Page 161 - Math_Genius_V1.0_C5_Flipbook

E:\Working\Focus_Learning\Math_Genius_5_(05-10-2023)\Open_Files\CHAP_07
\\November 22, 2023 4:45 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Pascal’s triangle

Look at the numbers arranged in the shape of a triangle.
This is called Pascal’s triangle. 1
We can see many patterns in this triangle. 1 1
Š The first diagonal is ‘1’. 1 1 3 2 3 1 1

Š The next diagonal has the counting numbers, that 1 4 6 4 1
is, 1, 2, 3, ... 1 5 10 10 5 1

Can you find any other pattern?

Knowledge Desk

Pascal’s triangle is a special arrangement of numbers named after Blaise Pascal, a famous
French mathematician and philosopher. In this arrangement, the numbers are arranged in a
triangular array such that number 1 is there at the end and the beginning of all the rows and
the remaining numbers are the sum of the nearest two numbers in the row just above.

Some more number Patterns

Let us observe the following number patterns and try to write the missing numbers in the
next term.

1. 1 4 9 16 25 2. 0 2 6 12 20 30

+3 +5 +7 +9 +2 +4 +6 +8 +10 +12 +14 +16
3. 4. 5.
1 × 1 = 1 1 × 9 + 2 = 11 1 × 8 + 1 = 9
11 × 11 = 121 12 × 9 + 3 = 111 12 × 8 + 2 = 98
111 × 111 = 12321 123 × 9 + 4 = 1111 123 × 8 + 3 = 987

1111 × 1111 = 1234321 1234 × 9 + 5 = 11111 1234 × 8 + 4 = 9876
___________=________ ___________=_______ ___________=______

___________=________ ___________=_______ ___________=______
Multiplication tables also show some beautiful patterns.
Look at the tables of 6 and 8 given below:

table of 6:
6 12 18 24 30 36 42 48 54 60

The ones digits repeat themselves after the fifth multiples.
table of 8:

8 16 24 32 40 48 56 64 72 80

The ones digits repeat themselves after the fifth multiples.

Mathematics-5 159