In the early 1900's a 3700 year old tablet was found, and when they eventually figured out what was on it, it completely shook everyone involved.
What it contained was that 1500 years before the Greeks (what has always been touted as the intellectual capital of the time), the Babylonians had an advanced Trigonometry table that was in some ways better than what we have today.
This tablet has been called Plimpton 332, and was found in Southern Iraq by the inspiration for the Indiana Jones movies, American archaeologist and diplomat Edgar Banks.
Until 2017 they were unable to decipher the writings on it, and eventually the university of New South Wales in Australia found that it contained trig table.....something that all the math teachers and students will be well aware of.
The back of the tablet
The reason why it is more accurate than what we use these days is interesting. I will see if I can explain it.
We currently use metric calculations with a base of 10. Think of it this way, every time we count or divide, it is essentially around the figure of 10. 10, 100, 1000, 10000 etc.
When we divide this number we get only a few that are divisible into the base of 10.
All we have is 2 and 5.......so half of 10 = 5, and divide it by 2 leaves us with 5.
So there are not many divisible calculations available to a 10 base number.
The Babylonians however worked their numbers with a base of 60! This was most probably due to the connection with time. Working in their base of 60 in correlation with 60 minutes per hour.
This however opens up many more divisible options. Now you have multiple divisible options off that base, 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30 which allows you many more calculations without having to go into fractions of numbers.
Dr Daniel Mansfield says the following about the tables found:
*"Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles, It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.
By the size of the tablet, it looks like it was a functional tool for building or planning...I think of current tablets. Below is Dr Mansfield with the tablet
Credit
This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education"*
Before this discovery, the oldest Trig table was considered to be by Greek astronomer Hipparchus in 120BC, while this tablet dates back to around 1822 and 1762BC.
The tables are 15 calculations of the a decreasing angle on a right angled triangle, and it is apparent that there were more rows that were on the tablet but have been lost to damage (should be around 38).
Instead of using the modern method that stemmed from the Greek times, which is using angles and approximations (due to rounding off), they were able to use calculations based on a rectangle base, and have them exact due to the Base 60 numbers they work off of.
Thus allowing them to have exact calculations to work from for quite a few right angle designs
The right diagram shows the Babylonian table visual rather than the traditional method on the left.
It is similar to dividing an hour by 3, you get 20 minutes....an exact number. But when you divide 1 Rand, or 1 Dollar by 3 you get 33.3333333333333c.
Their numbering system then would have changed even the money rates to something divisible by 60, thus allowing and hour that was divided by something like 48, would then be a 1 minute and 15c remaining....exact answers.
So simple, but so effective!
Here is a video showing how the actual figures on the tablet work in an actual triangle:
There is speculation as to why such exact methods of calculation fell away, but they speculate that it may be because the approach using angles is better suited to astronomy.
But without any evidence as to this, this is only speculation.
Truth is, the further we delve into our histories we are realizing more and more that the ancients were not some backward people scratching a living, but a highly civilized people with knowledge and systems and language that we are currently losing.
You just have to think on the great writers of all history, few are really modern writers, but many historic....600BC - 400BC seemed to have an explosion of knowledge and wisdom.
Nothing wrong with learning from our pasts....right?
[Information credit is YouTube, here]