The illustration below, fashioned by means of a triangle of base length 756 units, with a height of 480 units, reflects the, in my opinion, GP measurements.
Although we observe heptagons within the three circles formed via the steps illustrated below, there remains a requirement to adjust, not “fiddle” merely to adjust the measurements to ensure the heptagons, in reality, are within, and not simply figments of my imagination
Moreover where the three top circles merge we observe a "chamber", there is much more within the drawing, as will be explained as we progress
Therefore I contemplated, were we intended to observe a “triangle” of base length 756 units with a height of 480 units?
Accordingly, many a year ago, I delved into the feasible innovative designs that may perhaps be within this 756 by 480 triangle, as a result I drew numerous sketches by the use of my old Technical College paraphernalia, moreover became confident I located the mysterious Heptagon, and much more
Nonetheless, seeing as the advanced computer software taken for granted today, not being accessible at that time, I neglected the sketches, to while away their time, unproven
Subsequently, within GHMB {
We subsequently corresponded furthermore formed a fine affinity exchanging concepts, subsequently I recalled my, cobweb strewn GP triangle sketches, as a result I mentioned these to Rob
The following sketches being the product of my initially hand drawn sketches allied with the first-rate artistic flair with reference to Rob, except for the industrious labour of Rob, the computer software sketches may perhaps never have been created.
Accordingly I owe him a great deal of appreciation, furthermore the subsequent being a joint venture, via which we both benefited
The GP Triangle
Disregard appellations such as feet, inches, cubits or whatever, we employ “units”
{1} we construct a triangle, base length 756 units, and a height of 480 units, label the base line: A-B, the apex being: C
{2} from the base centre {at 378 units} draw a vertical line to the apex {C}
{3} from the base centre {378} draw a semi-circle, that observably originates at A ending at B
{4} at the point where the semi-circle cuts across the triangle sides {between A-C} label that point: D
&
{5} at the point where the semi-circle cuts across the triangle sides {between B-C} label that point: E
Disregard circles, lines, distances etc, just remember points C…D…C…E not what they are supposed to represent or provide, they are simply points: C to D and C to E
{6} on both sides of the triangle, regard the distance from C to D and C to E as the radius of a circle {although we observe no circle}
Moreover as we observe, the apex being point: C
{7} therefore we require placing the compass on point C, then elongate it to point: D afterward we draw a circle.
{8} Locate the centre points of lines: E-B and D-A, then draw a line from theses points to connect to the base centre
Then locate the centre point of lines: A-D we label this F, and when we locate the centre point of lines B-E, we label this G
It will be seen that these points {F and G} will be the apexes of two miniature pyramids, in other words the distance from the new point F to the base point A is one side of a triangle, the same will apply to the new point G to the base point B
Then draw a perpendicular line from Point G to the main GP triangle base also extend the same perpendicular line so it reaches as a minimum as high as the main GP triangle top, similar with Point F
Then, for example, the now extended perpendicular line formed by points G and F, ought to be the rims of the circles that will eventually contain the heptagons, since points D-E will be the circle centres
So when we draw a horizontal line joining points: D-E and extending this line so that it extends passed the GP triangle base {A-B} this new extended line: D-E, will hit the newly drawn perpendicular lines created from points F and G
The assist of