Table of contents | |
What is a Pattern? | |
Understanding Number Patterns | |
Border Patterns | |
What are Tiling Patterns? |
A pattern is formed by repeating a unit, which may be a set of numbers or shapes, according to a rule.
Patterns of squares using dots can be made in two different ways.
I. Rita uses coloured dots to make patterns of squares as follows:
The number of dots in each square contains a square number and this is so called because the dots are arranged in a square shape.
A square number is obtained by multiplying the number by itself.
Now, can you name the next two square numbers and draw the square patterns?
II. Abhinav makes the square patterns as:
Thus, we observe that,
First square number = 1 = First odd number
Second square number = 4 = 1 + 3 = Sum of first two odd numbers
Third square number = 9 = 1 + 3 + 5 = Sum of first three odd numbers
Fourth square number = 16 = 1 + 3 + 5 + 7 = Sum of first four odd numbers
Thus, we observe the pattern as:
First triangular number = 1 = First natural number.
Second triangular number = 3 = 1 + 2 = Sum of first two natural numbers.
Third triangular number = 6 = 1 + 2 + 3 = Sum of first three natural numbers and so on.
Now, see what happens if you add two consecutive triangular numbers?
1 + 3 = 4
3 + 6 = 9
6 + 10 = 16
10 + 15 = 25
Square numbers
EduRev Tips: We get a square number by adding two consecutive triangular numbers. The square numbers are shown in a multiplication square as given alongside. They lie on a diagonal line.
To understand better, let us take an example.
Consider the symbol as the basic unit or shape in the border pattern. We can get the following patterns when follows the different symmetries as shown below.
The most familiar examples of translations are the patterns formed by pairing stones or bricks and the cross-section of beehives.
A tiling pattern is formed by the repetition of a single unit or shape which when repeated, fills the plane with no gaps and no overlaps.
Look at the following patterns.
Now, observe these patterns. Are they tiling patterns? If not, then why not?
Thus, the above patterns are not tiling patterns.
Tiling patterns are found in things around us.
Multiple tiling patterns can be made using a single shape as shown.
58 videos|112 docs|40 tests
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1. What is a pattern in mathematics? |
2. How can we identify number patterns? |
3. What are border patterns and how are they used? |
4. What is tiling pattern and how can it be created? |
5. Why are patterns important in mathematics? |
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