It is known that two of the oldest civilizations are Indian and Chinese.

Both of them have contributed to the world in terms of Knowledge.

Orientals are reticent in divulging their History because their attitude to Life and the conviction that what they know is nothing when compared to what is to be known.

Because of philosophical approach, Indian History is mired in allusions , the Chinese History is hidden!

Indians have contributed to Mathematics by inventing 0 and Infinity ,apart from mathematical calculations.

There is a special branch of Mathematics by using which on can calculate Mathematical problems in a very short time mentally.

There are aphorisms for Addition, Subtraction,Multiplication and Division.

I am providing the link towards the end of the Post.

The timeline of these is at least 5000 years.

Now a Chinese Table of Multiplication had been found, hidden among bamboo sticks.

This is at least 4000 years old!

”

Five years ago, Tsinghua University in Beijing received a donation of nearly 2,500 bamboo strips. Muddy, smelly and teeming with mould, the strips probably originated from the illegal excavation of a tomb, and the donor had purchased them at a Hong Kong market. Researchers at Tsinghua carbon-dated the materials to around 305 bc, during the Warring States period before the unification of China.

Each strip was about 7 to 12 millimetres wide and up to half a metre long, and had a vertical line of ancient Chinese calligraphy painted on it in black ink. Historians realized that the bamboo pieces constituted 65 ancient texts and recognized them to be among the most important artefacts from the period…

As in a modern multiplication table, the entries at the intersection of each row and column in the matrix provide the results of multiplying the corresponding numbers. The table can also help users to multiply any whole or half integer between 0.5 and 99.5. Numbers that are not directly represented, says Feng, first have to be converted into a series of additions. For instance, 22.5 × 35.5 can be broken up into (20 + 2 + 0.5) × (30 + 5 + 0.5). That gives 9 separate multiplications (20 × 30, 20 × 5, 20 × 0.5, 2 × 30, and so on), each of which can be read off the table. The final result can be obtained by adding up the answers. “It’s effectively an ancient calculator,” says Li.

The researchers suspect that officials used the multiplication table to calculate surface area of land, yields of crops and the amounts of taxes owed. “We can even use the matrix to do divisions and square roots,” says Feng. “But we can’t be sure that such complicated tasks were performed at the time.”

”

To remember Multiplication Table, consider the sum of multiplicand and multiplier.

Remember the values for the sum < 10 (2 times table upto 8 x 2; 3 times table upto 7 x 3; 4 times table upto 6 x 4; 5 times table upto 5 x 5;).

We may call these basic Multiplication facts to be remembered.

Using these basic Multiplication facts, We arrive at the values for the sum > 10 (all other values of the multiplication Table) using simple technique from Vedic Mathematics.

The method we follow, here, is very simple to understand and very easy to follow.

The method is based on “Nikhilam” sutra of vedic mathematics.

The method will be clear from the following examples.

**Example 1 :**

Suppose, we have to find 9 x 6.

First we write one below the other.

9

6

Then we *subtract the digits from 10* and write the values (10-9=1; 10-6=4) to the right of the digits with a ‘-‘ sign in between.

9 – 1

6 – 4

The product has two parts. The first part is *the cross difference* (here it is 9 – 4 = 6 – 1 = 5).

The second part is *the vertical product* of the right digits (here it is 1 x 4 = 4).

We write the two parts separated by a slash.

9 – 1

6 – 4

—–

5/4

—–

So, 9 x 6 = 54.

Let us see one more example.

**Example 2 :**

Suppose, we have to find 8 x 7.

First we write one below the other.

8

7

Then we *subtract the digits from 10* and write the values (10-8=2; 10-7=3) to the right of the digits with a ‘-‘ sign in between.

8 – 2

7 – 3

The product has two parts. The first part is *the cross difference* (here it is 8 – 3 = 7 – 2 = 5).

The second part is *the vertical product* of the right digits (here it is 2 x 3 = 6).

We write the two parts seperated by a slash.

8 – 2

7 – 3

—–

5/6

—–

So, 8 x 7 = 56.

Reference:

http://www.nature.com/news/ancient-times-table-hidden-in-chinese-bamboo-strips-1.14482