11-10-2019, 10:35 PM

...

Grand Unification of Ancient and Modern Geometry and Mathematics

Khufu Pyramid sacred seked 5.5 -- as an angle tangent.

Review my last post and image for complimentary data involved <---

In the last post image:

You see different angle combinations that equal the Khafre pyramid slope in degrees.

arctan{1 / 2} -- plus -- arctan{1 / 2} = Khafre Pyramid side face in degrees.

26.56505118 26.56505118 = 53.13010235 degrees

arctan{1 / 3} -- plus -- arctan{180 / 260} = Khafre Pyramid

18.43494882 34.69515353 = 53.13010235 degrees

The angle tangent {180 / 260} encodes pure ancient calendar count system dynamics.

It aligns the 360 count into the numerator,

and the 260 Tzolkin count into the denominator.

Angle tangent {180 / 260} = 360 / by {2 x 260 Tzolkin}.

The reduced form of the fraction 180 / 260 = 9 / 13.

The 9 and the 13 are as Mayan and MesoAmerican in count as can be hoped for.

9 x 13 = 117 -- an important number in the Dresden Codex.

Their own cultural geometry no doubt took into account this angle tangent,

as an important angle in the 3-4-5 triangle generated Khafre Pyramid geometry.

The ancient and modern code unifies within the sine and cosine as well {next post}.

This angle tangent {180 / 260},

can be subdivided as well.

arctan{1 / 2} -- plus -- arctan{1 / 7} = arctan{180 / 260}

26.56505118 8.130102354 = 34.69515353

Thus the interconnected angle tangent combination follows as such:

arctan{1 / 2} -- plus -- arctan{1 / 3} -- plus -- arctan{1 / 7} = Khafre pyramid

26.56505118 18.43494882 8.130102354 = 53.13010235

To then proceed along the same routes of approach,

the simple fundamental pathway to arctangent 5.5 <---

goes like this:

arctan{1 / 2} -- plus -- arctan{1 / 2} = Khafre pyramid -- plus --> arctan{1 / 2} = arctangent 5.5

26.56505118 26.56505118 = 53.13010235 26.56505118 79.69515353

artan{1 / 3} -- plus -- arctan{1 / 2} = arctan 1 -- plus --> arctan{180 / 260} = arctangent 5.5

18.43494882 26.56505118 = 45 34.69515353 79.69515353

--------------------------------------------------------------------------------------------------

My last image introduced the most basic fundamentals,

in simplistic angle tangent connectivities,

attached to Khafre Pyramid geometry.

The next step,

is to integrate ---> golden rectangle phi geometry into the Kahfre pyramid geometry constructs,

while also exposing how the Khufu Pyramid sacred seked 5.5,

functions as an angle tangent within those geometry infrastructures.

This is a bridge post between my last post,

and the summation of it all in my last post on this subject.

What was "magic simplicity" in previous posts,

suddenly can become quite complex,

when phi dynamics are introduced.

I felt that this geometry display was needed to help the viewer,

understand how specific angles with tangents like:

{1 / 3}, and {1 / 7}, or {11 / 2} = 5.5 {Khufu Pyramid seked},

integrate with phi geometry angle tangents,

to account for the Khafre Pyramid geometry.

Khafre Pyramid side face slope tangent = 4 / 3 <---

Khafre Pyramid inverse slope tangent = 3 / 4 <---

Remember,

that angle tangent 5.5 = {11 / 2} = {99 / 18},

the Khufu pyramid seked,

has the inverse angle tangent:

{18 / 99} = 2 / 11.

If you are doing the math seen in the images,

it is ALL exact

but you have to perform the math processing correctly.

Scientific hand calculators,

round off at the tenth decimal placement,

so you have to use proper process to get exact results.

In other words,

if you use the golden rectangle -- angle tangent = Phi,

you cannot just calculator click the numbers:

1.618033989 = Phi.

You have to do it like this,

for your calculator to properly calculate the decimal placements:

click:

Square root 5 <---

add ONE. ------ your result will be: 3.236067977,

Now,

divide by Two,

equals,

true Phi placed into your calculator properly for exact results <---

You cannot just type in:

1.618033989

into your calculator,

you have to perform the process then continue the equations.

So using that exact process,

to obtain inverse phi <---

you simply click:

1 / x

function on your scientific calculator.

If your calculator does not have the option {1 / x},

you cannot perform geometry tangent work,

that has square roots and so forth.

----------------------------------------------------

IMAGE

Top section of the image.

Where you see the angle letter designation:

c a b = arctangent Phi,

that means:

angle c + angle a + angle c = the angle with tangent Phi.

This design is created to show how the angle with tangent 5.5,

integrates with these angles tangents:

Phi and {1 / phi},

Khafre Pyramid slope tangent {4 / 3},

and especially,

simple building block angles,

with tangents:

{1 / 3} and {1 / 7}.

Angle c,

in the image,

is subdivided into angles d and e.

Note that the building block angles,

d and e,

are functions of square root 5 and phi geometry tangents.

Look at the angle a b b a = arctangent 5.5

The premier angle featured in this study,

with the tangent 5.5 -- Khufu pyramid seked 5.5,

is constructed in a primary combination of these two angles:

arctangent {1 / 7}

and

arctangent {1 / phi}.

Now look to the central section of the image.

The exact same geometry is offered,

with an addition of the -- inverse phi tangent-- angle a,

on each side of the original design in the top section of the image.

This creates a perfect half circle of 180 degrees.

Now,

look to the -- Khafre pyramid -- inverse slope angle:

angle a e <---

Here the combination of two phi related geometry angles,

come together to form the Khafre inverse slope.

angle a + angle e = K* = inverse slope Khafre Pyramid = arctangent {3 / 4}.

K* = 36.8698765 degrees.

But here is where the "magic simplicity" comes back into play:

K* = arctangent{3 / 4} = angle a + angle e <---

K* = arctangent{3 / 4} = angle c + angle c <----

angle c = arctangent {1 / 3} = 18.43494882 degrees

thus:

arctangent{1 / 3} + arctangent{1 / 3} = K* = arctangent {3 / 4}.

Last but not least,

by adding the inverse phi tangent angles to the original design,

angle a c a = arctangent 7

emerges in the angle infrastructures.

Note angle: b + b -- featured as arctangent {2625 / 9000} = 2625 / by {25 x 360}.

You see the extrapolation at the top of the image,

using the number: 2625 <---

fibonacci ancient phi progression starts like this;

5 / 8 = 365 / 584

5 / 8 = 0.625

0.625 ---> + 1 = 1.625 ---> + 1 = 2.625

-------------------------------------------------------

The bottom section of the image goes through related data,

to aid the viewer in understanding,

both the simplicity and complexity of these building block angles.

In particular,

angle b + b = arctangent {21 / 72},

is featured.

I have supplied the extrapolations of the angle tangent fraction,

to point to the ancient code within.

Most dynamically,

the square root two cubit 20.62394778,

functions within this tangent infrastructure.

But look to last equation presented there.

in that sequence of angle tangent equations.

This is the ancient code within.

angle b + angle b <----

equals:

arctan{1 / 7} + arctan{1 / 7} = arctan {21 / 72} --- {21 / 72} = {105 / 360}.

To access the dynamic ancient angle tangent code,

you set the -- denominator -- to pure 360 count.

angle bb = arctan{105 / 360} = arctan{21 / 72}.

105 = 16 x 6.5625

Thus the tangent of angle bb,

equals:

16 x 6.5625 -- divided by -- 360.

The ancient code key is in the number 6.5625:

aPi = 22 / 7

6.5625 x aPi = cubit 20.625

6.5625 x 3.1416 = cubit 20.61675

6.5625 x 3.14 18 18 18~ = cubit 20.618 18 18~

6.5625 x pi = pi cubit 20.61670179,

thus to access,

the mirror or complimentary pi cubit,

you use the formula:

{18 / 360} -- divided by -- Pi value = cubit.

{18 x 360} -- divided by -- Pi = pi cubit 20.62648062

Multiply the two pi cubits together:

20.61670179~ x 20.626489062~ = 425.25

and

the corresponding ancient cubits:

20.618 18 18 18~ x 20.625 = 425.25 = 162 x 2.625 <---

Much more to follow,

with magnificent ancient angle tangent code to be revealed.

Check out the sine and cosine of arctangent 5.5,

or 79.69515353 degrees,

in the meantime.

...

Grand Unification of Ancient and Modern Geometry and Mathematics

Khufu Pyramid sacred seked 5.5 -- as an angle tangent.

Review my last post and image for complimentary data involved <---

In the last post image:

You see different angle combinations that equal the Khafre pyramid slope in degrees.

arctan{1 / 2} -- plus -- arctan{1 / 2} = Khafre Pyramid side face in degrees.

26.56505118 26.56505118 = 53.13010235 degrees

arctan{1 / 3} -- plus -- arctan{180 / 260} = Khafre Pyramid

18.43494882 34.69515353 = 53.13010235 degrees

The angle tangent {180 / 260} encodes pure ancient calendar count system dynamics.

It aligns the 360 count into the numerator,

and the 260 Tzolkin count into the denominator.

Angle tangent {180 / 260} = 360 / by {2 x 260 Tzolkin}.

The reduced form of the fraction 180 / 260 = 9 / 13.

The 9 and the 13 are as Mayan and MesoAmerican in count as can be hoped for.

9 x 13 = 117 -- an important number in the Dresden Codex.

Their own cultural geometry no doubt took into account this angle tangent,

as an important angle in the 3-4-5 triangle generated Khafre Pyramid geometry.

The ancient and modern code unifies within the sine and cosine as well {next post}.

This angle tangent {180 / 260},

can be subdivided as well.

arctan{1 / 2} -- plus -- arctan{1 / 7} = arctan{180 / 260}

26.56505118 8.130102354 = 34.69515353

Thus the interconnected angle tangent combination follows as such:

arctan{1 / 2} -- plus -- arctan{1 / 3} -- plus -- arctan{1 / 7} = Khafre pyramid

26.56505118 18.43494882 8.130102354 = 53.13010235

To then proceed along the same routes of approach,

the simple fundamental pathway to arctangent 5.5 <---

goes like this:

arctan{1 / 2} -- plus -- arctan{1 / 2} = Khafre pyramid -- plus --> arctan{1 / 2} = arctangent 5.5

26.56505118 26.56505118 = 53.13010235 26.56505118 79.69515353

artan{1 / 3} -- plus -- arctan{1 / 2} = arctan 1 -- plus --> arctan{180 / 260} = arctangent 5.5

18.43494882 26.56505118 = 45 34.69515353 79.69515353

--------------------------------------------------------------------------------------------------

My last image introduced the most basic fundamentals,

in simplistic angle tangent connectivities,

attached to Khafre Pyramid geometry.

The next step,

is to integrate ---> golden rectangle phi geometry into the Kahfre pyramid geometry constructs,

while also exposing how the Khufu Pyramid sacred seked 5.5,

functions as an angle tangent within those geometry infrastructures.

This is a bridge post between my last post,

and the summation of it all in my last post on this subject.

What was "magic simplicity" in previous posts,

suddenly can become quite complex,

when phi dynamics are introduced.

I felt that this geometry display was needed to help the viewer,

understand how specific angles with tangents like:

{1 / 3}, and {1 / 7}, or {11 / 2} = 5.5 {Khufu Pyramid seked},

integrate with phi geometry angle tangents,

to account for the Khafre Pyramid geometry.

Khafre Pyramid side face slope tangent = 4 / 3 <---

Khafre Pyramid inverse slope tangent = 3 / 4 <---

Remember,

that angle tangent 5.5 = {11 / 2} = {99 / 18},

the Khufu pyramid seked,

has the inverse angle tangent:

{18 / 99} = 2 / 11.

If you are doing the math seen in the images,

it is ALL exact

but you have to perform the math processing correctly.

Scientific hand calculators,

round off at the tenth decimal placement,

so you have to use proper process to get exact results.

In other words,

if you use the golden rectangle -- angle tangent = Phi,

you cannot just calculator click the numbers:

1.618033989 = Phi.

You have to do it like this,

for your calculator to properly calculate the decimal placements:

click:

Square root 5 <---

add ONE. ------ your result will be: 3.236067977,

Now,

divide by Two,

equals,

true Phi placed into your calculator properly for exact results <---

You cannot just type in:

1.618033989

into your calculator,

you have to perform the process then continue the equations.

So using that exact process,

to obtain inverse phi <---

you simply click:

1 / x

function on your scientific calculator.

If your calculator does not have the option {1 / x},

you cannot perform geometry tangent work,

that has square roots and so forth.

----------------------------------------------------

IMAGE

Top section of the image.

Where you see the angle letter designation:

c a b = arctangent Phi,

that means:

angle c + angle a + angle c = the angle with tangent Phi.

This design is created to show how the angle with tangent 5.5,

integrates with these angles tangents:

Phi and {1 / phi},

Khafre Pyramid slope tangent {4 / 3},

and especially,

simple building block angles,

with tangents:

{1 / 3} and {1 / 7}.

Angle c,

in the image,

is subdivided into angles d and e.

Note that the building block angles,

d and e,

are functions of square root 5 and phi geometry tangents.

Look at the angle a b b a = arctangent 5.5

The premier angle featured in this study,

with the tangent 5.5 -- Khufu pyramid seked 5.5,

is constructed in a primary combination of these two angles:

arctangent {1 / 7}

and

arctangent {1 / phi}.

Now look to the central section of the image.

The exact same geometry is offered,

with an addition of the -- inverse phi tangent-- angle a,

on each side of the original design in the top section of the image.

This creates a perfect half circle of 180 degrees.

Now,

look to the -- Khafre pyramid -- inverse slope angle:

angle a e <---

Here the combination of two phi related geometry angles,

come together to form the Khafre inverse slope.

angle a + angle e = K* = inverse slope Khafre Pyramid = arctangent {3 / 4}.

K* = 36.8698765 degrees.

But here is where the "magic simplicity" comes back into play:

K* = arctangent{3 / 4} = angle a + angle e <---

K* = arctangent{3 / 4} = angle c + angle c <----

angle c = arctangent {1 / 3} = 18.43494882 degrees

thus:

arctangent{1 / 3} + arctangent{1 / 3} = K* = arctangent {3 / 4}.

Last but not least,

by adding the inverse phi tangent angles to the original design,

angle a c a = arctangent 7

emerges in the angle infrastructures.

Note angle: b + b -- featured as arctangent {2625 / 9000} = 2625 / by {25 x 360}.

You see the extrapolation at the top of the image,

using the number: 2625 <---

fibonacci ancient phi progression starts like this;

5 / 8 = 365 / 584

5 / 8 = 0.625

0.625 ---> + 1 = 1.625 ---> + 1 = 2.625

-------------------------------------------------------

The bottom section of the image goes through related data,

to aid the viewer in understanding,

both the simplicity and complexity of these building block angles.

In particular,

angle b + b = arctangent {21 / 72},

is featured.

I have supplied the extrapolations of the angle tangent fraction,

to point to the ancient code within.

Most dynamically,

the square root two cubit 20.62394778,

functions within this tangent infrastructure.

But look to last equation presented there.

in that sequence of angle tangent equations.

This is the ancient code within.

angle b + angle b <----

equals:

arctan{1 / 7} + arctan{1 / 7} = arctan {21 / 72} --- {21 / 72} = {105 / 360}.

To access the dynamic ancient angle tangent code,

you set the -- denominator -- to pure 360 count.

angle bb = arctan{105 / 360} = arctan{21 / 72}.

105 = 16 x 6.5625

Thus the tangent of angle bb,

equals:

16 x 6.5625 -- divided by -- 360.

The ancient code key is in the number 6.5625:

aPi = 22 / 7

6.5625 x aPi = cubit 20.625

6.5625 x 3.1416 = cubit 20.61675

6.5625 x 3.14 18 18 18~ = cubit 20.618 18 18~

6.5625 x pi = pi cubit 20.61670179,

thus to access,

the mirror or complimentary pi cubit,

you use the formula:

{18 / 360} -- divided by -- Pi value = cubit.

{18 x 360} -- divided by -- Pi = pi cubit 20.62648062

Multiply the two pi cubits together:

20.61670179~ x 20.626489062~ = 425.25

and

the corresponding ancient cubits:

20.618 18 18 18~ x 20.625 = 425.25 = 162 x 2.625 <---

Much more to follow,

with magnificent ancient angle tangent code to be revealed.

Check out the sine and cosine of arctangent 5.5,

or 79.69515353 degrees,

in the meantime.

...