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The resulting geometry shows that the Ushtogai square is inclined inside a larger perfect square orientated along the cardinal directions and dived into nine internal squares, in the manner of a chinese magic square. Fig. 8 : The sides of the Ushtogai square can be seen to be the diagonals of double squares orientated on the cardinal directions.

Figure 8 The resulting geometry shows that the Ushtogai square is inclined inside a larger perfect square orientated along the cardinal directions and dived into nine internal squares, in the manner of a chinese magic square. Fig. 8 : The sides of the Ushtogai square can be seen to be the diagonals of double squares orientated on the cardinal directions.

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Fig. 2: A satelite image from Google Earth shows the Ushtogai square's orientation. A Google Earth image of the site shows its orientation (see fig. 2). It can be seen that its sides are not aligned to the cardinal directions, as is the case for the square base of the Great Pyramid at Giza, for example. Geometrical Considerations As the lines are very straight, various researchers have wondered if they have some astronomical meaning, being aligned to particular celestial objects, but no specific hypothesis has been put forward on this subject for the moment.
Fig. 2: A satelite image from Google Earth shows the Ushtogai square's orientation. A Google Earth image of the site shows its orientation (see fig. 2). It can be seen that its sides are not aligned to the cardinal directions, as is the case for the square base of the Great Pyramid at Giza, for example. Geometrical Considerations As the lines are very straight, various researchers have wondered if they have some astronomical meaning, being aligned to particular celestial objects, but no specific hypothesis has been put forward on this subject for the moment.
Fig. 1 : NASA image of the Ushtogai square. In 2007, Dmitriy Dey, an archaeology enthusiast, found a unique square-shaped geoglyph in the Kostanai region of Kazahkstan using Google Earth. It has become known as the Ushtogai Square. On 15" October 2015, Nasa brought worldwide attention to the site by publishing high definition satelite photographs of it along with several other recently discovered geoglyphs in the same area (see fig. 1). Archaeological dating suggests that the site is between 3000 and 8000 years old. between 3000 and 8000 years old. It is composed of 101 circular earth mounds, similar to the barrows around Stonehenge in England, which trace a perfect square and its diagonals. Each mound is now approximately | metre high and 10 metres across, but it is thought they may have been up to 3 metres high originally (New York Times, 30/10/15). Seventeen earth mounds create sixteen intervals to mark out each side making a total of 64 earth mounds around the square's perimeter. One barrow marks the square's centre whilst nine barrows form each of the four half diagonals making a total of 37 barrows for the diagonals. Each diagonal is consequently divided into 20 intervals.
Fig. 1 : NASA image of the Ushtogai square. In 2007, Dmitriy Dey, an archaeology enthusiast, found a unique square-shaped geoglyph in the Kostanai region of Kazahkstan using Google Earth. It has become known as the Ushtogai Square. On 15" October 2015, Nasa brought worldwide attention to the site by publishing high definition satelite photographs of it along with several other recently discovered geoglyphs in the same area (see fig. 1). Archaeological dating suggests that the site is between 3000 and 8000 years old. between 3000 and 8000 years old. It is composed of 101 circular earth mounds, similar to the barrows around Stonehenge in England, which trace a perfect square and its diagonals. Each mound is now approximately | metre high and 10 metres across, but it is thought they may have been up to 3 metres high originally (New York Times, 30/10/15). Seventeen earth mounds create sixteen intervals to mark out each side making a total of 64 earth mounds around the square's perimeter. One barrow marks the square's centre whilst nine barrows form each of the four half diagonals making a total of 37 barrows for the diagonals. Each diagonal is consequently divided into 20 intervals.
Fig. 3 : The square's diagonal inclined at an angle of 18.44° ouest of north. Figure 3 shows the orientation of one of the square's diagonals to be 18.44° east of north which is the exact angle of the diagonal of a triple square whose long sides have been aligned along the north-south axis. It follows that the other diagonal, turned at 90° to the former, corresponds to the diagonal of a triple square whose long sides are aligned to the east-west axis. (see fig. 4)
Fig. 3 : The square's diagonal inclined at an angle of 18.44° ouest of north. Figure 3 shows the orientation of one of the square's diagonals to be 18.44° east of north which is the exact angle of the diagonal of a triple square whose long sides have been aligned along the north-south axis. It follows that the other diagonal, turned at 90° to the former, corresponds to the diagonal of a triple square whose long sides are aligned to the east-west axis. (see fig. 4)
Fig. 7 : The side of the square is inclined at 26,56° from north.
Fig. 7 : The side of the square is inclined at 26,56° from north.
Fig. 5: The triple square in the Carnac alignments.
Fig. 5: The triple square in the Carnac alignments.
Fig. 4 : The diagonals of two triple squares orientated exactly on the cardinal directions coincide with the diagonals of the Ushtogai square.
Fig. 4 : The diagonals of two triple squares orientated exactly on the cardinal directions coincide with the diagonals of the Ushtogai square.
Fig. 6 : The triple square between the Statior Stones at Stonehenge (Plan by John North).
Fig. 6 : The triple square between the Statior Stones at Stonehenge (Plan by John North).
Fig. 9 A 24 by 24 square grid containing th Ushtogai square. It is also important to consider the numbers involved. The builders could have constructed the same monument using far fewer barrows and creating themselves a lot less work. They chose to create 16 spaces along the sides of the square and 20 spaces along the diagonals. This gives a ratio of side number to diagonal number of 16:20 which can be reduced to 4:5 or 1:1.25. Now the ratio between the side of a square and its diagonal is 1:V2 or 1,1,4142 so if the builders has used the same spacing along the diagonal as they had along the sides, they would have needed 22.63 spaces. So 22 spaces would have been a much closer whole even number to use to trace the diagonal than 20 spaces. We must consequently consider the fact that the builders volontarily modified their measuring unit to obtain 10 spaces along each half diagonal and in so doing, introduced the decimal notion but the study of the measurements involved goes further than the object of this present paper. The numbers involved, however, lead one to pence Diaepk Shee: aetedewsl acoder veered coreeeereus
Fig. 9 A 24 by 24 square grid containing th Ushtogai square. It is also important to consider the numbers involved. The builders could have constructed the same monument using far fewer barrows and creating themselves a lot less work. They chose to create 16 spaces along the sides of the square and 20 spaces along the diagonals. This gives a ratio of side number to diagonal number of 16:20 which can be reduced to 4:5 or 1:1.25. Now the ratio between the side of a square and its diagonal is 1:V2 or 1,1,4142 so if the builders has used the same spacing along the diagonal as they had along the sides, they would have needed 22.63 spaces. So 22 spaces would have been a much closer whole even number to use to trace the diagonal than 20 spaces. We must consequently consider the fact that the builders volontarily modified their measuring unit to obtain 10 spaces along each half diagonal and in so doing, introduced the decimal notion but the study of the measurements involved goes further than the object of this present paper. The numbers involved, however, lead one to pence Diaepk Shee: aetedewsl acoder veered coreeeereus
Related topics:
Prehistoric ArchaeologyArchitectural GeometryNeolithic ArchaeologyGeometryHistory of Numbers
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