The most symmetrical objects in the world
If you have ever tried to get a haircut on your own, you know how hard it is to achieve perfect symmetry. We appreciate so much symmetry in particular because it is difficult to achieve.
We offer you the five most symmetrical objects ever created by man, and an explanation of why they are so difficult to create.
In 2004, the US space mission Gravity Probe B (GP-B) was launched into space on a Delta II rocket. She had to test the general theory of relativity. On the satellite in Earth orbit, among other things, there was a set of gyroscopes capable of measuring two phenomena predicted by GR: space-time curvature ( geodetic precession ) and space-time curvature of large objects ( dragging of inertial reference systems ). To measure these phenomena, the gyroscopes had to be incredibly accurate. An error greater than one hundred billionth degree degrees per hour would spoil the experiment. The accuracy of standard gyroscopes used on submarines and military aircraft is 10 million times worse.
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To build such accurate gyroscopes, it was necessary to create perfectly symmetrical rotors, rapidly rotating elements, allowing gyroscopes to maintain their position in space. They had to be perfectly balanced and homogeneous. The GP-B team made these small spheres from pure quartz blocks grown in Brazil and baked in Germany. The surface of each gyroscope is almost perfectly spherical, and differs from the sphere by no more than ten millionth of a centimeter.
According to the Guinness Book of Records, these are the roundest objects ever created. The Stanford team that worked on them claims that only neutron stars are more spherical.
The only real competitor to GP-B in the realm of ideal spheres is the ball that will soon determine the kilogram. This area is the result of the work of the Avogadro project, in which only the cost of raw materials exceeded one million dollars. The goal is to exceed and replace the international kilogram prototype (IPK). A kilogram is the last unit of measurement in the international system of units (metric), still defined by a physical object — a cylinder made of an alloy of platinum and iridium — and not by physical principles. This cylinder is located under three enclosed glass lids in a temperature-controlled storage facility located near Paris.
The problem is that the current IPK has lost a bit of weight, compared to 40 cylinders similar to it, stored in other countries - and this is a serious disadvantage of an object designed to determine mass. In the Avogadro project, two small spheres of almost perfect form, completely consisting of silicon-28, were created, which should almost always keep a weight of exactly one kilogram. Silicon-28, used in the fields, was pre- cleaned on Russian centrifuges , which once produced nuclear weapons. Purified silicon was sent to Germany, and crystals were grown from it.
The final sphere differs from the ideal one by no more than 25 nm, and most likely, it will soon displace the sphere from GP-B from the first place. “If our spheres were the size of the Earth, then the irregularities on them would be from 12 to 15 mm in size, and they would differ from the sphere by only 3-5 m,” said Achim Leistner, chief optics specialist, from the Australian State Association scientific and applied research.
The spheres are ready, and now researchers from different countries will try to calculate the exact number of atoms they contain, in order to work out a universal agreement about what the mass of one kilogram is.
Without burdening themselves with the annoying properties of the physical world, mathematicians can imagine unrealistically symmetrical structures. For example, the Li group E8 is a set of 248 different forms of symmetry applicable to a theoretical 57-dimensional object. The structure was invented at the end of the 19th century, but only recently researchers from Britain and Germany announced the creation of a physical system representing E8 in the real world.
Computer-based embroidery
To see the symmetry of E8, the researchers cooled the crystal from cobalt and niobium to temperatures close to absolute zero. They then placed the crystal in a magnetic field, and as its force increased, the electron spins inside the crystal began to line up according to the E8 structure. The observation of this symmetry speaks not only about the possibility of creating very symmetric systems - it also says that in the quantum world there are hidden symmetries that determine the self-organization of electrons.
Most people will never encounter a GP-B sphere or a kilogram of silicon-28. But they will be able to see a surprisingly symmetrical structure by visiting India. The Taj Mahal was built by Padishah Shah Jahan as a mausoleum in memory of his wife Mumtaz Mahal, who died in childbirth of the 14th child. Jahan wanted the building to represent harmonious relationships, and asked the architect to depict something two-sidedly symmetrical. The result is a structure in which symmetrical parts are found from close-ups to decorative elements.
The Taj Mahal is often called the key example of symmetry in buildings, but it is rather difficult to determine which of the buildings ever built was perfectly symmetrical, since many architects used symmetry in their designs. For many years, mathematics and architecture were one discipline, and architects valued buildings that looked like their reflection.
To create something man-made and at the same time very symmetrical is difficult even with the current development of technologies. Therefore, the discovery of these surprisingly symmetrical ear ornaments, which are attributed to the age of hundreds of years, so aroused lovers of conspiracy, claiming that in principle they could not be done without modern tools. Archaeologists do not agree with this. These plugs are really made surprisingly clever, but they were not made by aliens or pranksters on modern machines, but by particularly skilled Aztecs . The archaeologists, who were torn off and the workshops where they were made, say that many of them were made with stone, ceramics and wooden tools.
“It's amazing not only that they were created with such art and precision, but also that they survived to this day without being crushed,” says John Millhauser, an anthropologist from North Carolina State University who found similar tunnels in the city of Xaltocán , north of Mexico City. So, even if they look supernatural, they actually just serve as an example of amazing craftsmanship.
We offer you the five most symmetrical objects ever created by man, and an explanation of why they are so difficult to create.
Quartz Gyro Rotor for Gravity Probe B
In 2004, the US space mission Gravity Probe B (GP-B) was launched into space on a Delta II rocket. She had to test the general theory of relativity. On the satellite in Earth orbit, among other things, there was a set of gyroscopes capable of measuring two phenomena predicted by GR: space-time curvature ( geodetic precession ) and space-time curvature of large objects ( dragging of inertial reference systems ). To measure these phenomena, the gyroscopes had to be incredibly accurate. An error greater than one hundred billionth degree degrees per hour would spoil the experiment. The accuracy of standard gyroscopes used on submarines and military aircraft is 10 million times worse.
')
To build such accurate gyroscopes, it was necessary to create perfectly symmetrical rotors, rapidly rotating elements, allowing gyroscopes to maintain their position in space. They had to be perfectly balanced and homogeneous. The GP-B team made these small spheres from pure quartz blocks grown in Brazil and baked in Germany. The surface of each gyroscope is almost perfectly spherical, and differs from the sphere by no more than ten millionth of a centimeter.
According to the Guinness Book of Records, these are the roundest objects ever created. The Stanford team that worked on them claims that only neutron stars are more spherical.
Silicon kilogram Avogadro project
The only real competitor to GP-B in the realm of ideal spheres is the ball that will soon determine the kilogram. This area is the result of the work of the Avogadro project, in which only the cost of raw materials exceeded one million dollars. The goal is to exceed and replace the international kilogram prototype (IPK). A kilogram is the last unit of measurement in the international system of units (metric), still defined by a physical object — a cylinder made of an alloy of platinum and iridium — and not by physical principles. This cylinder is located under three enclosed glass lids in a temperature-controlled storage facility located near Paris.
The problem is that the current IPK has lost a bit of weight, compared to 40 cylinders similar to it, stored in other countries - and this is a serious disadvantage of an object designed to determine mass. In the Avogadro project, two small spheres of almost perfect form, completely consisting of silicon-28, were created, which should almost always keep a weight of exactly one kilogram. Silicon-28, used in the fields, was pre- cleaned on Russian centrifuges , which once produced nuclear weapons. Purified silicon was sent to Germany, and crystals were grown from it.
The final sphere differs from the ideal one by no more than 25 nm, and most likely, it will soon displace the sphere from GP-B from the first place. “If our spheres were the size of the Earth, then the irregularities on them would be from 12 to 15 mm in size, and they would differ from the sphere by only 3-5 m,” said Achim Leistner, chief optics specialist, from the Australian State Association scientific and applied research.
The spheres are ready, and now researchers from different countries will try to calculate the exact number of atoms they contain, in order to work out a universal agreement about what the mass of one kilogram is.
Li group E8
Without burdening themselves with the annoying properties of the physical world, mathematicians can imagine unrealistically symmetrical structures. For example, the Li group E8 is a set of 248 different forms of symmetry applicable to a theoretical 57-dimensional object. The structure was invented at the end of the 19th century, but only recently researchers from Britain and Germany announced the creation of a physical system representing E8 in the real world.
Computer-based embroidery
To see the symmetry of E8, the researchers cooled the crystal from cobalt and niobium to temperatures close to absolute zero. They then placed the crystal in a magnetic field, and as its force increased, the electron spins inside the crystal began to line up according to the E8 structure. The observation of this symmetry speaks not only about the possibility of creating very symmetric systems - it also says that in the quantum world there are hidden symmetries that determine the self-organization of electrons.
Taj Mahal
Most people will never encounter a GP-B sphere or a kilogram of silicon-28. But they will be able to see a surprisingly symmetrical structure by visiting India. The Taj Mahal was built by Padishah Shah Jahan as a mausoleum in memory of his wife Mumtaz Mahal, who died in childbirth of the 14th child. Jahan wanted the building to represent harmonious relationships, and asked the architect to depict something two-sidedly symmetrical. The result is a structure in which symmetrical parts are found from close-ups to decorative elements.
The Taj Mahal is often called the key example of symmetry in buildings, but it is rather difficult to determine which of the buildings ever built was perfectly symmetrical, since many architects used symmetry in their designs. For many years, mathematics and architecture were one discipline, and architects valued buildings that looked like their reflection.
Obsidian Ear Tunnels
To create something man-made and at the same time very symmetrical is difficult even with the current development of technologies. Therefore, the discovery of these surprisingly symmetrical ear ornaments, which are attributed to the age of hundreds of years, so aroused lovers of conspiracy, claiming that in principle they could not be done without modern tools. Archaeologists do not agree with this. These plugs are really made surprisingly clever, but they were not made by aliens or pranksters on modern machines, but by particularly skilled Aztecs . The archaeologists, who were torn off and the workshops where they were made, say that many of them were made with stone, ceramics and wooden tools.
“It's amazing not only that they were created with such art and precision, but also that they survived to this day without being crushed,” says John Millhauser, an anthropologist from North Carolina State University who found similar tunnels in the city of Xaltocán , north of Mexico City. So, even if they look supernatural, they actually just serve as an example of amazing craftsmanship.
Source: https://habr.com/ru/post/403221/
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