© Copyright Lorena Loo
Out of Africa Via Mercury
©Lorena Loo
©Lorena Loo
This is a tale of three planets, the first three planets out from the Sun: Mercury, Venus and our beloved Earth. These three have a rather unusual connection, at least Mercury and Venus do with respect to Earth. Leonardo's Vitruvian Man fits into the picture as well. But let's begin with Earth and how Mercury leads us to Africa.
In the previous article (The Circle and the Pentagon) I phi cut Leonardo's Vitruvian Man. Now I get bolder and phi cut a planet, planet Earth. The blue circle to the left represents a cross-section of Earth cut through its center and in the plane of its polar axis. In reality, the Earth is not a perfect sphere so there is a bit of idealization here...but not by very much. The thick blue line represents the polar radius of the Earth. Yes the polar axis of the Earth is, like the Leaning Tower of Pisa, tilted. I depicted it as vertical because it is easier to see what is going on.
If you have read the previous article, you know how to phi cut a line. That is exactly what I have done in the next diagram here: phi cut the polar radius of the Earth. I cut it from the center out to the circumference so the ratio of the lengths from the center to the circumference is 1 to phi.
See that orange circle in this next diagram? It has the same center as the Earth (blue) circle and it just touches (tangent to) the larger greeen circle used in the phi cut. To an accuracy of 99,52%, that orange circle represents the planet Mercury. Actually, it represents a cross-section cut through its center and either along the polar axis or equatorial. I say either because the polar radius and the equatorial radius of this planet are the same, unlike Earth. If you stick Mercury inside the Earth so that their centers coincide, then the "north" pole of Mercury phi cuts the upper polar radius of Earth and the "south" pole of Mercury phi cuts the lower polar radius of Earth. This is quite remarkable if you think about. But there is even more.
In the diagram to the left below, I focussed the attention on the "Mercury" circle (orange) and the second circle (green) used in the phi cut. Joining the two points where the green circle intersects the "Earth" circle (blue), forms the thick green line in the diagram. I can take the endpoints of that line as centers of two circles whose radii are exactly the length of that line. If you are familiar with a Vesica Piscis and how it is formed, then you understand that what I just described is simply two circles of equal size overlapping to create a Vesica. Each circle will have its center lying on the circumference of the other. I can repeat this process around the circumference of the Earth circle to form exactly 5 Vesicas. The 5 circles forming these Vesicas are the thin orange ones in the diagram to the right below.
Notice how these overlapping orange circles form a 5-petalled flower just within the Earth circle? Notice also how a smaller 5-petalled flower just within the Mercury circle is formed. It actually more resembles a pentagram with curved lines rather than straight. In both cases, the circle which just encloses the 5-petalled flower is said to circumscribe it or is its circumcircle.
Joining the centers of those 5 outlying orange circles forms a regular pentagon circumscribed by the Earth circle. Joining the vertices (points) of the pentagon forms the pentagram within the Earth circle. (See diagram to the left below) The pentagram forms another smaller pentagon within it. That smaller pentagon just fits within the Mercury circle. What is the ratio between the sizes of the pentagon inscribed in the Earth circle and of the one inscribed in the Mercury circle? , the golden ratio times itself! The Earth's radius/diameter is also Mercury's radius/diameter.
Joining the centers of those 5 outlying orange circles forms a regular pentagon circumscribed by the Earth circle. Joining the vertices (points) of the pentagon forms the pentagram within the Earth circle. (See diagram to the left below) The pentagram forms another smaller pentagon within it. That smaller pentagon just fits within the Mercury circle. What is the ratio between the sizes of the pentagon inscribed in the Earth circle and of the one inscribed in the Mercury circle? , the golden ratio times itself! The Earth's radius/diameter is also Mercury's radius/diameter.
If you form a square that just encloses the Mercury circle and extend the lines of the square outward until they intersect the circle, by connecting those four points of intersection in a certain way, you can form an octagram. That is exactly what I have done in the diagram to the right above. The octagram just encloses Mercury. Well yes it is two dimensional so it just encloses the cross-section of Mercury.
The ratio of the perimeter of the square that just encloses the Mercury circle
to the circumference of the Mercury circle is which equals 1.27 to two
decimals. This also happens to be the square root of phi to two decimal accuracy. This means that if you walk the perimeter of the square, you would walk a distance 1.27 times more than if you walked the circumference of the
circle. The area of the square is also that of the circle. In three dimensions,
the square becomes a cube which just encloses a sphere. Here the relative
sizes of their surface area (cube to sphere) is . The same applies to
the relative sizes of their volumes. If you filled the cube with a liquid, the cube would hold 1.9 times more than the sphere. Once again we encounter the number of 1.9, a number from Egyptian biometrics. Now this is true for any square and the circle it just encloses and three dimensionally a cube and the sphere it just encloses. It does not apply only to Mercury. The number 1.9 also
is one of the phi cut lengths of 5. i.e.
The ratio of the perimeter of the square that just encloses the Mercury circle
to the circumference of the Mercury circle is which equals 1.27 to two
decimals. This also happens to be the square root of phi to two decimal accuracy. This means that if you walk the perimeter of the square, you would walk a distance 1.27 times more than if you walked the circumference of the
circle. The area of the square is also that of the circle. In three dimensions,
the square becomes a cube which just encloses a sphere. Here the relative
sizes of their surface area (cube to sphere) is . The same applies to
the relative sizes of their volumes. If you filled the cube with a liquid, the cube would hold 1.9 times more than the sphere. Once again we encounter the number of 1.9, a number from Egyptian biometrics. Now this is true for any square and the circle it just encloses and three dimensionally a cube and the sphere it just encloses. It does not apply only to Mercury. The number 1.9 also
is one of the phi cut lengths of 5. i.e.
With Mercury centered inside the Earth, its poles correspond to 22.49º N and S latitude on Earth. That is just a little over 1º within the Tropics of Cancer and Capricorn respectively. The tropics are the latitudes of the solstices. Due to a tilt in the Earth's polar axis, the Sun changes its north-south position over the course of the year as the Earth revolves around the
Sun. Its furthest point north is the Tropic of Cancer, time of the summer solstice in the northern hemisphere but the winter solstice in the southern hemisphere. The Tropic of Capricorn is the latitude of the Sun's furthest point south, occuring on the winter solstice for the northern hemisphere but summer solstice for the southern hemisphere. It is remarkable that Mercury's poles correspond to within about 1º of the solstice latitudes on Earth.
Incidentally, the Tropics of Cancer and Capricorn obtained their names from the constellations in the sky their positions corresponded to some 2,000 years ago when they were named. As a result of precession, the Sun's position has shifted so that it is in the constellation of Gemini on the summer solstice and Sagittarius on the winter solstice. But we still call the solstice latitudes Cancer and Capricorn. Some things just don't change apparently.
If you look at a world map, you will find the continent of Africa is virtually symmetrical with respect to the Earth's equator. Its furthest point south (34°51'15" S latitude) is almost as far below the equator as its furthest point north (37°21' N latitude) is above the equator. That is a difference of about 172 miles from being perfectly symmetrical about the equator. In the diagram below, the red line indicates the equator while the gold ones locate where the poles of Mercury correspond on the world map. Africa's near symmetrical position about the equator means that Mercury's poles are positioned almost symmetrically within Africa.
Incidentally, the Tropics of Cancer and Capricorn obtained their names from the constellations in the sky their positions corresponded to some 2,000 years ago when they were named. As a result of precession, the Sun's position has shifted so that it is in the constellation of Gemini on the summer solstice and Sagittarius on the winter solstice. But we still call the solstice latitudes Cancer and Capricorn. Some things just don't change apparently.
If you look at a world map, you will find the continent of Africa is virtually symmetrical with respect to the Earth's equator. Its furthest point south (34°51'15" S latitude) is almost as far below the equator as its furthest point north (37°21' N latitude) is above the equator. That is a difference of about 172 miles from being perfectly symmetrical about the equator. In the diagram below, the red line indicates the equator while the gold ones locate where the poles of Mercury correspond on the world map. Africa's near symmetrical position about the equator means that Mercury's poles are positioned almost symmetrically within Africa.
If we take Mercury and stick it inside the Earth so that one of its poles is located at the North Pole of the Earth, then the other pole of Mercury phi cuts the polar axis of the Earth (see diagram below). That phi cut point is, like in Leonardo's Vitruvian Man, the "navel" of the Earth. Corresponding to a latitude of 37.89° N, it is almost exactly located at the northernmost point of Africa. Sticking Mercury so that one of its poles is at the South Pole of the Earth produces a reverse phi cut. That point corresponds to 37.89° S latitude which is almost the southernmost tip of Africa. It is a little further south but still absolutely remarkable how Mercury so correlates with the continent of Africa and as a phi cut of both the polar radii and diameter of our planet.
Earth and Venus too have a sacred geometric relationship in terms of phi. These two planets are almost twins in size. Venus is slightly smaller than Earth and like Mercury, both its polar and equatorial radius/diameter are the same. In The Circle and the Pentagon, I showed three sucessive phi cuts on Vitruvian Man brought us to the brow. If we place Venus inside Earth with their centers coinciding, the "north pole" of Venus corresponds to three sucessive phi cuts of the Earth's upper polar radius and its "south pole" corresponds to three successive phi cuts of Earth's lower polar radius. The degree of error is only 0.82%. which means this is accurate to 99.12%. In the diagram to the left below, I show the combined Earth-Venus-Mercury alignment with their centers coinciding. Venus is in green, Mercury in orange and Earth in blue. I used thin circles because Venus and Earth are so close in size that thick circles would have overlapped one another. In this alignment, the poles of Venus cut the diameter of the Earth at points corresponding to 71.59° north and south latitude which are inside of the Arctic and Antarctic Circles. Any place located within the region between the North Pole and the Arctic Circle and the South Pole and the Antarctic Circle is in the land of the midnight sun. In these regions the sun is visible continuously for 24 hours at least once per year. During the winter, the opposite is experienced, the so-called polar night where there is very little or no sunlight at all as the Sun is below the horizon.
To the right above, I illustrated Mercury aligned inside Earth's North Pole and Venus aligned inside Earth's South Pole. In this alignment, the opposite pole of Venus determines the "brow" of the Earth. That corresponds to a latitude of 64.29° N which is just below the Arctic Circle at 66°33' N. If I had placed Venus with its pole just inside the Earth's North Pole instead of South, then the opposite pole of Venus would correspond to 64.29° S, just above the Antarctic Circle at 66°33' S.
Earlier I showed how Mercury's size within the Earth determines both a regular pentagon and octagram that just fits within the Earth. With Venus and Earth there also exists such a pentagonal and octagonal relationship. But this time instead of the result of their relative sizes to one another, they come about as a consequence of their relative orbital periods around the Sun! For each time Earth has completed one revolution about the Sun, Venus has completed 13/8 revolutions. If you mark the position of Venus in its orbit at yearly intervals, then connect these positions in order, over an 8 year period Venus describes an octagram. Eight years also equals 5 synodic periods of Venus. A synodic period of Venus means the time it takes for the planet to return to the same position relative to the Sun as viewed from Earth. If you view where Venus is relative to the Earth today, then one synodic period later it will have returned to the same relative position. Instead of marking the position of Venus at yearly intervals over an 8 year cycle we mark it at the end of each synod, then Venus describes a pentagram in the same period it describes an octagram. This is quite amazing.
Why these relationships exist between our planet and Venus and Mercury I do not know. But all these relationships tie in with the golden ratio or phi. Even the 13/8 revolutions of Venus per one revolution of Earth around the Sun for 13/8 is merely the ratio of consecutive Fibonnaci numbers which approximates phi. Perhaps we should call the first three planets in our solar system the "Golden Girls."
Earlier I showed how Mercury's size within the Earth determines both a regular pentagon and octagram that just fits within the Earth. With Venus and Earth there also exists such a pentagonal and octagonal relationship. But this time instead of the result of their relative sizes to one another, they come about as a consequence of their relative orbital periods around the Sun! For each time Earth has completed one revolution about the Sun, Venus has completed 13/8 revolutions. If you mark the position of Venus in its orbit at yearly intervals, then connect these positions in order, over an 8 year period Venus describes an octagram. Eight years also equals 5 synodic periods of Venus. A synodic period of Venus means the time it takes for the planet to return to the same position relative to the Sun as viewed from Earth. If you view where Venus is relative to the Earth today, then one synodic period later it will have returned to the same relative position. Instead of marking the position of Venus at yearly intervals over an 8 year cycle we mark it at the end of each synod, then Venus describes a pentagram in the same period it describes an octagram. This is quite amazing.
Why these relationships exist between our planet and Venus and Mercury I do not know. But all these relationships tie in with the golden ratio or phi. Even the 13/8 revolutions of Venus per one revolution of Earth around the Sun for 13/8 is merely the ratio of consecutive Fibonnaci numbers which approximates phi. Perhaps we should call the first three planets in our solar system the "Golden Girls."
The cube that just encloses the Earth "sphere." The width and height of Vitruvian Man defines the dimensions of the faces of the cube as well as the diameter of the Earth "sphere."
