Babylonian Math History

Much of the mathematics we study today using graphic calculators and other modern devices was first developed in the 18th Century BCE! This was the time when the Vedic Age in India and the Bronze Age in China were just about to start. Yet, in Babylon (Present Day Iraq), people were so advanced that they could calculate the path of Jupiter using Calculus!

Babylonian mathematics has been derived from about 400 clay tablets unearthed since the 1850s. Several multiplication and reciprocal (division) tables, tables of squares, square roots and cube roots, problems on geometry and division exercises have been found on clay tablets unearthed from Sumer (Iraq). These tablets were dated back to 2600 BCE. Later Babylonian tablets dating from about 1800

Below are four of the symbols.

For the purpose of understanding their system, we will use just the first two symbols ∨ = 1 ≺ = 10. All numbers can be formed from these. Example: ≺≺≺≺≺ ∨∨∨∨∨∨∨ = 57

The evolution of Babylonian mathematics was possibly due to a unique property of the number ‘60’. This number was used as a base for all the arithmetic in the Babylonian number system because 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 and it is also the smallest integer divisible by all the numbers from 1 to 6). The use of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle is derived from the ancient Babylonian Number System.

The Plimpton 322 tablet, which dates from 1800 BCE, suggests that the Babylonians may have known the relationship between the three sides of right-angled triangles many centuries before the Greek Mathematician Pythagoras. The tablet lists 15 right angled triangles with whole number sides to find and prove the Pythagorean triplets. A Pythagorean triplet consists of three positive integers - a, b and c such that a^2 + b^2 = c^2. The numbers 3, 4 and 5 are an example of a Pythagorean triple, but the values on Plimpton 322 are often significantly larger, for example, the first row referencing to the triple 119, 120 and

Because 60 is far easier to divide by three, experts found that the Babylonian calculations are far more accurate than the current calculators. Further research revealed that the tablet illustrates the shapes of right angled triangles using a unique kind of trigonometry based on ratios instead of angles or circles. The tablet not only contains the world’s oldest trigonometric table but it is also the only completely accurate trigonometric table, because of the unusual Babylonian approach to arithmetic and geometry. Thus it holds great relevance for our modern world. Babylonian mathematics may have been obsolete for more than three thousand years, but it has the potential to bring about ground-breaking changes in the fields of education, computer graphics and surveying.

According to Hipparchus, a Greek astronomer who lived around 120BC and is regarded as the father of trigonometry, a trigonometric table allows a user to determine two unknown ratios of a right-angled triangle using just one known ratio. But this tablet is far older than Hipparchus himself, demonstrating that the Babylonians were well advanced in complex mathematics way earlier than the