Squaring the circle

Squaring the circle is a problem in geometry

first proposed in Greek mathematics. It is the challenge of

constructing a square with the area of a given circle

by using only a finite number of steps

with a compass and straightedge.

The area of the Smaller semi Circle 

is .785

The Area of the smaller lune

contained by the larger Circle

Overlaps with the adjacent Contained 

Curvilinear sector aka "Pizza slice"

a visible and perfect quarter of the larger Circle

This "pizza slice" or Curvilinear sector of 

The larger Circle

has an identified area of .785

The Curvilinear Sector contains then 

the smaller lune and a perfect triangle

with the Area of the perfect triangle being .5

the arithmetic to calculate the area of the 

smaller contained lune then is

.785 - .5 = .285

The Area of Uncontained Larger Lune

Then is the Area of the Smaller Semi Circle

Less the difference between the Curvilinear sector

and the perfect triangle

And by the basic arithmetic is seen to be

Exactly equal to the Area of the perfect triangle

described and contained in the Curvilinear sector 

.785 - .285 = .5

The Area of smaller circle is

Double the Area of the Semi Circle

.785 + .785 = 1.57

a square of Area of  1.57 has

side length = Square root of 1.57

This can be thought of as exactly that

The square root of 1.57 

or as an abstract number

= 1.25299640861

As it turns out

1.57 + 1.57 = 3.14

the Area of the unit circle with

 radius equal to one

Area of the Larger Circle

.5 X 4 = 2.00

.285 X 4 = 1.14

Total area =  3.14

Square root of 3.14 = 1.7720

Smaller circle

the small circle dimensions

Radius: square root of two 

                   divided by two

Diameter: square root of two

Cord Length: One

Area of Half the smaller circle

.785

Area of the Smaller circle

1.57

Larger Circle

Radius: One

Diameter: two

Cord Length: square root of two

Quarter of the larger circle

Area of Quarter of the Larger Circle

.785

Area of Half the Larger Circle

1.57

Area of the Larger Circle

3.14

The Doubling of the cube

A theoretical 'problem' that requires no more

than an comprehension of what a cube is

What the unit cube is 

and what a cube root is

When one understands all of music as 

nothing more than the expansion of the

twelfth root of two

The cube root of two becomes 

an idea requiring little

thought and can not

be in any way shape or form

described as a problem.

The volume of a Cube is 

the length of a side cubed

The volume of a cube with double the 

volume of a known cube

is equal to the side length

of the known cube 

Multiplied by 

the cube root of two

In the same way one can understand the tides

as a function of atmospheric pressure

generating electric activity

where Atmospheric pressure is a function of

 High electric activity Expansion of water

vs 

magnetic Low contraction

Activity/strength

When the sun is shining on water

The electric activity is high

The atmospheric pressure is high

The water expands

Yes, high atmospheric pressure correlates with the Moon fullness

Yes, high tides generally correlate with midnight and noon during a full moon

When the moon is full

the light of the sun reflects on the

surface of the earth

Atmospheric pressure increases

When the moon is 'new' and in the line

between the sun and the earth

electric activity in the atmosphere is low

Atmospheric pressure is low

Water contracts

When the sun stops shining on the

atmosphere

Electric activity is lower

Atmpospheric pressure

becomes lower 

Water contracts 

Tides fall

Yes, during new or near-new moons, The atmospheric pressure is low

Yes, during new or near-new moons  low tides correlate with roughly midnight and noon.