Chapter 1: Patterns in Mathematics
Look closely and you find patterns everywhere: in floor tiles, flower petals, calendars and counting games. Maths is the art of spotting a pattern and then finding out why it works. In this chapter we build number patterns and shape patterns, draw them, and find surprising links between the two.
In this chapter you will
- find the rule behind a number pattern and predict what comes next
- meet famous sequences: odd, even, triangular, square and cube numbers, Virahānka numbers and powers of 2
- use pictures to explain why a pattern happens
- find number sequences hidden inside shape patterns
Topics
- What is Mathematics? NCERT 1.1
Mathematics is the search for patterns, and for why they happen.
- Patterns in Numbers NCERT 1.2
A number sequence is a list of numbers made by a rule.
- Visualising Number Sequences NCERT 1.3
Pictures help us see why a sequence grows the way it does.
- Relations among Number Sequences NCERT 1.4
Adding the first n odd numbers gives n × n.
- Patterns in Shapes NCERT 1.5
Geometry is the part of maths that studies shapes.
- Relation to Number Sequences NCERT 1.6
Sides of regular polygons: 3, 4, 5 … (counting numbers from 3).
Key words
- Pattern
- something that repeats or grows by a rule
- Number sequence
- a list of numbers made by a rule
- Number theory
- the part of maths that studies patterns in whole numbers
- Triangular numbers
- 1, 3, 6, 10 … dots that make a triangle
- Square numbers
- 1, 4, 9, 16 … that is 1 × 1, 2 × 2, 3 × 3 …
- Virahānka numbers
- 1, 2, 3, 5, 8 … each is the sum of the two before
- Geometry
- the part of maths that studies shapes
- Regular polygon
- a closed shape with all sides and all corners equal
- Complete graph
- points where every point is joined to every other point
Summary
- Maths is about spotting patterns and explaining why they happen.
- A number sequence is a list of numbers that follows a rule, such as 'add 2 each time' or 'double each time'.
- Some sequences we met: counting, odd and even numbers, triangular and square numbers, cubes, Virahānka numbers and powers of 2.
- Sequences are linked: add the odd numbers 1 + 3 + 5 + … and you always get a square number.
- Drawing numbers as dots, squares or blocks shows why a pattern works.
- Shapes make sequences too (polygons, joined points, stacked squares and triangles, the Koch snowflake), and counting their parts gives number sequences again.