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Babylonians Knew Trigonometry 3,700 Years Ago & Their Tablet Plimpton 322 Could Help Students Today

Trigonometry is not quite an easy target to excel in for many students. But, is it possible that the Babylonians, whose culture thrived from 2800 to 1700 BC, to ease up this challenge with the help of a clay tablet, known as Plimpton 322?

An Australian mathematician, Dr. David Mansfield of the School of Mathematics and Statistics of New South Wales, who has been examining its application, recently stated his judgments. He explained how solving the mystery of the tablet could simplify the study of triangles.

Heretofore, the foundation of the trigonometry were the doctrines of angles and irrational numbers. The examination of Plimpton 322 reveals that Babylonians, in fact, used proportions.

“This gives us a different way of looking at trigonometry. The beautiful thing about it is that it’s much simpler,” said Dr. Mansfield.

Trigonometry is not only a branch of mathematics but is also an indispensable part of the architecture, engineering, astronomy etc.

Until now, only Greek principles were employed while studying it. Now, however, considering this tablet, we can conclude that Babylonians beat the Greeks in the discovery of trigonometry by about 1,000 years.

Researcher Edgar Banks discovered this tablet in southern Iraq. According to many, he was the inspiration for the modern-day movie Indiana Jones.

Banks was not collecting tablets as an archaeologist, but to sell them to universities, libraries, and museums.

According to mainstream history, the father of trigonometry is the Greek astronomer Hipparchus. But, the creation of Plimpton 322 happened a long time before his era.

Dr. Mansfield said: “Babylonian mathematics may have been out of fashion for more than 3,000 years but it has possible practical applications in surveying, computer graphics and education.”

More than 400 clay tablets with inscriptions still exist from the time of the Babylonians.

About its name, it got it after the American publisher and collector George Arthur Plimpton, who bought it.

In 1936, not long before he died, he donated it to the Columbia University. Right now, it locates in the Rare Book and Manuscript Library at this very same place.

n the 1940s, researchers who were analyzing the tablet concluded that the cuneiform numbers on it matched to the Pythagorean Theorem.

According to this theorem, the square of a right triangle’s hypotenuse is equal to the squared lengths of the other two sides.

“The tablet is a fascinating mathematical work that demonstrates undoubted genius,” says Dr. Mansfield.

“It not only contains the world’s oldest trigonometric table, but it is also the only completely accurate trigonometric tablet, because of the very different Babylonian approach to arithmetic and geometry.”

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Ancient

From “living” runes to a hologram. Ancient technologies are making a comeback

Human civilization develops thanks to accumulated knowledge. Without knowledge and experience, there is no movement forward to progress. People make discoveries, bring them to life and pass this information on to subsequent generations. The most faithful and reliable storage is memory. But, unfortunately, it is limited to the framework of one human life or generation.

Therefore, in past centuries, when people were closer to each other, the continuity of generations was maintained. Wisdom was passed down orally: from grandfather to father, from father to son. So, epics and legends were composed. The image embedded in them was able to live for centuries. After all, only that which is felt is remembered. All events in the senses are imprinted with all the multifaceted connections.

We can say that feeling is a kind of “hard drive” that is turned on with the help of a computer brain.

In that distant era, when our ancestors lived in harmony with themselves and nature, they had developed imaginative thinking. Sounds had a special meaning because they created reality. But the means for transmitting information or extracting it from the past were musical instruments. Each of them had its own purpose. With the help of some, people remembered their past lives, others were introduced into an altered state of consciousness, in which it was possible to perform miracles.

Various folk tales have preserved the legends of “magic words” that open doors and launch flying ships. The Byzantine chronicles say how the northern people came to negotiations without weapons, holding only a folk psaltery in their hands. The sounds drawn from the strings decided the outcome of the negotiations.

Runes – the first material carrier

Руны
Runes

At this level of interaction with information, any drawn symbol had a magical effect. The ancestors called these signs – Runes. Not everyone could “work” with them. Due to the ability to materialize thoughts instantly, only initiates had access to them. For everyday needs, they used features and cuts that did not have such tremendous power. As the spiritual decline and loss of skills, it was necessary to create books, but they were so amazing that for a modern person they seem completely fantastic.

Голографическая реальность
Holographic reality

Ancient stereo books

These were ordinary pre-Christian books, which were then burned as a devilish “black book”. Although they had nothing to do with the devilry. Their whole secret was the ability of our ancestors to use bioenergetics.

Such books have been carefully crafted for centuries. Every detail of her material had to have certain physical qualities.

The text of the future book was first written down with a metal stylus on wax-covered boards, where any corrections could be made. It is impossible to write straight away. Trying to accurately convey his thought, the author “runs after her”, not worrying about spelling. The well-known expression “to spread the thought along the tree” comes from there.

Nevertheless, the main thing in the creation of the book was not the author, but a scribe who would have had imagination and such body cells that emit bioenergy. In this case, all the pictures that appear in his imagination, together with the biocurrents, are absorbed into the parchment as on a film strip. The effect of titles is created, as if hanging in the air between a person and those living pictures that the suede parchment has absorbed. For these purposes, it was manufactured in a special way. As well as cinnabar for writing.

 Стерео-книга
Stereo book

Then the sheets of parchment were stitched like modern thick notebooks with a metal spiral on the spine. The cover was made of bog oak boards. Its name was engraved on the cover. To make it better read, silver and niello were poured into the grooves of the letters. At the same time, the same massive oak-copper case was made for the book, closed with copper clasps.

Ancient books
Ancient books

Incredibly, the natural ingredients and techniques used in this book produced a 3D effect. The only difference is that a modern person needs special glasses, and our ancestors developed such abilities. It’s just that some could emit biocurrents, while others perceive them. In short, living people were transmitters and receivers.

Gold and stone discs – the prototype of modern discs

In addition to such wonderful books, there were also discs that contained a huge layer of information in a compressed form. Perhaps they are “read” in the same way as “miracle books”, but it is possible that there was a certain computer into which these disks could be inserted.

Phaistos disc.
Phaistos disc

In any case, according to the first version, attempts were made to decipher the Phaistos disc, a phenomenon that made a lot of noise at one time. It was discovered that the disc contains layered information. It cannot be read like an ordinary letter.

The hologram is the library of the future

With the advent of Christianity, all ancient knowledge and skills were declared devilish, and the possessors of these abilities were witches and sorcerers. Both books and people were burning in the bonfires. In order to preserve the rest, the manuscripts were rewritten, but already in an ordinary linear letter. Of course, distortions were inevitable and the picture of past events, presented in this way, did not correspond to reality.

Pen books have proven to be a rather primitive way of conveying information. Although, for many centuries, they remained a guiding thread for knowledge. And yet, as we can see, important discoveries were and are being made as a result of practical research, often thanks to insight, which proves the existence of an information field, from where you can get the necessary information. 

Hologram
Hologram

Now, humanity is approaching again the stage when the need for the usual carriers of information will disappear. Everything will be transferred to a virtual memory base. But if earlier holograms were created and accepted by people themselves, now machines will do it for us.

In the event of another disaster, we will lose access to the electronic library. And then everything will have to start over. And our descendants, just like we are now, will believe that at this period people were illiterate, because they did not have a written language …

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Ancient

What secrets and mysteries of Angkor baffle modern scientists?

Ancient city of Angkor, Cambodia

Angkor was discovered in the Cambodian jungle by French naturalist Henri Muo in 1861. Almost 160 years have passed, and the mysterious city has not yet revealed its secrets to us.

Angkor is not only numerous temple complexes, among which Angkor Wat is the most famous. But there are also huge hydraulic structures of ideally verified shapes and gigantic dimensions. These are ditches with water surrounding each complex, and huge reservoirs – “man-made seas” – barai , and the famous river in the valley of a thousand lingams.plan-map of Angkor

Angkor Map Hobe / Holger Behr / commons.wikimedia.org

The view of Angkor from space resembles a plan-drawing perfectly calculated and executed by an engineer-architect. Historians cannot explain how the Khmers managed to “bring to life” such a grandiose plan in the 9th-12th centuries, while maintaining strict geometry. The lines are well-parallel for over 8 km, and all angles are straight. It was simply impossible to do this in those days with those instruments.

Angkor has been studied not only by historians and archaeologists, but also by enthusiastic researchers, including those from the Laboratory of Alternative History. And they came to the conclusion that the ancient architects either built the structures of Angkor using the preserved secret knowledge and technologies, or restored and completed what they inherited from more ancient civilizations.

According to legend, the capital of the Khmer state was founded in a different place, but the astrologers indicated where to build the city.

Many sources mention the correspondence of the location of the temples of Angkor to the constellation of the Dragon , and in the position in which the stars were twelve and a half thousand years ago. The Bayon Temple , according to legend, symbolizes the heart of the Dragon.

stone faces of Bayon Temple in Angkor

Stone faces of Zram Bayon

Why, in the 9th-12th centuries, correlate buildings with the most ancient map of the sky? And how could they know about her? This, perhaps, confirms the hypothesis of the creation of the city on the already existing foundations left over from prehistoric civilization.

In addition, most of the temples of Angkor are designed as five-step pyramids. And the pyramids around the world were built at a much earlier period than the officially accepted dating of Angkor Wat.

Bayon temple in Angkor

Bayon Temple in Angkor. lj-user yarowind /commons.wikimedia.org

All the temples of Angkor are oriented with front facades along the north-south line. The main entrance to all the temples is on the east side, and only Ankor-Wat, according to legend, being built as a place where King Suryavarman II was to be reborn, has a western entrance.

The moat around the temple complex raises many questions. This is a real hydraulic engineering miracle, the construction of which required the deepest knowledge in many fields of science.

Aerial view of the Angkor Wat temple complex

Aerial view of the Angkor Wat temple complex. Steve Jurvetson from Menlo Park, USA

The channel was “calculated” and built in the shortest possible time. Before starting the construction of the foundation of buildings. And the complex itself was under construction for about 35 years, which is extremely short, given the huge amount of work and the primitive level of technology (according to official science).

A number of towers and temples reach a height of 60 meters, this is the height of a twenty-story building. In the modern world, such structures are presented as high-rise objects of increased complexity. The foundations of such structures are performed on a pile foundation using sophisticated construction equipment.

According to the research carried out , the soil was dug out under the complex and sand was poured, which was carefully tamped. A layer of soil was laid on it, or, as modern builders say, backfill soil, and then another layer of compacted sand. Or, in modern construction language, preparation has been made for the base of a floating foundation.

This technology began to be applied in practice only in the 70s of the last century. Until now, they try to install high-rise buildings on a pile foundation, since they cannot foresee all the nuances.

And the ancient builders could. Apparently, they had a lot of experience (or possessed some knowledge) of erecting high-rise buildings and structures on floating foundations in tropical conditions.

It is also striking with what precision the ancient builders adjusted and processed stone blocks. And they did it easily, without thinking about the size and shape.

processed stone in Angkor

Treated stone in Angkor

There are also quite large blocks with polygonal masonry , typical of the ancient structures of South America.

polygonal masonry in Angkor

Polygonal brickwork in Angkor

polygonal masonry in Ollantaytambo, Peru

Polygonal masonry. Ollantaytambo. Peru. Pavel Špindler

In the temples of Angkor there are columns of different quality. Some show traces of processing on some kind of machine, as suggested by alternative researchers.

Traces of mechanical processing of columns in Angkor. Screenshot. youtube.com/LAI Research Center

Measurements of traces of processing of columns in Angkor. Screenshot. youtube.com/LAI Research Center

But not only the temple complexes of Angkor are surprising.

Valley of a Thousand Lingams – Kbal Spien River

For example, the river Kbal Spien , which originates in the mountains and reaches Angkor. The entire river bed is lined with stone slabs with lingams carved on them.

The Khmers believed that the lingas (lingams) fertilized and purified the water that irrigated the rice fields. It was believed that it was because of this that the Khmer empire had rich harvests and flourished.

Waterfall and lingams at Qbal Spien in Ankor

Waterfall and Lingams at Qbal Spien in Ankor, Cambodia Prerit

It is believed that the construction of Qbal Spien was started by King Suryavarman I (1001/06 – 1050). and later finished by King Udayadityavarman II . (1049/50 – 1066)

The researchers were interested in this fact. The length of the river channels is about nine kilometers. To accomplish such a task, it is necessary to run the river along a different channel, scoop out all the silt, light fractions along the entire length of the river and to the entire depth of river sediments, then add an unthinkable amount of sand and lay on top not just sandstone slabs, but decorated with bas-reliefs.

Kbal Spien river in Angkor

River of a Thousand Lingams. Kbal Spean

This requires special hydrotechnical knowledge and a huge number of working hands.

The Qbal Spien bed is covered with thousands of images of lingams, which are arranged in even rows. Alternative researchers believe that the lingams worshiped in Hinduism are in fact the oldest artifacts – the legacy of prehistoric civilization. And the purpose of the lingams was not religious and cult, but quite technological, as evidenced by its unusual design.

So, it is likely that the lingams of the Kbal Spien River performed some kind of technical function, which gave the water flowing through them special properties.

Is Kohker a “pyramid of death”?

90 km from Angkor there is a very unusual place called Kahkay or Kohker. This ancient temple complex. Of the surviving buildings in Kahkai: the Prasattom pyramid temple. It is seven-step, 32 m high and 55 m long, reminiscent of the stepped pyramids of South America.

The Garuda , carved into the stone block, guards the top of the pyramid. Henri Parmentier , a French architect, historian and archaeologist, estimates that the colossal lingam, which, according to the inscriptions, was erected at the top, reached at least 4 meters in height and weighed 24 tons.

According to legend, one of the rulers of Angkor was the sorcerer king – Jayavarman IV. It is believed that he erected this pyramid in one night.

In 921, Jayavarman IV laid claim to the kingdom and then left the capital and decided to create his own center of power. About 10,000 supporters fled with him, including women and children.

In 928, Jayavarman IV became the sole ruler of the Khmer Empire, but did not return to Angor. He died in 941, and Kahkay was the capital of the Khmer Empire until 944.

The most amazing thing is that in the Kohker area, archaeologists found an inscription carved on a stone, which indicates the exact date of illumination of the main lingam at the top of the pyramid – December 12, 921, at 8:47 am (translated from the ancient Hindu chronology). And Jayavarman IV came here just a few days before that date.

Experts cannot explain how this is possible. Clear the site from the jungle, cut down huge stone blocks, process, deliver and lay in the masonry walls, raising them to a height of 30 meters, and all this in one night?

Kohker pyramid in Cambodia

Kohker pyramid. Thomas Wanhoff

Official science does not study this issue, and ancient legends give their explanation for this.

In the 9th century, a certain nobleman of non-royal blood lived at the court, who married a woman from the royal family. He practiced witchcraft and communicated with the demon of the underworld, which helped the nobleman become king – Jayavarman IV.

Legend says that Jayavarman IV turned to a certain “architect” for help, who was able to create a pyramid overnight using a magic tool. Sources call this weapon “white fire”. They could whip enemies at a distance.

Legend also says that Jayavarman IV made sacrifices to this demon by throwing people into a deep well in the Kohker pyramid. Since then, it is believed that the pyramid is the gateway to the demon world. Locals call it the “pyramid of death” and do not like it.

Scientists are still exploring the jungle around Angkor and discovering new complexes . Since they are all covered with thickets, it is very difficult to explore them.

But everything discovered only confirms the hypothesis that Angkor was built in the deepest antiquity by some highly developed civilization. And its creation is unsubstantiatedly attributed to the Khmers, just as the construction of a grandiose monument in Baalbek is attributed to the Romans. The Khmer Empire was only completing and restoring the prehistoric heritage that it inherited.

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Ancient

The mystery of the ancient Chinese “magic mirrors”, over the solution of which scientists are still racking their brains

In the Ancient East, for more than two thousand years, there are expensive and rare mirrors, which are called magic to this day. Not for nothing, because the bronze from which they are made can become completely transparent. In China they were called “light-transmitting mirrors”, and in the West – simply “magic mirrors”. These artifacts are still a mystery to scientists around the world.

For more than ten centuries, this rare artifact from China has puzzled all researchers. This mirror is made of bronze, which has been carefully polished. On the back there is a molded pattern. 

The polished surface looks completely normal and can be used like a regular mirror. But when a bright light hits the surface of the mirror and it is reflected and projected onto the surface, then the pattern decorating the back side mysteriously appears in the projected reflection. 

It looks as if a solid bronze mirror suddenly became completely transparent. The Chinese name for these mirrors literally means “light transmitting mirrors.” In the rest of the world, they are called differently: “translucent mirrors” or “magic mirrors”.

Various magic mirrors.
Various magic mirrors.

The mystery of these mysterious ancient artifacts has plagued scientists since the 19th century. It took researchers a century before they figured out the technology for making these mirrors. Even in the homeland of these historical wonders, the technique of their production was considered lost. 

The secret was solved thanks to the ancient Chinese manuscript “Records of Ancient Mirrors”. Subsequently, the book was irretrievably lost. Now in the world there is only one master who owns the art of making these magic mirrors – this is Yamamoto Akihisa from Japan.

There is only one master left in the world who owns the secret of making a magic mirror.
There is only one master left in the world who owns the secret of making a magic mirror.

Master Akihisa learned about this mysterious art from his father. In their family, these secrets were passed down from generation to generation. Despite this, many of the manufacturing nuances were lost. I had to experimentally find out various details.

Many of the nuances of this ancient craft have been lost.
Many of the nuances of this ancient craft have been lost.

The mystery of the reflection of the image of the back of the mirror was solved in 1932 by Sir William Bragg. To do this, at the very beginning, patterns are created on the back of the mirror, then the desired bulges are made by scraping and engraving. 

At the end, it is all polished and coated with a special mercury alloy. As a result of all these actions, bulges and bends invisible to the eye remain on a smooth mirror surface. They faithfully reproduce the pattern of the reverse side.

Light on the surface of the mirror is reflected and refracted in such a way that the bronze appears transparent.
Light on the surface of the mirror is reflected and refracted in such a way that the bronze appears transparent.

For many years, various researchers have tried to recreate the “magic mirror”. For this, the materials were subjected to pressure and high temperatures. Nothing worked. All this only spoiled the mirror, and the desired effect did not appear.

Modern scientists have failed to comprehend the secret of the magical effect of the ancient Chinese mirror.
Modern scientists have failed to comprehend the secret of the magical effect of the ancient Chinese mirror.

Scientists have written dozens of books and scientific articles on the topic of studying these artifacts. Back in the 11th century, a Chinese scientist, Shen Gua, in his book “Reflections on the Lake of Dreams” wrote the following about this: if a bright ray of sunlight hits, then all these inscriptions become clearly visible and readable. “

Western scholars have tried to reproduce the effect of an ancient Eastern magic mirror using a compressor.
Western scholars have tried to reproduce the effect of an ancient Eastern magic mirror using a compressor.

The reflection of sunlight occurs on the uneven surface of the mirror as follows: convex parts scatter light, and concave ones collect it. As a result, the “magic mirror” effect is formed.

The art of making magic mirrors dates back to the Han Dynasty (206 BC - 24 AD).
The art of making magic mirrors dates back to the Han Dynasty (206 BC – 24 AD).

Science knows cases when such a mirror had one pattern on its reverse side, and reflected a completely different one! Scientists assume in this case that the front side of the mirror is polished, and then a certain pattern is etched on it with acid, and then polished again. It becomes quite obvious that there are a lot of recipes for making such items. Most likely, each master discovered and kept his secrets, which are now lost.

In China, the method of making a bronze alloy has been known since about 2000 BC.
In China, the method of making a bronze alloy has been known since about 2000 BC.

The bronze, from which the famous mirrors are made, was invented by the Chinese more than four thousand years ago! The oldest “magic mirror” found by archaeologists is more than one and a half thousand years old. The fact that it was unheard of in those days, a rarity and luxury is clear from the fact that such objects were found during excavations of the tombs of very noble nobles and emperors.

Mirrors ceased to be a rarity in the Middle Ages, during the reign of the Ming dynasty. Most of the discovered artifacts belong to these times.

This item was extremely rare and expensive.
This item was extremely rare and expensive.

Over the past century and a half, many researchers and scientists have puzzled over the mystery of the “magic mirror”. Methods for producing the artifact that would have been equal to ancient craftsmanship have never been discovered. World science offers the following options:

1. When casting, those parts that are thinner cool faster and the surface is deformed. Only it is very difficult to achieve this effect: only two or three mirrors out of a hundred can reproduce a magical effect.
2. A pattern is engraved on the mirror, then it is filled with bronze of a different kind and polished.
3. Drawing is done on the front side, and then covered with a special alloy of mercury and polished.
4. The patterns on the mirror are etched with acid, then polished.
5. The pattern is cut on the back of the mirror, resulting in bumps in the front.
6. The front side patterns are stamped onto the surface and then polished.

It is believed that it all works, but so far no one has been able to reproduce it. “Magic mirrors” were also made in Japan. There they were called makkyo. It is there that the last master who owns this art lives.

There is one interesting detail of these mirrors that makes them similar to modern disk storage media.
There is one interesting detail of these mirrors that makes them similar to modern disk storage media.

With all the variety of these artifacts, there is one detail that makes them all in common: a convex pattern element in the center. It becomes clear that this element must carry a certain function. Presumably in order to install and fix the mirror in the required place. Crazy assumption: is it really an ancient disk storage medium?

In fact, there is a lot in common. After all, the discs also have a certain pattern on the back. Information there is written in the form of spiral tracks, depressions that are squeezed out. These paths absorb light, and the base reflects it. 

Information is read from the disc media using a laser beam. Interestingly, someone tried to illuminate the “magic mirror” with a laser? For sure. It is believed that in ancient times they used the technology of steam generation, which made it possible to create real volumetric holographic images. While these are all theories, perhaps in the future, scientists will still be able to unravel the mystery of “magic mirrors”.

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