## Remarkable Foursome is a Mathematical Wonder

Remarkable Foursome is a Mathematical Wonder. It presents quite a take on the Fibonacci number series.  It develops into what is called the Golden Ratio. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. The Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.[14] What sequence defines this series?  Eventually the second of two consecutive numbers divided by the 1st = the Golden ratio: φ is the symbol  for this ratio.

In mathematics, the Fibonacci numbers are the numbers in a specific integer sequence.  Their defining feature is every number after the first two is the sum of the two preceding ones:[1][2]}

At 1st glance the “foursome” number square and Fibonacci seem in-congruent. But the remarkable foursome fuses the numbers on the 4 x 4 square as follows: Examine it numbers vertically left to right:

• First row: 4 + 9 = 13. Then  5 + 16 = 21.
• Second row: 14 + 7 = 21.  Then 11 + 2 = 13.
• Third row 15 + 6 =21. Then 10 + 3 = 13.
• Fourth row: 1 + 12 = 13. Then 7 + 13 = 21.

All total are either 13 or 21.  Of course, 13 = 21 = 34. This is just the tip of the iceberg. Fibonacci numbers on the square go further. Again look at the numbers vertically. Consider the four vertical rows again. This time add every other number as follows:

• Row one: 4 + 5 = 9. Then  9 + 16 = 25.
• Row two: 14 + 11 = 25. Then 7 + 2 = 9.
• Row three: 15 + 10 = 25. Then 6 + 3 = 9.
• Row four. 1 + 8 = 9. Then 12 + 13 = 25.

I know what my reader is thinking: 25 and 9 are not in the Fibonacci series. But, yes they are.  Three and five are both Fibonacci numbers:

• 3² = 9.
• 5² = 25.

Mathematician Mark Barr proposed using the first letter in the name of Greek sculptor Phidiasphi, to symbolize the golden ratio. Usually, the lowercase form (φ or φ) is used.

Michael Maestlin, first to publish a decimal approximation of the golden ratio, in 1597.

The golden ratio has been claimed to have held a special fascination for at least 2,400 years, although without reliable evidence.[13] According to Mario Livio.

### Number Square of the Remarkable Foursome

Number squares were once the backbone of a lost civilization. This time marked a Golden Age of peace and plenty. Tradition associates the 4 x 4 number square with Jupiter. Each planet had its own set of numbers.  Jupiter was the leader of the Olympian Gods; Jupiter means “Jovial King” and/or “Father of Thunder.” Jupiter is associated with luck and good fortune. It is the mentor/Guru /teacher of gods. More on internal link below.

## Enhancing Jupiter Creates Harmony

Keep checking the website for more to come for the remarkable four.

## Roses Contain Mysteries and are Favored by Mystics

Roses Contain Mysteries and are Favored by Mystics. First, consider the visible side of roses. Leaves on the bushes come in clusters. These clusters can be comprised of  3,5 or 7 leaves.  It has been proven that:”If you want the rose bush to keep blooming, cut the branches between clusters of five and three leaves.” For the roses to continuously blossom, they must be cut between the Fibonacci numbers 3 and 5.  Also significant for this blog: The rose has 5 strong petals and 13 weaker. Now the mysticism begins. The background for this blog is the preference that Neolithic cultures showed for number squares.

Mars=65
11247203
41225816
17513219
101811422
23619215

### ROSES CONTAIN MYSTERIES THAT APPLY TO  NUMBER SQUARES

Here are the two number squares that the rose draws on. Neolithic cultures knew that nature works on these squares. Today, many have yet to realize this. The 5 strong petals and 13 weaker draw on the key central numbers of 3 x 3 and 5 x 5. The core number of the 3 x 3 is #5. The core number of the 5 x 5 square is #13.

### Fibonacci Series Shares the Key Numbers With Roses

Fibonacci numbers grow numbers grow by  adding the two previous numbers to arrive at the next larger number. We thus find: 1,1,2,3,5,8,13,34…….The series can continue infinitely. Life both  favors and significantly uses the ratio of these consecutive numbers.  Note: The Fibonacci numbers that form the petals of the rose:  5 and 13.  As the series develops, the ratio of the by which the larger of the two is greater than the smaller gets closer and closer to the infinite number of phi:  1.618…    That number is called by the Greek word, phi, or the Golden Section.  The definitive phi number can never be reached. It is an irrational number that extends to infinity.  Could that be why man will always fall short of immortality?

### ANOTHER BIG ROSE CO-INCIDENCE

Consider the following about roses contain mysteries: I have already blogged extensively about these bullet points below . Both 5 and 13 define the strong petals on a rose. Both 5 and 13 define the core of the 1st two odd numbered squares as pictured above. The co-incidence extends to regular and semi-regular polyhedrons:

• There can only be 5 regular polyhedrons.
• There can only be 13 semi-regular polyhedrons.

The knowledge of many of prehistoric civilizations was also preserved by planting roses in Jerusalem. This knowledge today calls for a new vision of peace and co-operation. Let roses lead the way. Hooray for flower power!

## Phi Tie is Like Tied Musical Notes Crossing Many Measures

Phi Tie is Like Tied Musical Notes Crossing Many Measures. Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets.

There was once a Golden Age. It was maintained by a mathematical code. The code has been hidden from most for millennium. On appearance, it is strikingly simple. On the featured number square, we have the following:

• Any straight row of 3 numbers totals 15.
• Any opposite two numbers totals 10.
• The 8 perimeter numbers total 40.
• The central number is 5.

This featured number square shows the traditional arrangement of the numbers. There are other solutions. The only rules used in diagramming the number square is that; (1) Even numbers must occupy the four corners. (2) Odd numbers must be placed in between the even numbers. (3) The mathematical totals must be the same as those given above.

### So Where is the Phi Tie?

For this blog I will just show the obvious one. It is taken as a straight read across the bottom three numbers of the featured picture, from right to left. This code goes back to antiquity. Remember, Hebrew and many ancient languages were read from right to left. These civilizations would prefer the featured picture arrangement of the numbers. That exactly duplicates the first three numbers given as the quotient in the phi formula above:  .6180… In antiquity zero was not considered a number on its own. It was a synthetic number. As just mentioned: Any opposite two numbers totals ten. Primary numbers from 1 to 9 were given their own special place of honor on the square.

For those wishing to know about the hidden codes that I discovered and the story that goes with it, go to DSOworks.com and type in “phi”.

## Mathematical Love is More Prevalent Than You Think

Mathematical Love is More Prevalent Than You Think. The Egyptian and Hebrew civilizations placed the mathematics of love in their buildings. However for this particular blog, I will consider how the key word expresses mathematical love with the Hebrew language.

The Hebrew verb for “Love” is  אָהַב (Ahav).  The three letter verbal root for love is spelled Alef (אָ), which is also the symbol for number 1; Hei (הַ) which is also the symbol for number  5; and Veis (ב), which is also the symbol for number 2. The Hebrew verb for love has the same factors as this ratio.  The phi of natural growth from people to galaxies uses the love numbers as  phi= (√5 + 1) / 2. This equal 1.618… to 1. The 3 factors for love and phi are the same. Here are the first few of the series. As the numbers grow by successive addition, as 1,1,2,3,5,8,13,21,34,55… the larger divided by the smaller gets closer and closer to phi. Phi is an infinitely large number that cannot be reached. It is just like people. We can strive for perfection but are never quite able to reach it.

In Hebrew, to make “love” into a noun,  the letter   “hei” is added  at the end three letter verb. Keep in mind that in Hebrew the letter on the right is the 1st letter. The language is written backwards from English. Therefore, the letter that ends the noun is on the extreme left. אַהֲבָה   Hei (הַ), like before, is also the symbol for number  5.  Thus we have another  5  to add to the 8 of the verb. 5 + 8   = 13. Look at the Fibonacci series just given above: All three: 5,8 and 13  are members of the series.

A closing note:  Phi (uppercase Φ, lowercase  or Ancient Greekϕεῖpheî[pʰé͜e]; modern Greekφιfi[fi]; English: /f/[1]) is the 21st letter of the Greek alphabet. Note, phi is the 21st letter of the Greek alphabet. It just so happens that #21 is the 8th number in the Fibonacci series. Eight is also a Fibonacci number.

## Jupiter Offers Square Deal and Then Some

Jupiter Offers Square Deal and Then Some.  The word Jupiter translates to Jovial King. Jovial, according to Webster, is  characterized by hearty, joyous humor. We all need this influence in our lives. The question becomes, how did Jupiter acquire this meaning? And, what can we do to become more hearty and joyous in this trying day and age?

 Jupiter Jupiter Ζεύς (Zeus) गुरु, बृहस्पती (Guru, Brihaspati) ancient Leader of the Olympian Gods; Jupiter means “Jovial King” and/or “Father of Thunder”.

### Answer to Jupiter Offers Square Deal lies in its magnificent number square of antiquity

Every planet had its own number square. This squares were used to invoke the influence of their particular planet. Jupiter’s was 4 x 4. Below is the traditional arrangement. It hides a special code of numbers. This was called the Fibonacci series. Numbers are pictured and described below.

## Jupiter Number Square Sets Legal Ages

Jupiter Number Square Sets Legal Ages. Each planet was once connected to a number square. Here is the Saturn list. Saturn is 3 x 3. Jupiter is 4 x 4. Mars is 5 x 5. Sun is 6 x 6. Venus is 7 x 7. Mercury is 8 x 8. Moon is 9 x9.

Next, what are some primary legal ages?  Of course, there can be quite a few depending on the culture.  The two I pick belong to the 4 x 4 number square. They are of significance in our western civilization. These ages are 13 and 21. This is when a person takes reponsibility for their own actions. In Judaism 13 it is the year of  the Bat and Bar Mitzvahs. Then the legal age in many western cultures is 21. People are considered to be grown up or adults.

### By Jupiter, so where are 13 and 21 in the 4 x 4 number square?

The 4 x 4 number square hides the numbers of a special group of numbers. It is called the Fibonacci series. The numbers are set and always the same. The graph above starts the series. Numbers grow by  successive addition. We have 1,1,2,3,5,8,13,34…Of course the series contnues to infinity. Life favors the ratio of any two consequtive numbers as it develops. The ratio gets closer and closer to 1.618… The true number of phi can never be exactly reached. It is an irrational number.  Could that be why man falls short of immortality? This ratio has a special name, “phi”. It is also called the Golden Section of Golden ratio.

### Back to the 4 x 4 Number Square

Look at the numbers vertically two at the time: 16 + 5 = 21. Underneath, 9 + 4 = 13. Next, 3 + 10 = 13. Then, 13 + 8 = 21. The entire square is filled with Fibonacci numbers. Success is action, by tradtion, comes by this number series. Our Neolithic ancestors knew everything that you are reading about here. This was  atleast 11,000 years ago. Number squares played a large part in lost civilizations. I believe that a peaceful civilization can be restored by revitalizing such lost knowledge.

## Creation: Phi & Exponential factor are in Genesis 1:1

Creation: Phi & Exponential factor are in Genesis 1:1. בְּרֵאשִׁית, בָּרָא אֱלֹהִים, אֵת הַשָּׁמַיִם, וְאֵת הָאָרֶץ. Translated to English, “In the beginning God created the Heavens and the Earth.” First of all, please review my blog on the ““The Broadway Marquee of Megalithic Measure“. The picture below is the “Broadway Marquee” of antiquity referred to. That particular blog shows a few of its hidden codes. Here is a brief review:

• In Greek and Middle eastern languages letters doubled as numbers. Therefore, every letter, word, phrase, sentence, etc. had a numerical import.
• The 1st sentence of Genesis equals in Hebrew is 2701. One was often added by traditional of the Colel. I think “colel” represented the singular Deity, John Michell discusses the subject more thoroughly in his numerous works.   Work with your calculator to double check me. Add the numbers around the central 5. The eight numbers total 40. Then add them two at the time overlapping the numbers as 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Now take the number three at the time. Overlap the third with the first number as: 492 + 276 + 618 +  834 = 2,220. They come to the same totals in reverse. Let (P) stand for perimeter. Then (p-1)   is 40 + (P-2)  is 440 + ( P-3) is 2,220  = 2700. Add one for the Deity and you have 2701.This number square defines the perimeters of Creation.

### What Else Does the 1st sentence of Genesis Have to Say About Creation?

Those who know Hebrew can, and I’m sure will, double check my figures. To the best of my knowledge, they are accurate. Anyone can see the 1st sentence has seven words. Hebrew is read from left to right. The 1st letter of each of the first five words factor phi. That is the ratio by which nature unfolds by. If you never hear of it, check it out on line.

The number that nature loves to work with is called in Greek by the name “phi.”  The Greek letter phi ($\varphi$ or $\phi$) represents the golden ratio. Its value is:

$\varphi = \frac{1+\sqrt{5}}{2} = 1.6180339887\ldots.$(this was copied from Wikipedia).

Here are the factors of phi as found in Genesis. Take the first 5 letters (left to right) to get the picture.  Beis is 2. The 1st two words of the 7 letter first sentence each start with a “beis” or number “2”.   Aleph is 1: The next two words start with an aleph. The fifth word starts with a “hei”, the symbol for 5. Now, 1,5, and 2. Immediately, we have all 3 factors of phi: 1,2, and 5.
The next mathematical “gem” of nature is the exponential factor of growth. This is also a key part of the math of creation. It places limits on how quickly system can grow. The factor is 2.72 (rounded figure).  Look at the first letters of the last two words. The 1st letter is a “vav” which is the symbol for 6. The last letter is a “hei” which is the symbol for 5. The formula for the exponential factor is 6 X 5/6+5 or 30/11 = 2.727272……..
Pi is the classic circle and diameter as pictured below. The 7 words with “Elohim” representing the center becomes the 3rd mathematical gem. It also represents the central Sabbath surrounded by the other 6 days of the week. There is so much to blog about just on the 1st sentence of Genesis. More will appear, Keep watching.

## Black Elk of the Sioux

Black Elk of the Sioux. Black Elk was a medicine man for the Oglala Sioux Indians. He verbally related his story to John Neihardt who published a book in 1932 with Black Elk’s words called :Black Elk Speaks. If you think that the Book of Revelations of John in the New Testament can be confusing, Black Elk Speaks  is definitely on a par. It definitely has many similarities. His vision has both the wisdom and analogies used by the Bible which further leads me to believe the possibility that the American Indians branched out from a lost tribe of Israel.

“Younger brother,” he said, “with the powers of the four quarters you shall walk”… (quote from an ancient grandfather speaking to Black Elk  in Chapter 3 of Black Elk Speaks) Of course, two intersecting rivers have always been the location of concepts of Paradise. What do the 4 quarters refer to? The answer: even numbered, number squares, in particular the 4 x 4 number square of which I have written numerous blogs. Please review these on DSOworks.com

The  “horses took their places in their quarters, looking inward, four by four” (also chapter 3 of Black Elk Speaks). These 4 central numbers of this first and therefore prime even-numbered number square are 10,11,6, and 7.  They represent the four corners of the Earth. Here is the key:

### THE FORMULA OF BLACK ELK’S VISION

• In the majority of middle eastern civilization and elsewhere, the 4 x 4 number square represented the symbolic potential of the planet Jupiter for success is action, business, and creating opportunities. Each of the 7 planets were  assigned its own number square.
• All potential lies in the central four numbers of  even numbered squares for a totality of creation explained as follows:  Here is the formula: The upper left central number (10) I call UL. The upper right number I call UR. The lower left I call LL and the lower right I call LR. The sum of all the numbers in any even numbered number square can be represented by “S”. The formula becomes (UL  X  LR) + (LL + UR) = S. The prototype example above  becomes  (10  x 7) + (6 x 11) = 136 (sum of the numbers from 1 to 16)
• This number square was called upon on by God in Genesis on each day of creation. I’ve already blogged about this; but to summarize – on each day God called his work, “Good,” In Hebrew “good” has a numerical equivalent of 17, On the above number square, any opposite numbers total 17 as-  16 + 1;  10 + 7; 4 + 13 etc.
• Here is the clincher: As all life as we know it develops by  a mathematical ratio called “phi”, 1.618… to 1; this square holds are series of numbers called the Fibonacci that develops in that ratio. The first Fibonacci numbers are: 1,1,2,3,5,8,13,21,34,55…Now look at the above square: 16 + 5 = 21; 3 + 10 = 13; 2 + 11 + 13; 13 + 8 = 31 etc. Their totals are always the Fibonacci  numbers of life.

Conclusion: A find a strong parallel between the vision of Black Elk, medicine man for the Oglala Sioux, and Genesis of the Bible or Revelations of the New Testament. I can only conclude that if we but know it,  all mankind is one with our Creator and that we should all  reclaim our natural birthright in  this wonderful upcoming age to be filled with  peace and plenty. Finally, please keep watching for my book of poetry dictated to me by an old  Indian spirit, female of the matriarchal, Lennie Lenape tribe. It is called The Oquaga Spirit Speaks- 89 pages of poetry and pictures dictated to me by this spirit around Oquaga Lake. It will be listed for  on the products page of DSOworks,com very reasonably.

 An encampment of a Sioux Indian tribe

## BLOWING THE COVER OFF OF THE MEGALITHIC YARD

### BLOWING THE COVER OFF OF THE MEGALITHIC YARD

Where did the measure of 2.72 foot megalithic yard, re-discovered by Professor Alexander Thom of Oxford University in the 1960’s,  really come from?  Thousands of years ago, Plato called 272 the number of harmony. John Michell writes about the subject in his City of Revelation.  Thom found this unit at at 600 sites located in  England, Scotland, Wales and Brittany. In the 1900’s, Jay Hambridge discovered  that the megalithic yard was an extension of the Egyptian remen:  The 1.2165 foot remen x square root of 5 = 2.72 feet. Hambridge uncovered the source of numerous ancient measurements by multiplying the Egyptian remen by the square roots of 2,3, 4,5 etc.

### MUSIC AND MEASURE

I discovered that many older  measurements, including those that Hambridge uncovered are found in the 3 X 3 square pictured above. It was the cornerstone of ancient builders. In my blog on Genesis tunes to A-440, I talk about the hidden number codes. Please follow the numbers on the tick-tack-toe board above: By single digits the perimeter totals 40 as:  4 + 9 + 2 +7 + 6+1 + 8+ 3 = 40.  But overlapping double digits, the total becomes 440 as: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440 (we still tune to A-440). Overlapping the digits, three at the time, corner to corner, we have 2220 as: 492 + 276 + 618 + 834 = 2220. The formula for deriving the megalithic yard from this number square is: P1 (40) + P2(440) + P3 (2220)/(divided by) P3(2220)  times the square root of the central number,5.

### THE 3 MATHEMATICAL GEMS ARE HERE

The 3 X 3 magic square can have some different number arrangements, as books on number squares illustrate. John Michell, states that the above diagram is the traditional way it is viewed, Now why is the traditional solution important? Because, other key megalithic measures and mathematical amazements are found when looking at the bottom row horizontally: As the numbers across the bottom are 816 or in reverse 618 we find:  (1) One megalithic rod = 81.6 inches (2) One megalithic inch = 0.816 inches. When these three figures are reversed as 618, magically, the Golden Section appears. Ancient sites around the globe  used the 1 to 1.618 ratio for construction. After they were constructed by the Golden Section, they were measured by megalithic units. This will be the subject of future blogs. Jericho was such a site.  .618 is  diminutive expression of the Golden section: 1/1.618…= o.618…  Finally the megalithic yard as 2.72 references another mathematical gem: the exponential factor of growth: 2.72 is a close approximation that expresses the limits by which systems can grow. I will save the appearance of pi for another blog. Thank you for your patience.

## Our Music, Bodies, etc. Use the Same Numbers

THE SPIRALS ON THIS CLEF GROW BY THE SAME RATIOS AS THE HUMAN BODY. READ AND FIND OUT HOW

Our music, bodies, etc. use the same numbers. As Fibonacci  numbers develop by successive addition of numbers that are adjacent; man, music and even love, yes-love,  use the exact, same numbers.   When the larger number of the two in this series is divided by the adjacent smaller number; the ratio keeps getting closer to what is called the Golden Section or phi. This ratio never comes out evenly: It is 1.6180339… The Fibonacci numbers are named after an Italian mathematician.   Numbers that develop into this ratio, in order of size are: 1,1,2,3,5,8,13,21… The higher the numbers by successive addition,  the closer it comes to phi.

The Use of Phi in Music

The formula for the phi ratio is: square root of 5 + 1; whose total is then divided by two. The piano keyboard is set up by the Fibonacci series. We have two spacing of black keys. They are by 2’s and by 3’s for a total of 5. Taking C major as the prototype, from one “C” to the next is 8 tones on the white keys. Thus, from C to C’  in addition to the 1 octave we have, 2 black keys, then 3 black keys and 8 white keys. The total black and white keys are 13.

— USE OF PHI IN OVERTONES

All tones have what’s called overtones that vibrate sympathetically with  the fundamental tone. The 1st overtone  is the octave of 8 notes. The second overtone is the 5th, Both overtones are Fibonacci numbers. Not co-incidentally, the Great Pyramid of Egypt uses the same numbers in its 5 to 8 ratio of its height to one length of the square base.

THE HUMAN FORM FACTORS THE FORMULA OF THE GOLDEN SECTION

The factors of the Golden Section ( another name for phi) are 1,2 and 5 (as already described above). People have one torso, one head, two arms, two legs, five fingers on each hand and five toes on each foot. We are the mathematical manifestation of the factors of phi.   Most significantly, love ties the whole system together: The Hebraic verb for love (pronounced, Ahav) uses three Hebrew letters.  Spelled out in English they are: aleph, hei and beis. Aleph is also the Hebrew symbol for 1; hei is also the symbol for 5; and beis is also the symbol for 2. What is the lesson? Life and music are all about love.