical Patterns

Definition

Mathematics is all about numbers. It involves the study of different patterns. There are different types of patterns, such as number patterns, image patterns, logic patterns, word patterns etc. Number patterns are very common in Mathematics. These are quite familiar to the students who study Maths frequently. Especially, number patterns are everywhere in Mathematics. Number patterns are all predictions. [1]

Patterns include a series or sequence that generally repeats itself. The patterns that we observe in our daily lives are those of colors, actions, shapes, numbers, etc. They can be related to any event or object and can be finite or infinite. In mathematics, patterns are a set of numbers arranged in a sequence such that they are related to each other in a specific rule. These rules define a way to calculate or solve problems. For example, in a sequence of 3,6,9,12, . . ., each number is increasing by 3. So, according to the pattern, the last number will be 12 + 3 = 15. The following figure shows the different types of patterns and sequences that can be formed with numbers. [4]

The characterization of mathematics as the “study of patterns” seems to have been first made by the British mathematician, G. H. Hardy. Lamenting his waning mathematical powers, Hardy, perhaps as a curative for his despair, wrote a small book on his life as a mathematician. Although the book was, indeed, an account of what it is to be a mathematician, it naturally could not escape also being an account of mathematics itself. Thus, when Hardy wrote in A Mathematician’s Apology, [5]

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas”
Hardy, 1992 , p. 84

Who

Everyone uses patterns. If you observe closely, we are surrounded by patterns. Some are man-made, and there are patterns in nature too. These patterns can be found in animals, plants, and even outer space! [10]

Clapping Games
Colors
Dancing
Day and Night
Everyday Objects
Literature
Musical Patterns
Plants (e.g., sunflower seeds follow the Fibonacci sequence)
Seasons
Shapes
Symmetrical Patterns

What

There are 3 types of patterns: [9]

Shape Pattern
Letter Pattern
Number Pattern

Shape Patterns

When a group of shapes are repeated, the pattern or sequence is known as a shape pattern. Shape patterns follow a certain sequence or order of shapes, i.e., they are repeated. The shapes can be simple shapes like circles, squares, rectangles, triangles, etc., or other objects such as arrows, flowers, moons, and stars. [9]

Letter Patterns

A sequence that consists of letters or English alphabets is known as a letter pattern. A letter pattern establishes a common relationship between all the letters. [9]

Number Patterns

The some of the following number patterns are discussed in on other pages of the Mathematical Mysteries website.

In Discrete Mathematics, we have three types of patterns as follows: [1]

Repeating – A type of pattern, in which the rule keeps repeating over and over is called a repeating pattern.
Growing – If the numbers are present in the increasing form, then the pattern is known as a growing pattern. Example 34, 40, 46, 52, …..
Shrinking – In the shrinking pattern, the numbers are in decreasing form. Example: 42, 40, 38, 36

Why

In mathematics, patterns are more than a beautiful design (though they are often that too), patterns follow a predictable rule and that rule allows us to predict what will come next. Mathematicians say that mathematics is the study of pattern—of patterns and structure in numbers, and patterns and structure in geometry. Seeing pattern and structure in the world around us is a key mathematical habit of mind and one that children are developing from the first days of life. Children are naturally attuned to patterns because it allows them to predict what will come next and make sense of their world. When we see patterns we are able to predict—to count on things happening—and feel more secure and confident. [3]

Patterns allow someone to make educated guesses. Much science is based on making a hypothesis and hypotheses are often based on understanding patterns. Similarly, we make many common assumptions based on recurring patterns. Understanding patterns aid in developing mental skills. In order to recognize patterns one need to have an understanding of critical thinking and logic and these are clearly important skills to develop. [6]

Virtually all mathematics is based on pattern and structure. The power of mathematics lies in relations and transformations which give rise to patterns and generalizations. Abstracting patterns is the basis of structural knowledge, the goal of mathematics learning. [7]

A pattern is any regularity that might be spatial, logical, or numerical.
The ability to recognize and create patterns helps us make predictions.
Understanding patterns helps children learn complex operations of mathematics easily.
Patterns are the foundation of our numeracy skills. Looking for a pattern is a strategy that can be used to solve problems.
Patterns develop the basic concepts of algebra among learners. Rules and number sequences are there in algebra, which is also a pattern.
If the child is stuck with some numerical algebraic problem take the child to the basics which include patterns of colors, patterns of numbers, patterns of shapes, and such other concrete stuff
It promotes creativity amongst students and helps them to understand the properties of numbers and operations.
From the above points, we can conclude that ‘Patterns’ are an important mathematical concept at the primary level because patterns develop the basic concepts of algebra among learners.

See Theoretical Knowledge Vs Practical Application.

How

To find the rule in a pattern, observe the common change in the shapes or numbers. Pattern can be increasing or decreasing. Find the sum or difference between the terms to find the rule. [2]

Many of the References and Additional Reading websites and Videos will assist you with understanding and applying patterns.

As some professors say: “It is intuitively obvious to even the most casual observer.”

References

[1] ⭐ “Patterns In Maths (Definition, Types & Examples) | Arithmetic & Geometric Pattern”. 2023. BYJUS. https://byjus.com/maths/patterns/.

[2] “Types of Patterns in Math, Rules and Examples”. 2023. Study.com. https://study.com/learn/lesson/math-patterns-overview-rules-types.html.

[3] “Why are patterns and structure important in early math?”. 2023. youngmathematicians.edc.org. https://youngmathematicians.edc.org/math-topic/patterns-and-algebra/.

[4] “Patterns”. 2023. CUEMATH. https://www.cuemath.com/geometry/patterns/.

[5] “Mathematics as the Science of Patterns – Mathematics as the Science of Patterns”. 2023. maa.org. https://www.maa.org/press/periodicals/convergence/mathematics-as-the-science-of-patterns-mathematics-as-the-science-of-patterns.

[6] “10 Reasons Why It is Important To Understand Mathematical Patterns?”. 2023. Math Worksheet Center. https://www.mathworksheetscenter.com/mathtips/mathpatterns.html.

[7] “[Solved] ‘Patterns’ Is An Important Mathematical Concept At P”. 2023. Testbook. https://testbook.com/question-answer/patterns-is-an-important-mathematical-co–623c6a72f986d9cc6c94841e.

[8] “Number Patterns in Whole Numbers (Definition, Types and Examples)”. 2023. BYJUS. https://byjus.com/maths/number-patterns-whole-numbers/.

Numbers have fascinated humans since ages, be it the mathematicians or statisticians. There is so much that one can do with them, and there’s so much that is yet to be discovered. For example, we know that the whole numbers represent the set of all positive numbers, including zero, without any decimal or fractional parts. But did we know that we can derive relationships between the whole numbers by finding some kind of patterns between them? This is why numbers are so interesting or fascinating. In this article, we are going to discuss what are number patterns in Mathematics, charts, examples in detail.

[9] “What Are Patterns in Math? Definition, Types, Examples, Facts”. 2022. SplashLearn – Math Vocabulary. https://www.splashlearn.com/math-vocabulary/geometry/pattern.

[10] “What Are Some Examples Of Patterns In Real Life?”. 2022. BYJU’s Future School Blog. https://www.byjusfutureschool.com/blog/what-are-some-examples-of-patterns-in-real-life/.

Additional Reading

⭐ Bischoff, Manon. 2023. “Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern”. Scientific American. https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/.

Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators. It is also one of the hardest problems in mathematics. For centuries, experts have been studying the special properties of tile shapes that can cover floors, kitchen backsplashes or infinitely large planes without leaving any gaps. Specifically, mathematicians are interested in tile shapes that can cover the whole plane without ever creating a repeating design. In these special cases, called aperiodic tilings, there’s no pattern that you can copy and paste to keep the tiling going. No matter how you chop up the mosaic, each section will be unique.

⭐ “Pattern recognition and use in real life problem solving”. 2023. SureSolv.com. https://suresolv.com/problem-solving-techniques/pattern-recognition-and-use-real-life-problem-solving.

Pattern recognition forms the basis of learning and action for all living things in nature. Patterns are all around us – from human fingerprints, zebra crossings, warm current flows in oceans to the beautiful arrangement of a rose bud.

Platas, Linda. “The Mathematics Of Patterns And Algebra | DREME TE”. 2023. prek-Math-te.stanford.edu. https://prek-math-te.stanford.edu/patterns-algebra/mathematics-patterns-and-algebra.

Patterns are at the heart of mathematics. This article explains the basic math underlying the patterns that children encounter in their everyday lives and in preschool. Teachers need to understand these basic math concepts in order to help children build on their intuitive knowledge of them. One key concept is the generalization of patterns: the ability to apply a pattern (e.g., ABAB) to multiple materials and contexts. Other concepts covered include copying, extending, and creating patterns.

SHAMSHEER. “5 Mathematical Patterns in Nature: Fibonacci, Fractals & More”. 2023. https://owlcation.com/stem/Astounding-Ways-How-Mathematics-is-a-Part-of-Nature-.

The field of mathematics was invented, not discovered – it is just a creation of the human mind. Maths is the missing link between the physical and theoretical worlds. The physical world is what we see, observe and feel, meaning we can understand its technicalities just by feeling them or solve its problems by practical means.

TEDxIITGuwahati. “Mathematical Patterns In Nature”. 2020. Medium. https://tedxiitguwahati.medium.com/mathematical-patterns-in-nature-44a3c0f1a799.

Nature never fails to surprise us. Every creation leads us into a beautiful discovery, new or even repeating patterns. All these patterns hold great importance in literature or art, but as you have now seen, they can be very well explained by theories of mathematics and science. Mathematics is indeed a beautiful language. It subtly explains the mysteries of nature and the patterns emerging everywhere.

Videos

June 2018 Q7 (Sequence and Patterns)

Practice finding patterns in numbers | 3rd grade | Khan Academy

Sequences & Patterns

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.

The featured image on this page is from the Scientific American website.