Page 5 - Matematica_Mathematics - Puterea cu exponent natural a unui numar_The natural exponent power of a number

2
1
Also by convention, a = a, so: Calculating the value of 4 , we found out the
4 = 4 square of the number 4, since the second power of
1
4 = 4 × 4 = 16 a natural number is also called the square of that
2
number (“pătratul acelui număr”).
4 = 4 × 4 × 4 = 16 × 4 = 64
3
4 = 4 × 4 × 4 × 4 = 64 × 4 = 256
4
5
4 = 4 × 4 × 4 × 4 × 4 = 256 × 4 = 1 024

Practice

2. Calculate the square, then the third power of the numbers: 4, 6, 7 and 9.

An ancient Indian legend

The inventor of the chess game, SISSA ben Dahir, was offered-by the indian King Shirham – a
reward (of his choice) as a payback for the wonderful invention.
Modest, Sissa said:
- Your Majesty, I do not want much worldly riches, just give me one grain of wheat for the first
square of the chessboard, two grains for the second, 4 grains for the third, 8 grains for the Fourth
Square... and so on, until all 64 squares of the board are covered in wheat.
The King, surprised and delighted that so little was required of him, clapped his hands and
ordered a sack of wheat to be brought to him, in order to fulfill the
request of the cunning mathematician. But, to the King’s surprise,
the sack was quickly over and the board was not even a
quarter covered. The same happened with the bags
that were brought in afterwards, they were
emptied more and more quickly.
Only then did the King realize that
SISSA ben Dahir had asked him for an
unthinkable large number of grains of wheat, the
result of the sum
1 + 2 + 2 + 2 + 2 + 2 +… 2 = 2 − 1
3
5
4
63
64
2
This was far more than the agricultural
production of the whole of India, in fact 1000 times
the entire wheat production of the world.
This story shows both the origins of chess and
the degree of mathematical knowledge from the date of
the legend’s Foundation.