I would like to know about nappiers boxes , atopic in mathematics?

Answer 1

Nappiers Boxes come from "Napier's Bones". This was a method of multiplication developed by an Englishman who was frustrated that his workers couldn't multiply.

In order to use this method of multiplication, you would need to know the multiplication tables from zero to nine.
To multiply two one-digits numbers, draw a box, draw a diagonal line from upper right to lower left. Write one number on top of the box, and one to the left of the box. Multiply the two numbers, placing the tenth's digit in the upper-left box.
To multiply two two-digit numbers, place one number on the left, and one number on the top, like so(37 X 49):

X 49
3
7

There are 4 boxes: 2 boxes on the 3 row, and 2 boxes on the 7 row, each box with a diagonal line from lower left to upper right.
I can't demonstrate this on this forum, as the text gets mangled, so I'll have to discribe it.

In the box in the 3 row and 4 column, since 3 X 4 = 12, place a 1 on the upper left of the box, and a 2 in the lower right of the box.
Similiarly place a 2 and a 7 in the box for the 3 row and 9 column, place a 2 and an 8 in the box for the 7 row and 4 column, and place a 6 and a 3 in the remaining box.

Now add the numbers in the lower right diagonal (actually the one digit) 3 - that becomes the units digit of the answer.

Then add the next diagonal: 7 + 6 + 8 (=21)
write down the next digit 1, and carry the two.

Then add the next diagonal: 2 + 2 + 2 plus the carried 2 (=8)
Write that digit down

Finally add the last diagonal 1

The answer is: 1 8 1 3

37 X 49

'''1'''''2
'''''''2'''''7
'''2'''''6
'''''''8'''''3