Worksheet 2 Accelerating the acceleration

In Babylon a General had conducted a famous victory over an invading army. The King asked him to name his reward.

He called for a chessboard and said, “Just give me one grain of wheat on the first square, two grains on the second square, four grains on the third – doubling each time – until all the squares on the board are full.”

“You aren’t asking much,” said the King. “You can certainly have that.”

But one of the Court astronomers thought for a while and did some calculations on a wax tablet. Then he said to the King, “You may regret this.”

Use a calculator.

Give approximate answers using the first two digits followed by zeros, e.g. 1024 becomes 1000.

Fill in the’number of grains’ column by doubling each time until the weight of the grain reaches 1 tonne (2 000 000 grains).

The King’s grain store contained 1000 tonnes.The astronomer calculated that by the 30th square, the whole of the King’s grain would have been needed!

By continuing the table, or by another method, find out how he did the calculation, and explain why his calculation was right.

Fill in the third and fourth columns down to about square 8. Look at the pattern of the increases. Discuss with your partner how you can explain the difference between this and the pattern of increases for the rocket on Worksheet 1.