Let's Go Slow and Please See That:.
For what i try to present as lighter weight path to be wrong, 'normal' people's path would have to be wrong too; as arrives at same destination/answer.
For all the coordinate math is in fact equal; in that all correctly done leads to same answer.
As long as angle/relationship between force input and receiver are the same;
may turn same scenario to any compass reference and have same quantities; except direction.
Thus again i try to show cos:sin as ratio of alignment:deflecion percentages of reigning domain and it's non effects all as 1.
Agent Smith: How what i have been showing with this, be possibly so totally wrong?In fewer chess moves gets same answer;
but to point of thread title, sets up element-by-element consideration of internal dimensional relationships no matter the over all reigning dimensionality. Like i try to show on the arc90 from main overall dimensionality in it's own domain piping over to cross-axis and next arc90 piping/converting back to overall primary dimensionality of Bowline parts/elements.
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In Bowline(s), as Hitch or as Bend; or any Hitch or Bend USAGE(not naming convention):
A>for single Bowline over post against pull
>>the force line organically exists and i call cos starts at SPart as input of linear force
>>and continues linearly to opposing side (from force input) of host/post
>>here used as node swell type: termination , and any Hitch usage will be same:
>>from SPart as linear input to opposing side of anchor/host of output/termination of rope force as organic linear force line
B>double Bowline eye2eye against each other's pull
>>force line is now clearer as simply from 1 SPart as input of linear force
>>and continues thru arrangement to opposing side's SPart
>>here used as node swell type: continuation , and any Bend usage will be same:
>>from SPart as linear input to opposing side SPart is the domain of the reigning force; from input to output.
All to the commonality of measuring everything else from the finite domain of the peak, unfiltered input
>>as if outer genetic constraint possible
>>then how that is segregated to powerful usages, but never can exceed the original finite domain of force input.
>>and can do accounting as to balance sheet as trace force thru.
SPart, as linear input, is 1st measure as dormant laced structure is awakened by force just like plug in radio, and as radio trace force thru it; following the force(s) and utility processes enabled thru the 'circuitry'.
So, i see the domain of the peak reigning input force as force line, to then judge rest from, as already organically existing and throw with it as it is; w/o re-dictating same information into a static human framework to only then realize it. On an element, by element (arc0,90,180) breakdown can show arc90 conversion from major to cross-axis dimension, and would expect back again to maintain the major ruling dimension.
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This model relates to all displacements against distance (or force as distance unachieved)by how they are aligned to a given reigning domain of reach and/or force. Aligned or the opposite of Aligned(the non); and any gradients inbetween of some of each parent extreme as a hybrid mix of each. cos:sin ratio decoding how much of each parent extreme xTotalAttributePotential(length, speed, force etc.)that scenario can reach.
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A line is a single focused 1D entity of finite length with a center.
>>can show line of same properties of length etc. from same center dot position.
>>all possible 1D choices of that line, from that center, to a 2D staging, simply makes circle
>>of all distance and force diffused evenly to separate axises, not focused to 1 axis
>>similarly can take all possible 2D choices from that center to a 3D staging model and call orb etc.
Sunrays of linear light can be expressed too outwards in all directions from orb, just as model inner linears in all directions.
Line : focused mono axis from a given center and reach
circle: diffused multi axis from a given center and reach
cos:sin ratio can define properties of which single axis is used in reference to benchmark axis
>>Circle giving the buffet of axial choices
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Works recursively even then to find 3rd D:
>>as take pure cos as benchmark alignment, sin as drift can define how much 1D remains and how much into 2D space from that linear reference benchmark
>>THEN can take that calc'd 2D as cos benchmark reference and sin again as drift, now into 3rd D.
Stuff simply works, in all things.
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cos:sine ratio can decode percentages of a potential expression and where, also to what mix ratios of how much of each. This is how other sciences use same for peeking/probing into works.
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An arc180 geometry works same way in Bowline as it does Half Hitch. The whole theme of thread stated is only 3 repeating elements, Bowline or not, in organic(cornerless) ropework(meaning loaded). So, again any arc180 etc. comment, or reflection given, is meant also to lend light to Bowline etc.; not skip it.
Also, please see i have no idea where you got these hostility issues you state from me; anymore than know where i stated or ever claimed to be able to produce the tension numbers tracing thru Bowline as they reduce thru frictions homework assignment, like trying to break the bank. Closest i believe i came to the latter is indicating aware of pattern of reduction of tension from linear input. Also, can show if input output of tension of single element is known, can then show pattern of direction of dispersions of distances and forces thru that element to be 'expressed'.