Page 160 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\07_Chapter_5\Chapter_5
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Figure 1 Figure 2
In figure 1, 14 numbers are placed on the circle while in figure 2, 30 numbers are placed on a circle
so that the sum and difference of any two consecutive numbers are prime.
In figure 1, the shaded portion has two numbers 7 and 10 whose sum and difference are prime.

7 + 10 = 17 and 10 – 7 = 3 are prime numbers
Similarly, 12 + 5 = 17 and 12 – 5 = 7 are prime numbers.
Choose some random pair of numbers in figure 1 and verify Quick Check

for the same. Choose some random pair of numbers
In figure 2, the shaded numbers are 17 and 24. in figure 1 and verify for the same.
17 + 24 = 41 and 24 – 17 = 7 both are prime.
Again, 19 + 22 = 41 and 22 – 19 = 3 are prime.

Exploring Pair of Co-primes by Hands-on Activity
1
The teacher might get a group of students to stand in a circle and make the 8 2
stars with string (by passing a ball of string).

For your reference, let us assume that 8 students are standing in a circle. 7 3
Choose a student to start from and pass the ball of string to someone. What is 6 4
your step size? When there are 8 persons, step sizes can be 1, 2, 3, 4, 5, 6 or 7. 5
Continue to round the circle, holding the string that is the same step size 1
apart, until the ball gets back to the starting point. 8 2

If the ball of string is moved around the circle in step size of 2, some students
will not hold the string and form a star. 7 3
If it is done in step size of 3, the ball will reach to all forming a 8-pointed star. 6 4
5
1
8 2

7 3

6 4
5

Mathematics-6 158