Why does the world’s oldest multiplication table have 59 tables and the oldest uses the familiar decimal system to help us perform multiplication problems as detailed as 0.5?
Who invented the times table, scientists have not yet answered this question exactly. According to mathematics professor Marcus du Sautoy from the UK’s leading university, Oxford, it is possible that the ancient Babylonian civilization was the first civilization to create the times tables as far back as 4,000 years ago. At that time, the Babylonians did math on clay tablets and some are still available today for our study. As civilization developed, the Babylonians needed to perform more complex math problems in construction and trade. To speed up calculations, merchants carried clay tablets with times tables with them, much like modern-day engineers carry calculators in their pockets.
Babylonian clay multiplication table. (Photo: Slideserve).
You would think that those who can memorize these times tables will trade more successfully than those who take the time to pull them out. But think again about the ancient Babylonian students. Babylon’s number system is base 60, not the decimal system popular today. Therefore, they need to know the sum of all the multiplications up to the 59th multiplication table.
Babylonian numeral symbols.
The Babylonian base 60 system is the basis for today’s division of 1 minute into 60 seconds, 1 hour into 60 minutes, and a 360-degree circle. The factor of 60 is particularly useful in that 60 is a number with multiple divisors (divisible by many numbers: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), which helps in calculating math calculations with fractions easily. Also, Babylonian times tables have no zeros, go from 1 to 59, and no decimals.
When and where is the oldest multiplication table using the familiar base 10 system?
It’s a times table that has a value for zero, and holds numbers up to 99.5. This multiplication table is located on 2,500 bamboo spokes sent to Tsinghua University by a donor in 2008. Tsinghua University is China’s most prestigious university in the fields of natural sciences, technology, and engineering. and also very famous in Asia.
According to Nature, the bamboo slats may have been the result of an illegal catacomb excavation and the thieves sold them back in Hong Kong.
According to the results of carbon isotope assessment, these bamboo slats belong to 300 BC, the Warring States period (481-221 BC) including many vassal states before the Qin Dynasty unified China in 221 BC.
Each bamboo slat is 7-12 mm thick and about half a meter long, with ancient Chinese calligraphy written vertically in black ink. According to historians, these bamboo slats form 65 ancient texts and are considered one of the most important antiquities during the Warring States period.
The oldest decimal multiplication table in China dates back to 300 BC.
It took researchers up to 5 years to decipher the times table into the world’s most unique type. According to math historian Feng Lisheng from Tsinghua University, when the bamboo slats are in place, a matrix structure emerges. the top and rightmost columns contain 19 numbers of 0.5; integers 1 to 9, multiplications of 10 from 10 to 90, in order from right to left, top to bottom.
The intersection of each row and column in the matrix is the result of the multiplication of the corresponding numbers, similar to the modern times table. With this table, we can multiply any integer or odd number to 0.5 between 0.5-99.5.
A translation of the world’s oldest multiplication table in China. (Photo: Tsinghua University)
According to Feng, we do not multiply numbers directly, but first convert through a series of additions. For example, break down the multiplication 22.5 × 35.5 into (20 + 2 + 0.5) × (30 + 5 + 0.5)(20 × 30, 20 × 5, 20 × 0.5, 2 × 30) x … We have 9 individual multiplications can be read from the table. The final result is the sum of these products. This ancient times table is an efficient calculator, says Li Junming, a historian and ancient script researcher.
The world’s oldest multiplication table may have been used by the officials of the time to calculate land area, income from crops, taxes owed. It can even be used to perform division, square roots, but we are not sure if humans were able to perform such complex calculations at that time.
Another mathematical historian from New York University (USA) also confirmed this is the world’s earliest decimal multiplication table, representing a complex arithmetic that has been used for both commercial and theoretical purposes. during the Warring States period.
By the time of Qin Shi Huang, the first emperor in Chinese history to have unified this vast country, he ordered the burning of books and banning private libraries in an effort to reshape the intellectual tradition of China. nation.
Prior to this, the oldest Chinese multiplication tables belonged to the Qin Dynasty (221-206 BC), consisting of a series of short sentences such as “six times eight equals forty-eight ” and consisted of simple multiplications only. than many times tables on bamboo spokes above.
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