Amphitheatre Pompeii The Amphitheatre of Pompeii is the oldest surviving Roman amphitheatre. It is situated in the ancient Roman city of Pompeii and was buried by the eruption of Vesuvius in 79 ad. It is located to the east of the city and the edge of the eruption. It measures 135m long and 104m wide, the arena's pit is measured at 6m below ground level and was built in 70 bc. Coordinates 40.751827,14.494962 Measurements 135m x 104m (341ft x 443ft) 76.2m x 38.1m ( 250ft x 125ft) Angled at 60° towards northwest Area π×341×443= 474578 π×250×125= 98175 474578× 98175= 46591695150 46591695150÷223= 208931368 π×341×450= 482077 482077× 98175= 47327909475 47327909475÷223= 212232777 Roman Units The Roman cubit (cubitum) was 1½ Roman feet (17.48 inches) Five Roman feet made the pace (passus), 1.48 metres (58.23 inches). If considering a standardised unit, the Roman foot was probably used here, making the above whole units in 5's as if a passus. If applying again, the amph
Great Pyramid Trial passage
Great Pyramid Trial Passages, as they are called, are located near Khufu's pyramid in the northeast corner.
Passage in question is positioned north/south with a length 23m and depth 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. Quite similiar with 10×(1+0.523), the 41° angle at its location would equate as 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.
A distance of 157.5m by 4m produces an angle of 1.455°.
This angle is 0.025391 rad, using 25.4mm to an inch, and then the deviation is 4m 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.
1.455° is equal 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°, this 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 possible using just one 0.05425° This gives two numbers and the difference of 5.17, multiplying by 100 gives a distance of 517m.
131.4
136.57 (as half difference)
=5.17×100=517
191.2÷(100+(10×π))=1.455°
191.2÷131.4=1.455°
So 1.314 is the associated distance for 1.455°.
(1+(π÷10))×1.455=1.912
Sphinx
As an alternative to star measurements is a land based marker.
At a distance of 517m 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=99.978m
0.296 rad=16.959° side=157.658m
=57.68m
0.323 rad=18.499° side=173m
=73m (stated length, 7.55°)
Its measurements start at 10.7° giving a length of 61.309m, a total angle of 6.3° at 517m (this by itself produces a distance of 57.08m). The Sphinx can also be measured at an angle of 19° giving 75.42m as it's length but measurement has to be from the side nearer, 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
1 as 360°
1+18=378
378÷60=6.3
6.3= 10.7 - 17°
10.7°=97.688m
17°=158.063m=60.4m
17.245°=160.483m=62.8m
18.27°=170.688m=73m
=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° reaches an uncut tomb.
The 10.7° angle reaching the pile of bolders, 13°/15°/17° best describes the angles with the tombs. Inside of this 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 its radian into an angle, 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° - 18° and increasing the difference from 7.3° to 7.68°
So between 10.313° (0.18 rad) and 18° (π÷10 rad) measures 73.9m.
Between 18° and 10.7° it measures.
167.983−97.688=70.295m
But it is 73m
167.983−94.076=73.907
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 73m you get an angle of 17.909°.
94.076−167.067=72.99m
10.313°=0.18 rad
17.909°=0.31257 rad
18°=0.314159 rad
(10×0.312571016)+(1÷(6.3×10))=π
(2)
Also, 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 equates as 73m total length.
Conclusion
It is possible for the ratio at Khufu's pyramid to represent a 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 build sequence but isn't clear about 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 87.5m.
(1.455+87.5)=88.955
(1.455+87.5)÷17=0.523
(88.955÷17)÷(517×0.000117)=86.50
Or
1+(88.955÷170)=1.523
Also, they converted into feet and used the golden ratio.
87.50m=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.
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°.
(88.955÷17)÷(517×0.000117)=86.50
73 metres exactly is 239.4 ft, and converting into a year.
(239.50131÷10.7)÷π=7.12482
7.1248257449=2612 bc
This then implies that from
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.
Passage in question is positioned north/south with a length 23m and depth 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. Quite similiar with 10×(1+0.523), the 41° angle at its location would equate as 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.
A distance of 157.5m by 4m produces an angle of 1.455°.
This angle is 0.025391 rad, using 25.4mm to an inch, and then the deviation is 4m 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.
1.455° is equal 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°, this 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 possible using just one 0.05425° This gives two numbers and the difference of 5.17, multiplying by 100 gives a distance of 517m.
131.4
136.57 (as half difference)
=5.17×100=517
191.2÷(100+(10×π))=1.455°
191.2÷131.4=1.455°
So 1.314 is the associated distance for 1.455°.
(1+(π÷10))×1.455=1.912
Sphinx
As an alternative to star measurements is a land based marker.
At a distance of 517m 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=99.978m
0.296 rad=16.959° side=157.658m
=57.68m
0.323 rad=18.499° side=173m
=73m (stated length, 7.55°)
Its measurements start at 10.7° giving a length of 61.309m, a total angle of 6.3° at 517m (this by itself produces a distance of 57.08m). The Sphinx can also be measured at an angle of 19° giving 75.42m as it's length but measurement has to be from the side nearer, 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
1 as 360°
1+18=378
378÷60=6.3
6.3= 10.7 - 17°
10.7°=97.688m
17°=158.063m=60.4m
17.245°=160.483m=62.8m
18.27°=170.688m=73m
=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° reaches an uncut tomb.
The 10.7° angle reaching the pile of bolders, 13°/15°/17° best describes the angles with the tombs. Inside of this 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 its radian into an angle, 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° - 18° and increasing the difference from 7.3° to 7.68°
So between 10.313° (0.18 rad) and 18° (π÷10 rad) measures 73.9m.
Between 18° and 10.7° it measures.
167.983−97.688=70.295m
But it is 73m
167.983−94.076=73.907
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 73m you get an angle of 17.909°.
94.076−167.067=72.99m
10.313°=0.18 rad
17.909°=0.31257 rad
18°=0.314159 rad
(10×0.312571016)+(1÷(6.3×10))=π
(2)
Also, 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 equates as 73m total length.
Conclusion
It is possible for the ratio at Khufu's pyramid to represent a 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 build sequence but isn't clear about 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 87.5m.
(1.455+87.5)=88.955
(1.455+87.5)÷17=0.523
(88.955÷17)÷(517×0.000117)=86.50
Or
1+(88.955÷170)=1.523
Also, they converted into feet and used the golden ratio.
87.50m=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.
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°.
(88.955÷17)÷(517×0.000117)=86.50
73 metres exactly is 239.4 ft, and converting into a year.
(239.50131÷10.7)÷π=7.12482
7.1248257449=2612 bc
This then implies that from
(1+(π÷10))=(1+(π÷10))
that the angles don't need measuring, and all that is required is distance 87.5m, 1.455° and 17° elevation.
The year 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, 17.143° the slope with the stars as 1-17.143° giving them about 0.5° clearance and the Moon as 1+17.143 aligning with one node every 18.6 years and 1+17.143+10.7°.
Theory
Archeology77 ©
that the angles don't need measuring, and all that is required is distance 87.5m, 1.455° and 17° elevation.
The year 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, 17.143° the slope with the stars as 1-17.143° giving them about 0.5° clearance and the Moon as 1+17.143 aligning with one node every 18.6 years and 1+17.143+10.7°.
Theory
Archeology77 ©
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