Innings2
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Chapter 1: Patterns In Mathematics

    What is Mathematics?

    Patterns in Numbers

    Visualising Number Sequences

    Relations among Number Sequences

    Patterns in Shapes

    Relation to Number Sequences

    Summary

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

Chapter 1: Patterns In Mathematics > Patterns in Shapes

Patterns in Shapes

Other important and basic patterns that occur in Mathematics are patterns of shapes. These shapes may be in one, two, or three dimensions (1D, 2D, or 3D)—or in even more dimensions. The branch of Mathematics that studies patterns in shapes is called geometry.

Shape sequences are one important type of shape pattern that mathematicians study. Table 3 shows a few key shape sequences that are studied in Mathematics.

Table 3: Examples of shape sequences

PolygonEquilateral TriangleSquarePentagonHexagonHeptagon
Regular Polygon
Complete Graphs
Stacked Squares
Stacked Triangles
Koch Snowflake

Observe the given below pattern for a _Koch Snowflake.

Figure it Out

(1) Can you recognise the pattern in each of the sequences in Table 3?

Instruction

(a) Triangle, quadrilateral, pentagon, hexagon, (the number of sides increases by at a time). Hence it is a continuous number sequence starting from .
(b) Here number of lines is as follows: K2 = , K3 = , K4 = , K5 = , K6 =
The series formed is 1, 3, 6, 10, 15,……. Hence it is a number sequence.
(c) The series formed is 1, , , , ,……. Hence it is a presentation of numbers sequence.
(d) Hence it is also a number sequence shown by triangles.
(e) Number of sides in each becomes times.

(2) Try and redraw each sequence in Table 3 in your notebook. Can you draw the next shape in each sequence? Why or why not? After each sequence, describe in your own words what is the rule or pattern for forming the shapes in the sequence.