3,700-year-old Babylonian tablet rewrites history of Trigonometry

originally posted by: TinfoilTP

originally posted by: IAMTAT
If it's so much more accurate than Base 10...Why don't we use Base 60 today?

We do, 60 minutes, 60 seconds, 12 hours in a day. Them nephilim had 12 fingers and toes ya know.

There are (and have been) cultures that count to 12 by using one hand. What they do is open their hand and count each finger bone or segment on the four fingers (not the thumb). It's a very intuitive method once you try it. Being able to count to 12 on one hand is the basis for the base-60 numbering system (12 x 5 = 60) used by the Babylonians and other cultures.

No 12-fingered Nephilim are required


As for "why is a circle 360 degrees?"...

The Babylonians (probably borrowed from knowledge passed down from the Sumerians) also knew that if you take the radius of a circle, that radius can be used to build the six sides of a hexagon that will perfectly inscribe that original circle. Using that, plus their base-60 numbering system, one could see one possible way how the 360-degree circle came into being, as I demonstrate in the graphic below:

originally posted by: intrptr

originally posted by: rickymouse

originally posted by: intrptr
a reply to: seasonal

I agree but I can see another way. There maybe something we do not know and it could be a hidden secret.

Not if it involves building any large structure. Thats why the early ones are all pyramid shaped (piled up blocks).

One must use the Level, a Square and Plumb.

The old Finns and Italians here used to use a beer bottle as a level for putting in windows. It actually works, you drink it down to the label or ridge line then use that as the level mark. It was not the level that was off in most of the old houses, it was the amount of levels they had to make.

The Egyptians used water to level the pyramids. Before construction began, they made a small lake in the footprint of the pyramid, put a few inches of water in it, measuring the height all across the base of the pyramid.

Yeah, but aliens taught them to do that.

The ancient aliens were rude like that. The aliens obviously had specialized tools and equipment for that, but they made the ancient Egyptians flood the footprint of the pyramid.

Oddly why does this fall in line with an article I just read on our Universe being a simulation based on triangles being the basic building blocks?!?

We have been more advanced then we are now with different tech and superior culture, so what happened why was it buried and I think purposefully left forgotten...

originally posted by: abeverage
Oddly why does this fall in line with an article I just read on our Universe being a simulation based on triangles being the basic building blocks?!?

We have been more advanced then we are now with different tech and superior culture, so what happened why was it buried and I think purposefully left forgotten...

I don't think it takes a superior culture for ancients to figure out trigonometry.

Ancient human brains had the same capacity to figure things out that we have today, considering their brains were the same as our brains.

Finds like this further erode the "man were cavemen and stupid the further back we go, blah blah" narrative. It just seems that every year the finds they actually publicize are proof that assumptions about early man are skewed at best. We were far more intelligent then, I believe.

a reply to: JackSparrow17

This makes me wonder what is in all those Anunnaki tablets sitting untranslated in the basements of museums. What is on them?

a reply to: seasonal

Great now lets smash and tear down all of the Hipparchus statues

originally posted by: Soylent Green Is People

originally posted by: abeverage
Oddly why does this fall in line with an article I just read on our Universe being a simulation based on triangles being the basic building blocks?!?

We have been more advanced then we are now with different tech and superior culture, so what happened why was it buried and I think purposefully left forgotten...

I don't think it takes a superior culture for ancients to figure out trigonometry.

Ancient human brains had the same capacity to figure things out that we have today, considering their brains were the same as our brains.

What I am saying is we consistently think or are told we are at the pinnacle of society, science and culture. That we are the modern world when in fact we may have been here before several times, but the evidence is left undiscovered or (conspiracy theory here) hidden or erased.

originally posted by: seasonal
a reply to: JackSparrow17

This makes me wonder what is in all those Anunnaki tablets sitting untranslated in the basements of museums. What is on them?

Many of the tablets uncovered over the years are actually financial records and dedication/commemoration statements.

originally posted by: abeverage

originally posted by: Soylent Green Is People

originally posted by: abeverage
Oddly why does this fall in line with an article I just read on our Universe being a simulation based on triangles being the basic building blocks?!?

We have been more advanced then we are now with different tech and superior culture, so what happened why was it buried and I think purposefully left forgotten...

I don't think it takes a superior culture for ancients to figure out trigonometry.

Ancient human brains had the same capacity to figure things out that we have today, considering their brains were the same as our brains.

What I am saying is we consistently think or are told we are at the pinnacle of society, science and culture. That we are the modern world when in fact we may have been here before several times, but the evidence is left undiscovered or (conspiracy theory here) hidden or erased.

Maybe that's true. I can't prove it isn't (i.e., I can't prove the negative).

However, I'm simply saying it does not necessarily take an advanced technological civilization (more advanced or equal to our own) to figure out Trigonometry or figure out how to build something like the Great Pyramid or the Antikythera mechanism.

The ancient people who lived in those ancient civilizations may not have had the same accumulation of knowledge that we have today, but as I said, they had the same brain we have, and thus had the same capability to figure things out. that is, They were just as clever and intelligent as we are.

In fact, I'm sure they had specific knowledge of things that we do not have today -- things that are no longer part of our civilizations accumulated knowledge, because some things are invariably lost along the way. However, that's not the same as saying that there was once an ancient civilization that was MORE advanced than us overall,

Like I said, I can't prove the negative that there wasn't such a civilization that was erased from history, but the idea that some ancient civilizations knew stuff is not proof that there were civilizations more advanced than us, either.


Going back to the idea of "knowledge the ancients had that we no longer have", let's look at the Great Pyramid as an example. Looking at the history of stone construction in ancient Egypt, we can see a progression of pyramid building over the course of more than 1000 years, from flat-top masalas, to stacked mastabas, to stepped pyramids, to true pyramids, to the Great Pyramid.

Over those couple 1000 years of pyramid building, the Egyptians (who, remember, have the same intelligence and problem-solving capability as we have today, and share an equal intelligence with us) probably perfected many clever techniques for solving pyramid-building problems and they learned how to build bigger and better pyramids in a more efficient manner.

However, over time, and since civilization is no longer building pyramids, some of that advanced knowledge of pyramid building techniques are lost to time. There were almost certainly many clever ideas the Egyptians employed to build pyramids and clever maths they used to design them that our civilization no longer has knowledge of.

But that doesn't mean that the Egyptians acquired that knowledge from some ancient unknown civilization who was more technologically advanced than we are today, but disappeared from history. Rather, the Egyptians were smart enough to figure those things out on their own, and within the confines of their own civilization.

Saying that some secret super-advanced ancient civilization was required for the ancient Egyptians and/or Babylonians to have this knowledge is sort of an insult to the Egyptian and Babylonian people. They were by no means not intelligent enough to figure things out (such as Trig or Pyramid-building) on their own, without the help of some unknown super civilization.

A 3,700-year-old clay tablet has proven that the Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics which could change how we calculate today.

Ancient cultures are always awesome but the tablet contains nothing new to modern mathematics, Mansfield seems to be getting carried away a bit. Also keep in mind that it was already translated decades ago. The argument is about what it was used for. And whether it's a trigonometric table or not, though I'm not sure what exactly that means, sounds like a semantic argument.

The exact accuracy is possible because the triangles are handpicked with nice and neat lengths to their sides. Here's the table in decimals, and a drawing I made in paint to illustrate where the numbers are supposed to go on a triangle. I'm not a mathematician though, so take it with a grain of salt:

originally posted by: pheonix358
The Greeks learnt from the Egyptians. The Library of Alexandra was the ancient equivalent of a university. Many of the Greek Scholars spent time there learning their craft.

You can't build all of the ancient Egyptian monuments without this level of math.

So the Babylonians taught the Egyptians who taught the Greeks who taught us.

It is also very likely that the Babylonians were taught by an earlier civilization.

P

Not to be overly pedantic but Alexandria is a Hellenistic city. That is, it was built by the Greeks who ruled Egypt after Alexander conquered them and the Ptolemaic dynasties took over. That's not to say the greeks weren't knowledge sponges who wouldn't learn from anyone and everyone they could. Quite the opposite. Any ship that ported at Alexandria was subject to having any booms on board "temporarily" confiscated so that Greek scribes could copy the book and place a copy within the library. It's also a bit if a misnomer that all of the information stored there was lost when the library was destroyed as the Ptolomies were notorious for making muiple copies and sending them to other Greek libraries and likewise, many of the books in Alexandria were copies of books from other Greek libraries. I'm just going off the top of my head as I'm running on limited wifi without any of my resources nearby while on vacation at the lake house so all I have is my phone so perhaps Byrd can correct me if I'm off on the details here.

But as far as the Egyptians learning this from the Sumerians, the Grest Pyramid predates this text by nearly 1000 years and there is a steady increase in architectural complexity in Ancient Egypt leading up to the GP so I have some doubts that this predates Egyptian architecture.

1x2x3 = 6, 2x3x5 = 30, 3x4x5 = 60, 3-4-5 triangles are right, 2x5x6 = 60. 6x10 = 60, 5x12 = 60. 4x15 =60. 3x20 = 60. 2x30 = 60. Patterns like these are why a base 60 is better for trigonometry than a base 10, and why their civilization was more advanced than their neighbors. The usefulness of your base counting system grows with more factors. A base 5040 would allow computations of the 1-7 and 7-10 digits. Base 24 has its uses as well, but doesn't include units like 5 or 10. Base 120 has 5 and 10, but is more cumbersome than base 60, so base 60 might have been a deliberate compromise.

Greek mathematics have their origins in Mesopotamian mathematics.
Trig is an outgrowth of constructional geometry, and is nothing more than the study of the relationship of the sides of a triangle.
All you need to develop the basics of trig from scratch, is a straight edge, a line of a fixed or unit length and a scribe.
Any culture that starts to build "regular" structures will develop and under stand trig in its most basic form.
What we call trigonometry today has little resemblance to what the greeks, egyptian or babylonians used.
The defined trigonometric relations we use today werent defined until the advent of calculas.
I had three semsters of physiscs, taught by a former UC Berkely phys. prof., where were not allowed to use calculators. All of our trig computations were solved in terms of fractions of Pi and radians.

originally posted by: TinfoilTP

originally posted by: IAMTAT
If it's so much more accurate than Base 10...Why don't we use Base 60 today?

We do, 60 minutes, 60 seconds, 12 hours in a day. Them nephilim had 12 fingers and toes ya know.

A number of ancient calendars had a 360 day year.
Later they added 5 "unlucky" days,

a reply to: IAMTAT

a reply to: seasonal

Secrets. Ancient knowledge. I'd really like to know...

a reply to: seasonal

Saw this this morning. History is being re-written as we find out that human civilization was more advanced than we ever thought possible over 3,000 years ago. Who knows for certain how many advanced civilizations have been destroyed and covered by nature that we have not discovered yet.

Imagine this. The Earth has been undergoing geological changes since it was formed over 4.5 billion years ago. We know people like the Aztec, and Incas had to leave their cities because of dramatic climate changes. We have found dozens of cities underwater from a time when Earth was colder and our oceans heights were much lower than they are now. But we have also found several cities underwater which were put there by either dramatic geological changes, such as large earthquakes sending cities under the ocean in one sweep, and we have also found cities which slowly and for hundreds of years were sunk underwater.

I wish we could know more about the city that the Canadian engineer found off the west coast of Cuba which is over 6,000 feet underwater. But Cuba decided to stop investigating that city because "they have to use the money to expand communism to other parts of the world".

originally posted by: seasonal
a reply to: Aliensun

Of course it doesn't prove they developed it. But it does prove they had the knowledge and this is the earliest proof of tangible evidence yet.
So until earlier proof is found it is safe to say the Babylonians are the record holders.

Trigonometry - the study of triangle measures.
This in no way involves what modern people think of as trigonometry (if they think of trigonometry at all.)

As I see it, this is about Pythagorean triples, which are sets of three whole numbers that fit the Pythagorean Theorem.

sexagesimal, system.
"Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples," says Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.

A Pythagorean triple consists of three, positive whole numbers a, b and c such that a2 + b2 = c2. The integers 3, 4 and 5 are a well-known example of a Pythagorean triple, but the values on Plimpton 322 are often considerably larger with, for example, the first row referencing the triple 119, 120 and 169.

Read more at: phys.org...

The trigonometry that gives some people headaches is the study of the ratios of sides of triangles as functions.
This ain't that.

But it is a record, as far as documentation goes. And very extensive in the listing of Pythagorean triples.
More like numerical analysis than trigonometry if you ask me. You don't just come up with a Pythagorean triple like 119, 120, 169 of the top of your head.

Harte

a reply to: Harte

It is absolutley a trig table.
You have every thing you need, the value of the tangent, the length of the sine leg and the length of the hypotenuse.

How can that not be a trig table?


The table increments from ~44-3/4° down to 32°ish, by ~1/2° increments but varies a little.

The base 60 system make for very cumbersome computation, using only integers and all.