Essence of Division
Let us come straight to the point of our discussion which is 'division'. You must be wondering what is the use of division and why it is the first chapter of this book.We must take a circle to understand this topic. Let us take a circle and divide the circumference of the circle into 20 parts. Attach a weight to each part of the circle. The different part of the circle has the following weights attached to it.
4, 1, 3, 7, 10, 6, 4, 2 , 1, 3, 8, 5, 3, 5, 7, 1, 2, 9, 3, 5.
Group the divisions of the circle into different groups. The number of groups which will be created will depend on the number of divisions we group as one.We must group such that all the divisions are used once and no overlapping happens when we complete the groups.
This can be done by taking the factors of 20.
The factors of 20 are 1, 2, 4, 5.
If we divide 20 with two divisions as one group then we have 10 groups.
Similarly of 4 we have 5 groups. Of 10 we have 2 groups.
The weights of each group when the group has 2 divisions.
4+1, 3+7, 10+6, 4+2 , 1+3, 8+5, 3+5, 7+1 , 2+9, 3+5.
5,10,16,6,4,13,8,8,11,8
Similarly, we find the weight when the group has 4 divisions.
4+1+3+7, 10+6+4+2 , 1+3+8+5, 3+5+7+1 , 2+9+3+5.
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