You Go To Church And I Run For The Ship
{Aside: What's up with the 2 Mooning Moscovites kissing on the sofa across from me on 04.11.2012 at Webb Way?--all I have to say about it is, "Only the devil whispers, the rest of us speak aloud.--I do, however, wish to thank her for the help."}
Church Nave vs Naval v Ship's Hull vs Coracle vs Walnut vs Kernel
Notes: Projective geometry, like affine and Euclidean geometry, can also be developed from the Erlangen program of Felix Klein; projective geometry is characterized by invariants under transformations of the projective group. (re projective power/projective force)
The incidence structure and the cross-ratio are fundamental invariants under projective transformations. Projective geometry can be modeled by the affine plane (or affine space) plus a line (hyperplane) "at infinity" and then treating that line (or hyperplane) as "ordinary".
An algebraic model for doing projective geometry in the style of analytic geometry is given by homogeneous coordinates. On the other hand axiomatic studies revealed the existence of non-Desarguesian planes, examples to show that the axioms of incidence can be modeled (in two dimensions only) by structures not accessible to reasoning through homogeneous coordinate systems.
In a foundational sense, projective geometry and ordered geometry are elementary since they involve a minimum of axioms and either can be used as the foundation for affine and Euclidean geometry. Projective geometry is not "ordered" and so it is a distinct foundation for geometry.
There are many projective geometries, which may be divided into discrete and continuous: a discrete geometry comprises a set of points, which may or may not be finite in number, while a continuous geometry has infinitely many points with no gaps in between.
The only projective geometry of dimension 0 is a single point. A projective geometry of dimension 1 (1 D) consists of a single line containing at least 3 points. The geometric construction of arithmetic operations cannot be carried out in either of these cases.
For dimension 2, there is a rich structure in virtue of the absence of Desargues' Theorem. The simplest 2-dimensional projective geometry is the Fano plane, which has 3 points on every line, with 7 points and lines in all arranged with the following schedule of co-linearity...
The simplest 2-dimensional
projective geometry is the Fano plane,
which has 3 points on every line, with 7 points and lines in all.
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Winchester Cathedral is a good example (images below; Winchester Cathedral's nave and its reflection (reflected across the horizontal x-axis) reminiscent of a ship's hull, compare to a Viking ship's ribs).
Winchester Cathedral (Gothic Architectural Influence) See Sacred Geometry, Reuleaux Triangle |
Upside Down Image of Winchester Cathedral's Nave Compare with Ship's Hull Planking/Ribs vs Hull Sections |
Viking Vessel Hull Ribs (See Jonah vs Fish vs Whale vs 'knitted' paths vs. W-curve-Throw-Woof-Wales-Knots, etc.) |
The Anatomy of a Church v The Ship v The Human Being
Tradionally churches are oriented facing 'east' and in a cruciform church as depicted above the entrance is directly opposite the altar, or at the 'west' end which is situated in the church 'facade' (front of the building). In this example, the entrance at the facade of the 'church' corresponds to the ship's aft which corresponds to the human's feet (where the Human makes contact with the ground, Earth). (This establishes how the orientations of each body correlate--see Special Orthogonal matrix, SO(n, F) )The relevance or orientation and the Eastward direction may have its basis in navigating and piloting effectively along the Earth's Magnetic Norms , early article with respect to bird flight and overcoming the Earth's Coriolis effect; The Journal o f Applied Physics, Vol. 18, No. 12, A Preliminary Study of a Physical Basis of Bird Navigation, by Henry Yeagley, December 1947)
قَالَ بَلَى وَلَـكِن لِّيَطْمَئِنَّ قَلْبِي قَالَ فَخُذْ أَرْبَعَةً مِّنَ الطَّيْرِ فَصُرْهُنَّ إِلَيْكَ
ثُمَّ اجْعَلْ عَلَى كُلِّ جَبَلٍ مِّنْهُنَّ جُزْءًا ثُمَّ ادْعُهُنَّ يَأْتِينَكَ سَعْيًا
وَاعْلَمْ أَنَّ اللّهَ عَزِيزٌ حَكِيمٌ 2:260
2:260 And when Abraham said, "Lord, show me how you give life to the dead." (God) Said, "Do you not Believe (accept it as True)?" (Abraham) said, "Yes, (of course), but so that I am reassured (with) inner (certainty, in my heart)." (God) Said, "Take 4 birds and train them to obey you, then place a portion of them on each mountain and call them; they will seek you (come to you) at your command (in order); and know/teach that God is Wise, Powerful."
Watercraft Rotation Note Hull Front View vs. S Curve vs. Walnut Shell |
S-Curve Distribution Function In terms of the mean (mu) and scale (beta, positive) |
Bizarro Comics April 4, 2012 (I get it, I get it... There really is no need for You to rub it in...) |
The design is intended to evenly distribute the weight of the boat and its load across the structure and to reduce the required depth of water — often to only a few inches, making it ideal for use on rivers (see Rivers of Time).
The coracle, called quffa in Arabic, is mentioned in the Bible, Exodus 2:3 as the water craft in which Moses's mother launched Him down the river to protect Him from Pharoah's decree to do away with the first born male children while the Israelites were dwelling in Egypt.
It was also frequently mentioned by my Dad whenever He wanted to remind any of us not to rush into anything in the form of a rhetorical question, "Must we jump from the quffa onto it's ears (handles)?" The short answer, 'tho none is called for to answer a rhetorical question is, "No, no, for the simple reason that you may find yourself in an awkward position that looks something like Dilbert in the comic panel here."
Dilbert April 15, 2012 What it looks like to jump from the coracle onto its handles. |
The Welsh apparently have a saying about it, too. Since it is a light-weight flat-bottom boat, it can be carried by one man (or woman) on his (or her) back, the saying goes, "the load of a man is his coracle".
While inherently unstable by design because it sits "on" the water, rather than "in" it, a coracle can easily be carried by currents and the wind, the coracle makes for an effective fishing vessel since it hardly disturbs the water or the fish, being easily manuevered with one arm, while the other arm tends to the net. (Generally 2 coracles are required for 1 net).
Walnut, 2-D Cassini Ovals & 3-D Cassini Ovals vs. 2009 Homework Assignment (compare with geometry of Wankel engine)& Bean Curve |
Coracles vary in design, as they are tailored to the river conditions where they are intended to be used. In general there is one design per river, but this is not always the case.
Quranic Reference to Vessels, Ships, Ark, Orbits, Boats/Coracles & Orbits |
Walnut Halve Shell, Vietnamese Coracle (Watercraft, Ship, Naval Application), Boat Hull, Whole Walnut (note flange)
The Teifi coracle, for example, is flat-bottomed to negotiate shallow rapids, common on the river in the summer, while the Carmarthen coracle is rounder and deeper, better suited to negotiate the tidal waters on the Tywi, where there are no rapids.
Traditional Teifi coracles are made from locally harvested wood — willow for the lats (body of the boat), hazel for the weave (Y bleth in Welsh — the bit round the top) — while Tywi coracles have been made traditionally made of sawn ash.
Teifi coracles use no nails, and rely on interweaving the lats for structural coherence (see 'cracking open an alien spaceship'), while the Carmarthen ones use copper nails and no interweaving.
Modern working coracle boats are made of fiberglass.
The general idea for integrating the conepts above: (2-D representation from 3-D or higher dimensional equivalents involve orthonormal projection, reflection, translation, etc. to conceptualize real-world equivalents which may account for why UFO witnesses percieve the craft morphing/transfigures when it impinges on Earth's airspace).
While the coracle resembles the shape of a half walnut shell, the cross-section of a walnut shell is characteristic of the compression chamber of the Wankel rotary engine.
In the basic single-rotor Wankel engine, the oval-like epitrochoid-shaped housing surrounds a rotor which is triangular with bow-shaped flanks (reminiscent of the Reuleaux triangle, a three-pointed curve of constant width, but with the bulge in the middle of each side a bit more flattened).
In the Wankel engine, the expansion phase of the cycle is much longer than that of the Otto cycle, and the four strokes of a typical Otto cycle occur in the space between a 3-sided symmetric rotor and inside the housing.
The central drive shaft, called the eccentric shaft or E-shaft, passes through the center of the rotor and is supported by a fixed bearing. The shaft turns 3 times for each rotation of the rotor around the lobe and once for each orbital revolution around the eccentric shaft. The Wankel engine cycle is shown in the diagram below. |
In the diagram above:
The "A" marks one of the three apexes of the rotor
The "B" marks the eccentric shaft and
And the “white portion” is the lobe of the eccentric shaft
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This is a substantial safety benefit of use in aircraft, since there are no valves and valve trains to burn out, jam, break, or malfunction in any way, again increasing safety.
A further advantage of the Wankel engine for use in aircraft is the fact that a Wankel engine generally has a smaller frontal area than a piston engine of equivalent power, allowing a more aerodynamic nose to be designed around it.
The simplicity of design and smaller size of the Wankel engine also allows for savings in construction costs, compared to piston engines of comparable power output.
And the Wankel engine is capable of running at very high speeds and operates almost noiselessly.
For this reason, Wankel engines are very well suited to applications in remote places where a failure could result in fatalities; and aircraft, where abrupt failure is likely to lead to a crash or forced landing.
{ok, ok, I am more than a little weirded out that someOne is asking just how long this has been going on--not only did I think You Knew but I thought You Planned it!}
7:133 That We Sent them floods, and locusts, and lice, and frogs, and blood; Separate Signs (of severence, disentanglement, judgment, to decide...), yet they (continued) in their arrogance and were an immoral (criminal) community. (133/7==19)
Green Frog vs. Walnut Halves vs.Kernel |