## Friday, March 22, 2013

### MATHEMATICS of an ANALEMMA, at Central America to Mexico OFFSHORE- as shown on GOOGLE EARTH:

An analemma is a FIGURE 8, as shown by the SUN’S PATH over the course of a year:
Analemma:

This FIGURE 8, although shown in many SCALES on Google Earth, is NOT a continuous function on the earth’s surface, since any PORTRAYAL has some missing parts; the Virgin River path at the Hurricane fault, Hf, for example, makes an almost figure 8, but due to downhill motion of the water, a segment is missing.
Analemma Virgin:

The RISE is LARGER than the SINK, in DIAMETER (Sand Mtn and Little Creek Mesa):

Before continuing, COMPARE the OUTCROP ANALEMMA (2 photos down-1 meter maximum diameter) with the million times EXTENT of the Basin and Range 1000 km diameter: ,or any other INTEGRAL COMBINATION of the NUMBERS: 2, 4, 5. 8. 10, but  NOT 3 or 7; the 2 sided geometric ARCUATE FIGURE is not linear- it is the beginning of the OPENING or “RIP” of the LINEAR CHAIN, which has 2 arcuate sides OPENING the chain into 2 separate features. As TIME PASSES, the arc becomes more and more a SET of linears- forming a POLYGON (first a RECTANGLE- the normal BEDDED SCARP; secondly a PENTAGON, with 5 sides of 72 degree spacing; thirdly an OCTAGON, with 8 sides: and then the cycle repeats, with 10 sides- the first HARMONIC. I will investigate the HEXAGON later, since I have found it occurs in OUTCROPS (RARELY), and it involves the FORBIDDEN 3 NUMBERS. GEOMETRIC FIGURES with 50 sides may be expected, since this ‘FITS’ within the 800 multiple (50 segments, with 7.2 degrees spacing). Although 36 sides (1/10th of a circle) are expected, this does not yield an INTEGRAL RATIO: 800/360= 2..22222- an IRRATIONAL NUMBER, and this RESULTS in EARTH’S CRUSTAL CONFLICT!

Although the DIAMETER RATIO is a million to one, LATERAL GRAVITATIONAL ROTATION and shear has shaped both SIMILARLY- even the CENTER HOLE!  ANALYSIS above should more accurately measure a SUCCESSION of LINEARS ('JERKS"), but this is for PICTORIAL PURPOSES ONLY:
This has been MEASURED and shown as a DECAGON:

COMPARATIVELY, I have measured the BASIN RANGE, using LINEAR SEGMENTS (in WHITE); this allows a ROUGH MEASURE of the number of LINEAR SIDES for the TOTAL POLYGON. It will be more than 10 sided- PROBABLY 16 SEGMENTS. Probably, the ROCK OUTCROP has an EQUAL NUMBER, but there is SUBJECTIVITY in making the selections. I expect that the SEGMENT NUMBERS will be similar, since we are dealing with GRAVITATIONAL FORMULATION- where all appears to be mathematically-physically arranged:

CALCULATED more PRECISELY:

The POLYGON surrounding the Basin and Range province has un-measured north side segments, so that the total count of segments cannot be determined. Should the POLYGON have 16 sides, as appears likely (from estimation of the possible 256 km lengths which will fit), the TOTAL PERIMETER DISTANCE would be 256 km x 16= 4096 km- an approximate CIRCUMFERENCE. The DIAMETER is near 4096/17.48 km per m.y.= 147.763 m.y. (equivalent to 3.6 TILT CYCLES of 41 m.y. each)
Four segments (all but 1 measuring 256 km, from APPARENT LINEARS terminating at un-mistakable ANGLE CHANGES) yield 888 km distance with a 72 degree shift. This is 1/5th of a 360 degree circle, and the total PERIMETER = 5 x 4400 km, or 10% difference from the appraised distance by “EYEBALL”.
The EARTH CIRCUMFERENCE of 40,000 km/18 degrees- the average shift over the 4 LINEAR SEGMENTS= 2222.222 km/degree. This yields a RATIO = 2222.222/888= 2.5, the JUPITER mass ratio of total mass of bodies in the Solar system, excepting SUN. Additionally, 4,096 km circumference/40,000= 10.24/10, a HARMONIC of 1024, 10.24 mm/yr. and 1.024 b.y.- numbers predicted as being SIGNIFICANT by the BINARY THEOREM! Again, the POLYGON OCCURRENCE connects EARTH ANOMALIES to the ARCUATE CONFLICT with 2 dimensional GRAVITATIONAL LATERAL INFLUENCE! I have re-measured the Basin ELLIPSE, more carefully (influenced by the FINDING that "jerking" LINEARS are usually multiples of 128 km (256, 512, 1024, or 2048 km INCIPIENT TRANSFORMS- "ripping" with possible DISPLACEMENT). Follow the WHITE LINES and measurements:

Finally we see a TRIANGLE, which lies on the EDGE of a DIVIDER- LINEAR (white), and which delineates an EVAPORITIC BASIN, the lowest elevation of thr region:

Since AGE CALCULATIONS do NOT FIT the known UPLIFT of the region (CP started rising at 41 m.y. from AGE of the Llano Quemado VULCANISM- near Taos, NM), I have re-calculated ages from several orientations. There is some 10% variation, since I have used different angles (which have TIDAL RATES found by trigonometry). Consequently, I have used the average of 50 m.y., and this is near the Paleocene start of the Colorado Plateau rise. Known is that late Cretaceous exhibited a change from shallow seas to rising- as shown by the Dakota sandstone:

Central Valley-Sierras should be viewed as a VERTICALLY-ROTATING CELL, not quite reaching the MANTLE- therwise there would be EXTNSIVE VULCANISM. This can be explored further in the BLOG on Sutter Buttes:

Notice that the ELLIPSE extends from the Wasatch line to the Sierras; I have previously found that the Sierras have an AGE less than 50 m.y., and this infers that the Serras were joined 50 m.y. ago with the Wasatch Mountains. They have steadily separated- creating the various Mountain chains in NV with accompanying VALLEYS. This is EXTENSION of the Basin and Range ELLIPSE!The ranges are mainly Paleozoic or older, and have ROTATED UPWARD, as the valleys sunk! They mainly exhibit TILTING-UP-to the WEST (a CW rotation- viewing from the south), but past the centerline may tilt up to the east:

Since the Basin and Range TRIANGLE
has emphasized that the equation for Mars: {(360- x)/x= (360- 120)/120= 2} is indicated, we must determine which PROPERTY of Mars is creating this SINK. The closest property is that of the ratio of ORBITS: Mars/Earth= 687/365.24= 1.88. This involves a 6% variation, so is on the border of ACCEPTABILITY!

There is now a modified SERIES- 64/50, 64/40 (1.6 ratio), 64/32 (2 for Mars), 64/25.6- which last ratio is NOT a whole number for Jupiter, but which does fit the series:125/50 (2.5); 125/40, for Saturn, etc. The INFLECTION in the trend occurs at Jupiter- which is the 1st planet after the FORBIDDEN zone of the Asteroids! Again, the asteroid belt represents the DIVIDER in 3D- equivalent to the CRUSTAL DIVIDER in 2D. This is a zone of DISRUPTION, where ARC REVERSAL occurs.

Now, the INFLECTION at the Asteroid belt yields a change of mathematical series: requiring WHOLE NUMBERS (INTEGERS) to exhibit the results. The ratio from the SERIES: 125/64 = 1.953125 is within 4% of the expected 2.0 ratio fo Mars! Since this is “on-the-edge” of the planetary MATHEMATICAL INFLECTION, this may be as good as we can get with my OVERALL ERRORS of 5%!

BELOW is Qsna- the North American QUADRANSPHERE (Quadrant), where the YELLOW LINES show the CCW trend of the OCEANIC LINEARS (lineaments, with traces sufficiently saved to indicate CONTINUED MOVEMENT). NOTICE that the divider passes through the Basin and Range SINK (center hole). This feature is the 1.6 RATIO separation of the GULF STREAM  N-S meridian and the HI-Emperor sea mount TRACE:

Analyzing the North Pacific- where the OBVIOUS ANALEMMA of the Aleutian SPIRAL is exhibited, there are LINEARS to determine the regularity of POLYGONS:

LINEARS trend generally WESTWARD, OPPOSITE to those near Central America- where the WEDGE (pointing westward- a "rip" opposite to the CCW shift) is oriented E.W:

A RARE westward E-W arrangement of weather clouds (presaging ON-COMING BAD WEATHER) was photograhed near my Hurricane house:

The FEATURE to observe is the PATTERN of ANALEMMA EXHIBITS; the earth continually forms these with GRAVITATIONAL INFLUENCE, and a smaller one may lie WITHIN or ADJACENT to the larger. These are continually forming on the earth's crust- even on the OCEAN BOTTOM, as SEA MOUNT JERKS, or as a succession of EARTH TIDAL ADVANCES (when there are SEAMOUNTS, there is an ABSENCE of GRID LINES)!

EXPANDED:

Look at Vancouver Island, BC- where the CRUST has made a 60 degree turn to the NW, exhibiting a 512 km LENGTH (adding the RISES at the ends):

EXPANDING, the connection to the Whidbey Island and surrounding ARCHIPELAGO can be determined:

On a clear day, the Island of Vancouver, British Columbia, Canada can be seen from Whidbey Island, and from the location of the RECENT LEDGEWOOD SLUMP-FAULT at Fircrest and Driftwood Streets. A house CONCRETE SLAB was measured for the MOVEMENT over 40 years: wooden form nails were bent- showing the direction of movement (left-lateral) and the rate of about 1 mm/year. Camano Island to the east:
These photos are at right angles to N-S, allowing maximum viewing of the N-S ORIENTED Island:
The LANDSLIDE at Ledgewood is within 10 km  of my domicile, and the REGULAR SLUMPS have been cataloged by myself in the last 10 years:
PHOTOS cover a period of about 14 years, but I missed the older slump:

The LEDGEWOOD, Whidbey Island FAULT-SLUMP has a CYCLICITY of about 16 years, and the LATEST occurred at the FULL MOON of 27 Mar- The time of MAXIMUM OPPOSITION of sun and moon- EXTENDING the earth by ATTRACTION in 2 opposing directions (making NORMAL FAULTS, as the earth expands slightly at the BULGE)

EXPERIMENTALLY, I have found that a FORWARD "S" indicates RISING, REVERSE means SINKING- except for MAJOR ANOMALIES- such as the Caspian Sea. Notice that sea mounts have a FORWARD "S "arrangement:

You'll have to look at this Oregon offshore HAYSTACK analemma from above (Google Earth), but there is no mistaking the ISLAND CHAIN RISE and CONTINENTAL SHELF "S":

CAVEATS:

The Geometry and Geology of the Earth’s CRUST are dominated by the relations between small numbers,  created by the INTERACTION of SOLAR SYSTEM MASSES: 32/25= 1.28, Mercury; 4/2= 2.0 for Mars; 13/8= 1.625 (Earth/Venus orbit ratio- MOST IMPORTANT), 8/5= 1.6, 3/2= 1.5, and 2.5/2= 1.25. All of these RATIOS result from calculations made with measurements from LINEAMENTS (linears) and ARCS on the CRUST by Google Earth.

You may want to make your own CALCULATIONS, regarding the RATIOS which are displayed for ANALEMMAS on Google Earth: the RATIO for the ORBITAL days for Earth/Venus= 365.24/224.7= 1.625+ (1.5 for rotation period, 1.6 for irregular eccentricities).
This 1.625 ratio is exhibited most- of all those found from calculations made for DIAMETERS of simple small ARCUATE Crustal masses- such as Islands in Puget Sound.
Campbell Lake Island:

Ben Ure Island:

There occur other ratios which are near 1.6, such as LINEARS shown on the ocean floor- which may be related to lineaments radiating from a FULCRUM- such as the Antilles or the New Georgia-Sandwich Islands. These follow the SERIES: 1.28, 1.6, 2.0, 2.5, 3.125, 3.906, 4.883- which is related to Planets in the series: n2= n1 x 1.25. This is 1.28: Mercury, 1.6: Venus orbital ratios, 2.0: Mars, 2.5: Jupiter mass ratio for all Solar mass, excepting the Sun, etc.

An analemma in ATMOSPHERIC TIDES always has an incomplete path, since the air will never spiral back to the original position:
Weather analemma:

The analemma in Central America is likewise incomplete, since the EARTH’S CRUST never rotates back to the initial point of instigation;
Central America analemma:

This is FURTHER EXAMINED to ILLUSTRATE the various POLYGONS-ROTATIONS:

I have explored the various possibilities of PARTIAL FIGURE 8s for the Central American chain DEVELOPMENT; the analysis shows the ROTATIONAL CENTER and the mean ratio is between 1.4 and 2.0, so that 1.6 may be the median (these are especially DEVELOPED by the COINCIDENCE of 3 FACTORS: Longitude  TIME- 1, 4, 16, 64, 256, 1,024 m.y. by the BINARY THEOREM, are especially important, and Latitude- where 360 degree FRACTIONS occur, e.g. 360/9N= 40, 360/8= 45, etc.):

Blocks of CONTINENTAL crust always have the complication of somewhat arbitrary EROSION, and the oceans portray the development better:
Central America hexagon:

There DO OCCUR fairly sharp angles on Google Earth- they form POLYGONS, but MINOR PROCESSES WEATHER the corners:

West of Mexico is exhibited the GEOLOGIST'S BANE- the PLATE THEORY'S DESTRUCTION:

Google earth photo above yields the path to understanding the 100 million year development of the ROTATION of the SEA BOTTOM CRUST- offshore Mexico. Several exhibits yield the MATHEMATICAL SOLUTION:
Lineaments (linears, my simpler term) occur in the sea bottom, which are multiples of 256: 512, 1024, 2048 km- at angles that yield information about their relation to the LOCATIONAL DEVELOPMENT (POSITION in relation to Latitude and a NATURAL PRIME MERIDIAN). The fractions of the 360 degree earth are GRAVITATIONALLY important- such as 45 degrees being 1/8th of the total. Offshore Mexico, there occur anomalies at 8, 10, 12, and 15 degrees of Latitude, and any one of these has the POTENTIAL of influencing the development of an ANOMALY! This evidently is due to the WAVE NATURE of GRAVITATION.
Radiating from a FULCRUM there are linears of 1200 km length. This would at first thought to be a simple “rounding” of the measurement. It is NOT, since 1200 represents 3 TILT CYCLES of 400 km each (1/100th of the 40,000 km circumference, or 3.6 degrees- which is 1/100th of the 360 degree COMPASS ROSE)! I first noticed that the separation of POLAR Gakkel and Lomonotov Ridges was 400 km, on the average, and this was due to the 41 m.y. SHIFT of the POLAR POSITION (the last MAJOR shift, by my scan of the whole earth).
A fulcrum occurring at 8N and 104W, as shown by INTERSECTING LINEARS is a clue that the OFFSHORE CRUST is rotating at that location. This is 1/45th of the 360 degree rose, and 66E of the PRIME MERIDIAN REFERENCE. 66 is not an even fraction of 360, and will be shown later to have IMPORTANCE on the GLOBAL SCALE.
The distance 1200 km/40,000 km circumference = 3/100, and the RECIPROCAL FRACTION/TIDAL RATE is the same approximately as the ORBITAL RATIO of Earth/Venus (days per travel around the Sun). This is shown as:
100/3/20.48 mm/yr. tidal rate= 1.6276, compared to 1.625 for the earth/Venus ratio (.2% variation). THIS IS NOT the GOLDEN MEAN phi, 1.618 (with .4% variation), or pi/2= 1.57 or anything connected with the Fibonacci series. This is a PECULIARITY of the Earth’s crust, where 2D GRAVITATIONAL STRESS is placed on a 3D CURVILINEAR CRUST- resulting in a RESTRICTION being placed on the EXTENT which a “RIP” in the crust can form. I presume that these LINEARS are INCIPIENT TRANSFORMS, where the shear occurs as the dominant action (allowing for some VERTICAL DISPLACEMENT).  A SIMPLER way of ANALYSIS is via the ratio: 1200/3.6 degrees= 333.333, and divided by 204.8= 1.6276 RATIO. The NUMBER 2048 or its MULTIPLES occurs FREQUENTLY with Google Earth MEASUREMENTS!

Looking at a larger view, including the Pacific, almost to the Equator, there occurs the VERY NOTICEABLE WEDGE (even on a weather map):

Below is a photo from 22,000 miles above EARTH; NOTICE the prominant LOW PRESSURE WEDGE! The clouds below 10,000 meters altitude are the WEATHER-PRODUCERS, and these EXHIBIT ATMOSPHERIC TIDES:
(EVEN the SMALL GYRATIONS are repeated for the LOW PRESSURE RISING CLOUDS)

IMPORTANT CORRELATIONS to be remembered, as we go forward:
1. The 512 km measurement, and its MULTIPLES x 2, 4, 6, and 8 are PHYSICALLY SIGNIFICANT, as are the TIME INTERVALS of 40.96, 102.4 k.y. and 1 million years. They result from RESTRICTIONS placed on the EARTH ORB of 40,000 km circumference by a 2D stress being placed on a CURVILINEAR 3D globe;
2. The EARTH CRUST is fairly rigid, so that there is a LAG between the stress and the STRAIN RELEASE (faulting, quakes, and SHEAR);
3. The BINARY THEOREM predicts that the following sets of numbers, ratios, and measurements are SIGNIFICANT: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, up to 4096 years; .02, .04, .08, .16, .32, .64, .128, .256, .512, 1.024, 2.048, 4.096, etc.
4. RATES 10.24, 20.48, 40.96, even 30.72 mm/yr (out of series);
5. TIDAL RATES are given by QUADRANTS (20.48 mm/yr in the exact NW QUADRANT), but there occur essentially 0 movements laterally at a FULCRUM- where the energy is absorbed by SPIRALING UPWARD!

Now that the IMPORTANCE of Polygons, Linears, and 360 degree FRACTIONS of the EARTH'S CRUST has been found, look at a case I have hiked considerably  where the FRACTIONAL LATITUDES are more widely spaced:

This is CRATER HILL- an EXTRUSION at the boundary of Zion NP, which is somewhat less than 1 m.y. AGE. Reinforcing the finding that the 2048 and MULTIPLES measurements are SIGNIFICANT, WORLD-WIDE, and on may SCALES, we see that there is 20.48 km SEPARATION from the Virgin OCTAGON, and 10.24 km from a N-S DIVIDER (FAULT) to the west:

This CONE is very near HIWAY 9 towards Zion NP, and has an interesting trail. It is STILL MOVING- creating a small ANTICLINE to the SE, which yields a 7F  TEMPERATURE INCREASE and STINK at the intersection of a SIDE CANYON st the south end of the COMPRESSIONAL FEATURE:

Crater Hill can be seen from the HORSE CANYON TRAIL- which is a great ARC and part of the Virgin ROTATION about Little Creek Mountain:

TIME and ARC are related by the CONVERSION: 40,000 km (circumference of EARTH)/360 degrees in a circle= 111.111, which is an ARBITRARY DIVISION of a CURVED SURFACE. However, 1 degree of Latitude north or south represents 60 minutes of arc (which is also artificial), and 60 minutes of Longitude in both East and West directions at the Equator. 60 minutes of longitude at latitudes distant from Equator is not a constant distance relationship, since the MERIDIANS CONVERGE!

Continuing, the conversion of NAUTICAL MILES (minutes of Latitude, in ARC measurements) = 1.85185 km, and 111.111/1.85185= 60- the Nautical Miles per degree of Latitude. This is the RATIO of CIRCUMFERENCE/666.667.  The number 666.667 has dimensions of km/6 degrees of ARC (sixtieth of a circle), and is a fifteenth of a QUADRANT of the earth. It also happens to be 666.667/41= 16.26, which is the TIDAL RATE for south-moving ARCS on the earth’s CRUST, by trigonometry. Although Milankovitch calculated 41 k.y. for the EARTH WOBBLE CYCLE (AXIAL), I use 40.96 m.y. from the BINARY THEOREM. There is a small 1/10th % difference, and the use of 40,000km for the earth circumference has a small 8-10 km variation also, because of EARTH BULGING. This is 1/4000 or 1/40th%, so that all these measurements have uncertainty of less than 1%.

Below are some COMPARISONS from the Northern Pacific- which will introduce the LARGER LATITUDES and PROXIMITY to the Aleutian Spiral (analemma) as PERIPHERAL FACTORS:

ALEUTIAN SPIRAL or ANALEMMA:
The ALEUTIAN CHAIN encloses an ANALEMMA (silted vs non-silted portions) which further ENCLOSES the Aleutian Spiral- which is a SMALLER-YOUNGER FEATURE (192 m.y./80 m.y.= 2.4, 2.5? for the PLANETARY SERIES). Should I have the usual errors, this could be 82 m.y. or 2 POLAR TILT CYCLES of 41 m.y, each:

This FINDING has input for the HI-Emperor SEAMOUNT CHAIN:
EXPANDING:

Now you may be able to "stomach" the finding that the HI-Emperor seamount chain is moving around a circle to the SE- which is the OUTER PERIMETER of the North American QUADRANT, Qsna. GPS may show the REVERSE, and that is the case for opposite sides of the ROTATION: