Earth is Vertically-ATTRACTED MONTHLY by the MOON- SUN COMBINATION. During FULL MOON, this produces BULGES on OPPOSITE sides of the crust; but during the NEW MOON, the sun and moon combine to produce the largest bulge- towards the sun. This can be treated with TRIGONOMETRY, since the water and land TIDES are simple SINE WAVES. Since the earth’s crust is somewhat BRITTLE-RIGID, there is a LAG between the force and the occurrence of the bulge. There is no need to invoke CENTRIFUGAL FORCE, since it has been observed that when there are no moons (Venus), there is no equatorial bulge, and when there are many moons (Jupiter) the BULGE IS MAXIMUM. The simplest sine wave is:
Bulge HEIGHT = constant C x (sine t), where t = angular rate of change x T, with T in time units. This relation applies whenever the couple either combines (for the maximum) or oppose each other (for a reduced tidal effect). In between, there is a lateral effect, where the Moon attracts the crust from an oblique angle- producing LATERAL LAND TIDES. This influence is more difficult to treat mathematically, but the results can be viewed on GOOGLE EARTH, and made to “FIT” a mathematical equation. Linear "JERKS" are effected, and they may approximate CURVILINEARS in some cases; we start with those which are more RARELY NOTICED:
The first DIFFICULTY relates to the ADJUSTMENTS the crust makes to “SHAPE UP” according to the NET FORCES APPLIED. This results in a POLYGON, with LINEAR SIDES, and which is formed by “JERKS”. The number of SEGMENTS or linear sides is a variable, depending on the size of the polygon and its TILT. It fits the EQUATION:
An INTEGER= (360 degrees - X)/X, e.g. where X = 24 degrees, for integer 14. There occur POLYGONS with at least 36 sides, which I have found on Google Earth: (360- 10)/10= 35, which is probably the largest possible. The integer for this case is 35, which occurs for each 10 degrees of MERIDIANAL LONGITUDE. These MERIDIANS are related to a NATURAL PRIME MERIDIAN- which is NOT the Greenwich Meridian 0. The width of the band is the same, but the REFERENCE is DIFFERENT!
The COMMON POLYGONS found in outcrops are:
4 (vertically-fractured strata), 5 (pentagons), 6 (hexagons), 8 (octagons)- as shown below:
LINEAR SEGMENTS are numbered for ease of counting- there usually occur 12-13 for the MOON CYCLE, but 6 are normally dipping DOWNWARD as opposed to 6 RISING, above.
The complete rotation of a POLYGON or CURVILINEAR cannot be found because of an intervening sink or rise (an example is the Honeymoon Spiral at the border of UT and AZ- along the Hurricane Fault, Hf):
Almost circular features (polygons) are exhibited along coastlines, and for volcanoes they are 24 sided, with an angular separation of 15 degrees. These are so common, that they produce small bays or protrusions for Cape Hatteras and Crater Lake, OR:
1. Two LINEARS separated by a measured angle allow determination of the number of sides in the polygon: e.g. two 300 km linears separated by 15 degrees rotation indicates a 24 sided figure with an ALMOST-CIRCUMFERENCE of 4500 km. The TIME to develop this large feature is approximately 4500/15 km/m.y.= 300 m.y. The Colorado Plateau, CP, is 800 km wide, and it has formed E-W, with a divisor of 20, yielding approximately 40 m.y. in development (you can check this with the initial VOLCANIC EXTRUSIONS at Llano Quemado, NM- near Taos: 41 m.y. AGE):
3. Great changes in Temperature T and Stress P are noticed for inflections or LINEAR DEVIATIONS. Mineral deposits, vulcanism, earthquakes, and violence can be ANTICIPATED!
You should now ask "Why have you invested all PREVIOUS EFFORT in CURVILINEARS, and now "launch off" toward jerking linears- which are NOT ARCS?"
I am still trying to determine which is DOMINANT, and suspect that GRAVITATION FROM PLANETARY INFLUENCE operates in yearly or multi-year cycles (such as Jupiter); These are smooth from the smallest view, but we can never find that view (or at least it takes considerably more effort). The SIMPLEST approach is to find the CURVILINEARS, and then expand these to view the details- which PROBABLY ALWAYS will be seen as "JERKS"! However, look at this SIMPLE SMALL DEVELOPMENT (on a few THOUSAND years SCALE- 8000, more precisely), and you will see a perfectly smooth CURVED BEACH- formed regardless of the trash impeding its progress: