Ancient Legacy – 360 and Pi

Introduction

The Columbia Encyclopedia, in its article titled “Civilization,” says that the earliest civilizations developed in the following parts of the world: Mesopotamia, Egypt, China, India, the central Andes, and Mesoamerica. A traditional theory of the spread of civilization is that it began in the Fertile Crescent and spread out from there by influence. However, scholars now believe that civilizations started independently at several locations in both hemispheres. [ Please read subject related article: Earth’s Earliest Civilizations: “Full Blown – Full Grown” ]

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Mesopotamia, an ancient Greek term meaning “the land between rivers,” is considered to be the cradle of civilization because this is where we find the origins of cities, agriculture, written language, law, astronomy and mathematics.

Most people today do not realize that foundations of modern distance and time measuring systems were created by earliest known civilizations (going back thousands of years to the area of Mesopotamia).
The key numbers for these counting systems were 12, 24, 60 and 360.

It is presumed that the Babylonians invented the division of the circle into 360 degrees. It’s not clear why they used 360. [ note: this article may provide the answers ] One theory is that back in early Sumerian times they divided the day into 12 “time-miles” – the time required to travel a “Babylonian mile” [ 360 m = 60 rods, each rod was 12 cubits, and each cubit was c.0.5 m ] . Since a day is one revolution of the sky, that corresponds to dividing a complete revolution into 12 parts. For convenience, the “Babylonian mile” was subdivided into 30 parts, and that gives 360 subdivisions of the circle. See e.g. Eves, “An Introduction to the History of Mathematics”, sec. 2-4.

We still divide 1 day into 24 hours, each hour into 60 minutes and each minute into 60 seconds.
We also do not question that circle should be divided into 360 degrees, each degree into 60 minutes, each minute into 60 seconds.
Big part of the modern world still uses Imperial units of length: feet which are divided into 12 inches

Note: 1 mile is divided into 5280 feet (12 x 440) feet, also 1 mile = 1760 yards (4x 440)
BTW, Great Pyramid of Giza has base = 440 Royal Egyptian Cubits which results in perimeter = 1760 Royal Egyptian Cubits).
1 mile = 63,360 inches. Now notice something strange: 63*360=22680 inches = 1100 Royal Egyptian Cubits

Considering that humans have 10 fingers and commonly use base 10 system* to express and count numbers, it is puzzling why we don’t apply decimal system to division of circle and time-measuring.

*The decimal numeral system (also called base ten) has 10 (ten) as its base and it is used in mathematics for writing numbers and performing arithmetic.
It is most widely used number system by modern civilizations.

The simplest, “natural” division of circle could by multiples of 2 or 10.
For example, circle could have 4 quadrants, each divided into 100 units (total 400 “degrees” instead of 360 ).

We could also use multiples of 2, for example we could divide circle into 64 (2x2x2x2x2x2), 256 or 512 parts and each part would be further divided into 10 or 100 sub-units.

There must be a good reason why we don’t use decimal system when it comes to measuring circles and time.
It seems that ancient people discovered (or were given) advanced principles of astronomy and mathematics which resulted in measuring systems we inherited from them and still use today.

1. Secrets of Pi and 360

The Pi is defined as the ratio of a circle’s circumference to its diameter. Pi is equal to 3.14159265358979323846… (the digits go on forever without repeating pattern.)
You cannot expect to reveal the actual last digit of pi – Because there isn’t one. A rough approximation is 22/7 (=3.1428571…), but that is not very accurate

For most numerical calculations involving “pi”, a handful of digits provide sufficient precision. According to Jörg Arndt and Christoph Haenel, thirty-nine digits are sufficient to perform most cosmological calculations, because that is the accuracy necessary to calculate the volume of the known universe with a precision of one atom. Despite this, people have worked strenuously to compute ? to thousands and millions of digits.

The Sumerians, Akkadians, Babylonians, Egyptians, Greeks, Romans and later Muslim scholars and the Western World adopted all these value and universal constants and we are just not sure how to use these to understand Divine Light and therefore achieve our goal. It seems we still are looking for Aliens and Atlantis – digging here and there and yet it is right in front of us, if we could only see!

Pi = 3.141 592 653 5…

3 x 1 = 3
3 x 1 x 4 = 12 (note: 12 divisions of zodiac, 1 foot=12 inches)
3 x 1 x 4 x 1 x 5 = 60 (note: 1 hour = 60 min, 1 min = 60 sec)
3 x 1 x 4 x 1 x 5 x 9 = 540 :::  540/360=1.5 (note: circle is divided into 360 degrees)
3 x 1 x 4 x 1 x 5 x 9 x 2 = 1080 :::  1080/360=3 (note: 1080 feet = 360 yards)
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 = 6480 :::  6480/360=18
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 = 32400 :::  32400/360=90
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 3 = 97200 :::  97200/360=270

Notice how 360 is hidden within the Pi.

Perhaps dividing circle into 360 degrees resulted from ancient knowledge of the exact value of the Pi?

Notice that time is connected to the circle since it is defined by rotation cycle of our planet (one spin cycle when sun returns to zenith):
1 day = 2x 12 hours = 1440 minutes = 864,00 seconds.

An interesting fact:
6+(2/3) = 6.66666…
(6 +2/3) x 129,600 =864,000

Here is another unbelievable “coincidence”:
“Pi” approximated to the 9^th decimal place is exactly:
Pi = 3.141 592 654
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 4 = 129,600

129,600 x 2 = 25,920 x 10
which is 10x Earth’s precession cycles
( 10 x period of precession of the equinoxes)

The Earth is spinning on its axis in a counter-clockwise direction, and rotating around the sun also in a counter-clockwise direction, while the earth’s spinning axis wobbles like a gyroscope in a clockwise direction. As the result, as the twelve constellations appear to move clockwise along/around the horizon during the course of its annual rotation around the sun during a year, the constellations, from spring or fall equinox to equinox,appear to move counterclockwise at the rate of 72 years/per degree, or one full wobble in 25,920 years (also known as Great Year).of the earth’s axis.
The galactic year is the duration of time required for the Solar System to orbit once around the center of our galaxy (the Milky Way). Estimated length of the galactic year is close to 1000 precession cycles of the Earth.

2. Connection of Distance and Time

Our planet spins on its axis and also moves on its orbit around the Sun.
No matter what units of time we apply, the property of Earth movement is such that it will rotate on its axis exactly 366.25 times while completes its full orbit around the Sun, however sun will pass above selected point on earth’s surface (e.g. Great Pyramid) exactly 365.25 times per orbit.

Note: The Earth makes 360 degrees rotation around its axis in relation to the distant stars in one “sidereal day”. However, in relation to the sun, due to the earth’s orbital movement, it rotates on its axis a bit more than 360° per (solar) day. This way in 1 year the Earth makes 1 extra rotation in relation to stars.However, we define our 24 hour “day” relative to the Sun, not relative to the Earth’s actual rotation. If we didn’t do this, then “Noon” would occur a little later each day until “Noon” was happening at night!
At present, Earth orbits the Sun once every 366.25 times it rotates about its own axis, which is equal to 365.25 solar days, or one sidereal year.

BTW, we can only wonder if our planet was originally set on a perfect orbit with 360 days per year and slowed down due to some major catastrophe (asteroid impact which slowed it down – and/or perhaps ejected the material to form the moon)…?

Also, selecting 365 for division of a circle into smaller units, would not be practical due to the fact that 365 is not good for further divisions: 365=5×73.
On the other hand, 360 can be divided in multiple ways:
360=3x1x2x3x4x5 = 3×5! = (0.5) x1x2x3x4x5x6=(1/2)x6!
and also 360= 10x (1+2+3+4+5+6+7+8).

Units of Length

There are many units of measure of length ( distance ) we use today (meter, km, mile, foot, inch etc).
Most of us don’t even know what their origin was.
Here are few mind-blowing facts:

Circle with Radius R has circumference 2 x Pi x R.
This formula is independent of units we use to measure R.

The formula can also be used to define units of length.
Let’s define a practical unit of length (convenient for measuring travelling distance on our planet) and make another smaller unit 12 times smaller.
Also, we want to make our unit to reflect our knowledge about 3 important numbers: 1000* (decimal system), 360 (degrees in a circle) and 365.24 (length of 1 year).

*Note: If we divide Earth equator into number of days in a year (365.24) each unit (very close to 1 deg) could be further divided into regular minutes and seconds (60×60) and 100th…

Circumference of Earth measured in “our units” of length:
2*Pi*R [units] = 360*365.24*1000 (we want this number to be the circumference measured in our units)
Therefore R [units] = 131,486,400/(2*Pi) = 20,926,710.51 [units]
The official measurement of Earth’s equatorial radius is 6,378.1 km = 20,925,525 feet.
20,926,710.51/20,925,525 =1.00005

This means that the unit we defined is equal almost exactly 1 foot , and the 12 times smaller unit is 1 inch.
This unit is called today “foot”.

Ancients defined Royal Egyptian Cubit as (Sqrt2)x 1 Remen, where Remen is 1/5000 part of 1 minute of arc.
When measured ancients measured distance of 1 ‘ of arc, they recorded it was equal 1852 m (in meters used today), therefore 1 Remen = 1852m/5000 = 0.3704m.
1 Royal Egyptian Cubit = (sqrt2) x 1 Remen = 0.523824 m = 20.623 inch.

BTW, Royal Sacred Cubit used during construction of ancient pyramids in Egypt ranges from 20.618 to 20.626 inches
represents sacred number:
circumference of the circle expressed in number of arc-seconds/2*Pi*10,000
(360x60x60 = 1,296,000)/2*Pi*10,0000

When we use perfect Pi = 3.14159 the REC = 20.6265
When Pi is approximated by 22/7 = 3.14286 the REC = 20.618

NOTE: Earth isn’t a perfect sphere, but is oblate at its poles, due to its rotation.
Therefore, the Earth radius isn’t constant, but it can be calculated for every location.
For this calculation, the longitude isn’t needed. Mathematically, Earth is a spheroid.
Earth radius at sea level is 6378.137 km (3963.191 mi) at the equator.
It is 6356.752 km (3949.903 mi) at the poles and 6371.001 km (3958.756 mi) on average.
The height above sea level of the location is added.

3. Tribute to Ancient Knowledge: Pyramids of Egypt

The Great Pyramid has proportions representing Pi:

Double Base/Height = 2*440/280 = 22/7 = 3.14286
(which is reasonable approximation of Pi.)

No matter what units of measure we use, the sides of the Giza Pyramids Rectangle (layout for all 3 pyramids) generate the base of the 1st pyramid:

If we use Royal Egyptian Cubits: 1732/1417 = 440/360

This rectangle shows also relationship of
the Royal Egyptian Cubit 20.62 inch
to the Sacred Cubit 25.2 inch:
1732/1417 = 25.2/20.62

Phi and phi

phi = 1.61803 39887 49894 84820 45868 34365 63811 77203 09179 80576
phi, 1.618 … is the Golden Ratio in life and the universe.

phi + 1 = phi²

Phi = 1/phi = 0.618034…
Phi = phi – 1

( 1 + sqrt(5) )/2 = 1.61803 3988…
which is an excellent approximation of Phi

The following formula connects “Pi” (3.14159…) and “phi ” (1.6180…):

(6/5 ) x phi² = Pi
or
(12/5) x phi² = 2 x Pi

sqrt(phi) nearly equals 4/pi
( 1.272 vs 1.273 )

It is incredible that this Formula is expressed by the numbers describing Pyramids of Giza !!!
Here is how:

Proportions (base to height ratio) of the 1st Pyramid: 11/7
Proportions (base to height ratio) of the 2nd Pyramid: 3/2
Proportions (base to height ratio) of the 3rd Pyramid: 8:/5

(24/10) x phi² = 2 x Pi

the same formula written with ratios of 3 pyramids:
2 x [ 2 x (11/7)] = (3/2) x (8/5) x phi²

Note: the Great Pyramid is a Golden Pyramid: length of the slope side (356) divided by half of the side (440/2 = 220) height is equal to 1.6181818… which is the Golden Ratio Phi

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