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The Silver Lining

This page was the result of me trying to calculate the central hinge point in this scissor-like shape.

ratio 3.5

Ratios as measurement or percentage:
64.28… / 35.71…= 1.8
97.40… / 75.76…= 1.28571428…
75.76… - 21.64… / 21.64…= 2.5
75.76… / 21.64…= 3.5
97.40… / 21.64…= 4.5

The two hinge point numbers 3.142857... and its inverse 3.141602... explained more in perfect ratios.

square and cube

Set side by side and facing straight on. Left a 2-d square and on the right a cube.

tilt 1.485

By tilting them 1.485° forward, the back of the cube lifts up matching the 2-d drawing.
360 : 1.485 = 242.4242...(8000 : 33)

13 lines

A simple construction including the blue infinity line.

reflection of the true reality

It occurred to me that perhaps our physical reality is like a projection unto a screen as
represented by the 2-d drawing. A mere reflection of the true reality which cannot be
reached physically as represented by the 3-d or cube drawing. So, no matter where we
are physically whether in space or earths’ surface, we always exist on a 2-d plane.
Perhaps this is where the flat versus round earth idea originated.

straight view

Left and right side enlarged in a straight on view.

tilted view

Left and right side tilted, exactly matching the π⁴ line, suggesting a precision surveying or
calibration devise. Although interesting there is no way to calculate the central hinge point
exactly and I changed tactic.

grid or net

Self explanatory as to how I did this and included are the pyramid lines. In this square all
of the measurements between either vertical or horizontal grid points can be reduced to
numbers without decimal point.

upper and lower grids

At some point I realized that in order to move forward it requires opposite squares. Everything
has an opposite.  This is where things get interesting, because how to know exactly where the
two grids/nets join? Unless they are joined exactly the measurements between upper and lower
grid points will not reduce to numbers without decimal points. However, match the upper and
lower grids perfectly, and the numbers can be reduced to simple numbers not requiring decimal
points. I have found a beautiful method not included here to do it. Also, if you look closely you
can see a number of circles within the joined grid squares.

joined grid squares

From here on remember the number 21.64... (from diagram one). Circled in red and right side of the
center line is the area of focus. Left of center line is its inverse and has the same information.

numbers without decimal places

Starting to zoom in to show beautiful measurements that can all be reduced to numbers without
decimal places by multiplying mostly by 9 as well as a few other key numbers such as 63.

additional measurements

Enlarging a bit more to show additional measurements.

inner lining of a tube

Enlarging more and moving to the right. These measurements are to the center line. Here the
idea of tube-like is apparent and where π represents the inner lining of a tube. Imagine looking
at a opaque tube which is cut perfectly in half, straight-on from the side. The inside is not visible
but angle it slightly and the inside lining is now visible. Naturally, all measurements in these
drawings are known except the π lines, which were added because we know what π is and
can be used to reverse engineer this design.

square and circle area

At this point I realized that I am dealing with equalizing the square and circle area as well.

red circle enlarged

The red circle enlarged.

the eye of a needle

Enlarged further and looking like the eye of a needle.

The three circles

The three circles and measurements to the left center line and right main circle edge
(several diagrams up).

More detail

More detail.

previous diagram enlarged

Black circled areas 1 and 2 from previous diagram enlarged.
And the The space between explanation.

unambiguous diagram

See the three circles diagram.

radius 12.5

5 pointed star

This equation and geometric construction to π is simple and easy to reproduce. Whether hand
drawn on paper, using Google Sketchup or some other drawing program, or laid out on a level
field as a surveying exercise, this design will reflect its exactness by the number of correct π
decimal places extracted from it.

A fun challenge for anyone to see how many π decimal places they can attain. I foresee this
diagram to be used as an educational, hands-on and learning about pi project for children.

Google SketchUp has a limit of 15-16 or so accurate measurement digits, and it parallels the
amount of pi digits. Even with a hand drawn diagram using only a pencil and straightedge one
can construct π to an accuracy of about 5 decimal places. The decimal places can be moved
depending on the size of the diagram, but obviously all of the numbers that belong to the
diagram must have their decimal places moved by the same amount. Once the " I " measurement
has been established the decimal must be moved in front of it to complete the equation.


blue line on pi

This method based on the constant π can be used as the standard to which the accuracies of
the various measuring, drawing and calibration programs can be compared. In other words,
measurements can be instantly compared to pi digits because they parallel them. At the decimal
place where pi digits go wrong the measurement is also inaccurate. For example, the distance
of a moving target is instantly gauged against π for accuracy.


net square circle


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