Roman Amphitheatre of Uthina The Roman Amphitheatre of Uthina is located in Uthina , near Tunis, Tunisia . Building for Uthina began in 40 BC and continued through to 135 AD. The amphitheatre may have been a later addition to what was already a large town. Also located there were a fortress, cisterns, an aqueduct, a triumphal arch, a theatre, and a basilica with a circular crypt . Coordinates 36.608598,10.169214 Description The amphitheatre, partly buried, measures 113 by 90 meters. The arena measures 58 by 35 metres, giving surface areas of 7988 and 1539 square metres respectively. There are four entrances, two main entrances at each end, with the seating area supported by three tiers of columns and arches. (Although these are no longer there, measurements and amphitheater descriptions rely on a complete building.) Measurements for the amphitheatre on site are 12 0 by 89 metres, with the arena measuring 67 by 36 metres. The surface areas measure 10680 an d 24...
Great Pyramid Trial passage
Great Pyramid Trial Passages, as they are called, are located near Khufu's pyramid in the northeast corner.
Description
The passage in question is positioned north/south with a length of 23m and a depth of 10m, angled towards north and separately south. Splitting the length in 2 × 11.5m for each, a triangle of 41° at 15.24m is produced. This is quite similar to 10 × (1 + 0.523), the 41° angle at its location would equate to 47.5°, sweeping along an arc of 7.0897° towards south and 7.0897° towards north. Although at 41° the effective angle could be up to 6° less.
In most situations, a gnomon is aligned east/west so it can measure a tilt year on year, an astronomical object, or a solar transit. A north/south alignment would just be a fixed point along an arc. In this situation, it is 17° above the equator.
Great Pyramid Trial Passages, as they are called, are located near Khufu's pyramid in the northeast corner.
In an article called, 'Moving heaven and earth for Khufu', the author (an expert in ancient architecture) states, 'Were the Trial Passages at Giza components of a rudimentary stellar observatory?’ (JAEA 4 (2020), p. 29-53). He also states that observation devices of the type described by Dash were installed within the Passages.
Description
The passage in question is positioned north/south with a length of 23m and a depth of 10m, angled towards north and separately south. Splitting the length in 2 × 11.5m for each, a triangle of 41° at 15.24m is produced. This is quite similar to 10 × (1 + 0.523), the 41° angle at its location would equate to 47.5°, sweeping along an arc of 7.0897° towards south and 7.0897° towards north. Although at 41° the effective angle could be up to 6° less.
In most situations, a gnomon is aligned east/west so it can measure a tilt year on year, an astronomical object, or a solar transit. A north/south alignment would just be a fixed point along an arc. In this situation, it is 17° above the equator.
(23.5 + 29.9 + 6.243) − (90 − 47.5) = 17.143°
Possible stars would be Eta Leonis in Leo, Aldebaran in Taurus, and Gamma Geminorum in Gemini, all at about 16.5°. Measurements assume that some devices are measuring any variation. In practice, a man would be sitting, marking faint variations of starlight, and as such, the angle would decrease towards the equator.
Measurements
The following distances and angles best describe the alignment of the Trial Passage.
Possible stars would be Eta Leonis in Leo, Aldebaran in Taurus, and Gamma Geminorum in Gemini, all at about 16.5°. Measurements assume that some devices are measuring any variation. In practice, a man would be sitting, marking faint variations of starlight, and as such, the angle would decrease towards the equator.
Measurements
The following distances and angles best describe the alignment of the Trial Passage.
A distance of 157.5 m by 4 m produces an angle of 1.455°.
This angle is 0.025391 rad. Using 25.4 mm to an inch, then the deviation is 4 m or 4000 mm.
4000 ÷ 25.4 = 157.4803 inches.
(This is from the misalignment due north).
Along with this is another possibility where the angle difference gives an error.
Along with this is another possibility where the angle difference gives an error.
1.455° is equal to 939 years = 1046 AD
From 1985-2020 = 0.05425°
From 1046-1985 = 1.40075°
Because it is over to the right from vertical by 0.05425°, it is actually 1.3465°, which then equates to 869 years or 1116 AD, which in turn equates to 3.7m over as an error with the angle equal to 0.0235 rad.
Also it is possible by just using one 0.05425°. This gives two numbers and a difference of 5.17; multiplying by 100 gives a distance of 517 metres.
131.4
136.57 (as half difference)
= 5.17 × 100 = 517
191.2 ÷ (100 + (10 × π)) = 1.455
191.2 ÷ (100 + (10 × π)) = 1.455
191.2 ÷ 131.4 = 1.455°
So 131.4 is the associated distance for 1.455°.
At a distance of 517 m at an angle of 11° to 17°, the Sphinx can be measured.
At 17°, it is 0.296 rad and at 11° is 0.191 rad.
0.191 rad = 10.945° side = 99.978 m
0.191 rad = 10.945° side = 99.978 m
0.296 rad = 16.959° side = 157.658 m
= 57.68 m
0.323 rad = 18.499° side = 173 m
= 73 m (stated length, 7.55°)
Its measurements start at 10.7°, giving a length of 61.309 m, a total angle of 6.3° at 517 m (this by itself produces a distance of 57.08 m). The Sphinx can also be measured at an angle of 19°, giving 75.42 m as its length, but measurement has to be from the nearer side, thus reducing the overall length.
Also, this could equal 19 as it then equates with the Sphinx's length (π = 180°).
Its measurements start at 10.7°, giving a length of 61.309 m, a total angle of 6.3° at 517 m (this by itself produces a distance of 57.08 m). The Sphinx can also be measured at an angle of 19°, giving 75.42 m as its length, but measurement has to be from the nearer side, thus reducing the overall length.
Also, this could equal 19 as it then equates with the Sphinx's length (π = 180°).
(1 + (π ÷ 10)) = 1 + 18°
Or
(1 + (π ÷ 10)) × 1.455 = 1.912
And
(1.912 ÷ 1.455) - (1 + (π ÷ 10)) = 0.00007
(1.912 ÷ 1.455) = (1 + (π ÷ 10))
(1 + (π ÷ 10)) = (1 + (π ÷ 10))
(1 + (π ÷ 10)) ÷ (1 + (π ÷ 10)) = 1
Using the number 1 from this:
Using the number 1 from this:
1 as 360°
1 + 18 = 378
378 ÷ 60 = 6.3
6.3 = 10.7 - 17°
10.7° = 97.688 m
10.7° = 97.688 m
17° = 158.063 m = 60.4 m
17.245° = 160.483 m = 62.8 m
18.27° = 170.688 m = 73 m
= 7.57° difference off 6.3° = √(1.618)
Because 17 - 18.27 = 1.27, then the angle is made up of √(1.618) + 6.3
Connecting from Sphinx
From the Sphinx, a 10.7° and 17° angle reaches the Rock Cut Tombs of Khafre's pyramid; a 19° angle reaches an uncut tomb.
Connecting from Sphinx
From the Sphinx, a 10.7° and 17° angle reaches the Rock Cut Tombs of Khafre's pyramid; a 19° angle reaches an uncut tomb.
The 10.7° angle reaches the pile of boulders; 13°/15°/17° best describes the angles with the tombs. Inside of this, at 6.3°, there are three tombs.
Connecting from Khafre's pyramid
From the 10.7° (0.187 rad) and 17° (0.297 rad), another two angles are produced by converting their radians into degrees: 18.7° and 29.7°. Where the two angles from the Sphinx met at Khafre's pyramid (at three locations), the angles of 18.7° and 29.7° follow towards Menkaure's pyramid, aligning with the Queen's pyramid peaks. An angle of 50° is required for the third point. Then, a 10.7° and 17° angle connect towards the tombs.
Alternative analysis
(1)
Using radians again and starting from 10.7° to 18° and increasing the difference from 7.3° to 7.68°
Between the numbers 10.313° (0.18 rad) and 18° (π ÷ 10 rad) measures 73.9 m.
Between 18° and 10.7° it measures.
Connecting from Khafre's pyramid
From the 10.7° (0.187 rad) and 17° (0.297 rad), another two angles are produced by converting their radians into degrees: 18.7° and 29.7°. Where the two angles from the Sphinx met at Khafre's pyramid (at three locations), the angles of 18.7° and 29.7° follow towards Menkaure's pyramid, aligning with the Queen's pyramid peaks. An angle of 50° is required for the third point. Then, a 10.7° and 17° angle connect towards the tombs.
Alternative analysis
(1)
Using radians again and starting from 10.7° to 18° and increasing the difference from 7.3° to 7.68°
Between the numbers 10.313° (0.18 rad) and 18° (π ÷ 10 rad) measures 73.9 m.
Between 18° and 10.7° it measures.
167.983 − 97.688 = 70.295 m
The correct distance is measured as 73 metres.
The correct distance is measured as 73 metres.
167.983 - 94.076 = 73.907
10.7° - 10.313° = 0.387°
10.7° - 10.313° = 0.387°
So if you subtract 0.387°, a number which is 0.00675 rad, from 0.18675 rad (10.7°) leaves 0.18 rad (10.313°), then add 73 m, you get an angle of 17.909°.
94.076 - 167.067 = -72.99 m
10.313° = 0.18 rad
17.909° = 0.31257 rad
18° = 0.314159 rad
(10 × 0.312571016) + (1 ÷ (6.3 × 10)) = π
(2)
It is possible that it is 10.7° - 17.87°, a difference of 7.17°. With this, a width of 69m is created, but with the 4m (1.455°) offset, it equates to a 73m total length.
Conclusion
It is possible for the ratio at Khufu's pyramid to represent the number 1. This is then followed through to Khafre's pyramid and then Menkaure's pyramid. Both of these connect with the angles 10.7° and 17°; a third angle isn't available. This could suggest a build sequence, but it isn't clear about the second or third. Also, the overall length of 73m hasn't always been this length, with a number of arguments as to its original length.
The distance off Khufu's pyramid is 87.5 m.
(2)
It is possible that it is 10.7° - 17.87°, a difference of 7.17°. With this, a width of 69m is created, but with the 4m (1.455°) offset, it equates to a 73m total length.
Conclusion
It is possible for the ratio at Khufu's pyramid to represent the number 1. This is then followed through to Khafre's pyramid and then Menkaure's pyramid. Both of these connect with the angles 10.7° and 17°; a third angle isn't available. This could suggest a build sequence, but it isn't clear about the second or third. Also, the overall length of 73m hasn't always been this length, with a number of arguments as to its original length.
The distance off Khufu's pyramid is 87.5 m.
(1.455 + 87.5) = 88.955
(1.455 + 87.5) ÷ 17 = 5.23
(88.955 ÷ 17) ÷ (517 × 0.000117) = 86.50
Or
1 + (88.955 ÷ 170) = 1.523
Also, converting into feet and using the golden ratio.
Also, converting into feet and using the golden ratio.
87.50 m = 287.07 ft
287.07 ÷ 1.618 = 177.425
177.425 ÷ 17 = 10.437°
When using 10.437° - (π÷10)°, which is derived from converting into feet, the Sphinx's measured length of 73m is produced (with 73m equal to 240 ft).
Assuming.
When using 10.437° - (π÷10)°, which is derived from converting into feet, the Sphinx's measured length of 73m is produced (with 73m equal to 240 ft).
Assuming.
17 = 1 - (π ÷ 10)°
18 = (π ÷ 10)°
19 = 1 + (π ÷ 10)°
If the angle is 18°, then 86.50m would equal 1 less, implying the use of 17°.
If the angle is 18°, then 86.50m would equal 1 less, implying the use of 17°.
(88.955 ÷ 17) ÷ (517 × 0.000117) = 86.50
73 metres exactly is 239.4 ft, and if converting into a year an angle of 7.12° would assume a year of 2612 BC.
73 metres exactly is 239.4 ft, and if converting into a year an angle of 7.12° would assume a year of 2612 BC.
(239.50131 ÷ 10.7) ÷ π = 7.12482
7.1248257449 = 2612 BC
This then implies that from the ratio of numbers: (1 + (π ÷ 10)) = (1 + (π ÷ 10)). That the angles don't need measuring, and all that is required is a distance of 87.5 m, 1.455°, and a 17° elevation.
The year 2612 BC would put it under Sneferu (this would not be far off accurate), with length playing a part in this number. As the Sphinx was not thought to be increased in size after the 17th dynasty, this measurement and build would suggest a dating of the 17th dynasty and later. Also, 0.523 and 1+0.523 were used as errors when arriving at this, something the Egyptians wouldn't do. Some invading force, possibly like the Greeks in 322 BC, might have implied this or maybe even later. They might have included the numbering as at the time there was doubt as to the build order.
(Lunar and stellar alignment could also be considered, with a 17.143° slope. The stars would be at 1 - 17.143°, giving them about 0.5° clearance, and the Moon at 1 + 17.143°, aligning with one node every 18.6 years, and 1 + 17.143 + 10.7°. But the numbers 1 + 17.143 + 10.46 = 28.6° would be more accurate)
The year 2612 BC would put it under Sneferu (this would not be far off accurate), with length playing a part in this number. As the Sphinx was not thought to be increased in size after the 17th dynasty, this measurement and build would suggest a dating of the 17th dynasty and later. Also, 0.523 and 1+0.523 were used as errors when arriving at this, something the Egyptians wouldn't do. Some invading force, possibly like the Greeks in 322 BC, might have implied this or maybe even later. They might have included the numbering as at the time there was doubt as to the build order.
(Lunar and stellar alignment could also be considered, with a 17.143° slope. The stars would be at 1 - 17.143°, giving them about 0.5° clearance, and the Moon at 1 + 17.143°, aligning with one node every 18.6 years, and 1 + 17.143 + 10.7°. But the numbers 1 + 17.143 + 10.46 = 28.6° would be more accurate)
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