Threesology Research Journal: Linear, Circular, Triangular examples
Linear, Circular, Triangular configurations
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~ The Study of Threes ~

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Some of us have looked towards the sky and seen a flock of migrating birds in a pattern that is characteristically referred to as a V (or Vee)-shaped flight formation. And there are a few of us who have pondered the reason why many species of migrating birds use such a pattern. In my own attempts at discerning the reason for this, I have come across various reasons:

  • The wisest bird always takes the lead and others follow in the pattern best for conserving energy over long distances.
  • The wings overlap so as to provide a benefit to the bird behind, such as when a racing car "draughts/drafts" behind a lead car. (And so the "Lead" bird gets the brunt of the wind whereby they get no benefit?)
  • No bird gets lost if they remain in a standard formation.

Note: Several observers have mentioned that it is not necessarily the wisest bird of the group that takes the lead position. They have witnessed substitutions in the lead position take place amongst "leader" birds that drop back into the formation to take up some other point whereby another bird takes over the lead position.

Please understand that I am not talking about the reason why birds are migrating, nor where they are migrating to, but the reason for using such a pattern of flight during the migrations. While this is not the only pattern, it and its two primary additional variations are the main focus of this short discussion:

V-shaped formation v-shaped J, L, or 7 formation J, L, or 7 line Diagonal flight formation Diagonal line

(note: the J, L, or 7 formation could also be called a check mark as well as a hook)

Image adapted from:

--- Anchorage Daily News ---

If the usage of the "V" (or Vee)-shaped formation by migrating birds is related to some form of instinct that was developed specifically for conserving energy over long distances via a "drafting" mechanism (that has also been identified and used by long distance car racers), then why do migrating birds use a diagonal or "L" shaped formation and not simply adopt a smaller V-pattern? Clearly, there seems to be some other (than drafting) reason for the usage of such other-than-V-shaped patterns. Why not break down the other flight patterns into smaller V formations, unless some measure of a "phantom limb" phenomena is taking place with respect to migrating birds adopting the usage of a partial V-shape (from our perspective) flight pattern that, from their perspective, is a complete V-formation. Do the birds somehow imagine themselves to be flying in a V-formation even though they are exhibiting a mere portion of the overall "VEE" shape? Do we consider that a less-than V-shaped flight formation is due to the presence of birds that, like automatons, fly in positions that they are most familiar with, like horses traveling along a well-worn path or a human working as a production worker in a monotonous routine? In other words, are those birds who are seen in a diagonal line (or L-shaped formation), filling flight 'spots' (positions) that they are most accustomed to and thereby do not recognize an incomplete "VEE" pattern because, in their minds, from their perspective, there exists the image of a complete V-shape?

Note: the "Phantom Limb" phenomena occurs amongst some human amputees who still imagine, with varying degrees, that the missing limb is still present. Hence, a type of "after-image" impression remains, depending on duration and intensity of exposure. An example would be the after-image of a television (or computer screen) that is seen when it is turned off in a dark room after staring at it for several hours. Likewise, the development of life on a fast spinning planet (which encounters transitional interludes of light/dark in the form of day/night sequences) will be exposed to the patterns exhibited portrayed by the Sun/Earth proximity.

Have changes in the rotation rate of the Earth influenced biological development in a fashion which replicates such an impression; thereby giving another "tweaking" of the definition to the phrase: That God made man in his image, by describing How God did it? Is it a three-patterned image (formula) somehow related to the changes in the Earth's rotation rate in relation to the auxiliary consequential effects?


Was due to an
accelerated rotation rate:

Night/Day-sequence was due to
Earth's slowing rotation:

Triangle image "Flashing"
of Dawn~ Noon~ Dusk
was due to further slowing:
fast spinning Earth slow spinning Earth
noon day sun

rising Sun
slower spinning Earth

setting Sun
These "patterns" are related to the intensity and duration of illumination as well as darkness, which are key influences of biological processes. However, we cannot dismiss such things as planetary polarity reversals and gravity as having no influence. With respect to gravity, it is speculated that one of the influences in the evolutionary development of the heart is due to changes in gravity, with more gravity requiring a stronger heart, and a change in gravity thus affects the types of species inhabiting the land at that time.

When we witness humans using the V-shaped flight formation while flying planes, most of generally consider this behavior to be an imitation of the flight pattern exhibited by birds. However, for those of us who have witnessed the V-shaped formation of migrating fish, we generally do not consider such an activity to be a form of copy-cat activity of fish watching birds. Nor do we consider the V-shaped wake of a boat in water to be an imitation of the V-shaped bird formation. And by encompassing a larger array of V-shaped examples, we begin to ask the same question as to the origin of the usage of the V-shaped flight formation used by birds, from the perspective of what could have influenced the various V-shaped expressions such as:

  • "V"-shaped antlion burrows (pits)
  • "V"-shaped mounds of "higher" Termites
  • Inverted (upside down) V-shaped Native American Teepees
  • Inverted V-shaped stone and dirt (mound) pyramids
  • Pyramidal brain cells
  • V-shaped engine blocks
  • The idea of a "V"-tapered human torso as having some measure of perfection.
  • etc...

Antlion burrows
v-shaped antlion pits/burrows
Antlion below burrow antlion and pit
Termite mound
V-shaped termite mound
Pyramid mound
v-shaped pyramid mound
Pyramidal brain cell
pyramidal cell
Giza Pyramids
3 giza pyramids
3 teepees
3 teepees
V-shaped plane
Zigzag skiing
(or multiple 3?)
zigzag skiing (1K)

Zigzag alternatives
skateboarding, water skiing, skating, zigzag running while doddging bullets, sewing, graphs/charts, pipelines, traveling, vehicle radiator fins, hairdo style, drawing, doodling, shooting pool, moves in checkers/chess, control gain in a descending wheelchair, etc...

Earth's Precession
Precession of Earth's Axis (4K)
wakeboarding (12K)

Wakeboarding, just as in water skiing, exhibits the zigzag/triangular (multiple 3's) configuration while the person is pulled forward as they go from side to side. While the triangular (zigzag) image is not easily recognized by most observers viewing the person from eye level, a birdseye view enhances this perspective.

Image sources:

Because I have not as yet come across an image on the internet which displays the v-shaped formation of fish whether in migration or otherwise, (perhaps because so many of them dart and dash about in several directions... resulting in the need for using an image taken from time elapsed film footage), I did come across an image illustrating an overall triangular pattern:

possible migrations patterns of fish

--- The Sand Dab ---

Let us not also forget to mention the V-shaped bottoms of some bodies of water and the Vee pattern used in some industrial plants related to fishery:

--- Tracy Fish Facility ---

However, we must ask whether there is in fact an overall triangular pattern used by (some/all) fish, or is this merely a projected image of an underlying pattern relative to the human psyche?

Let us also include the traditional single V-design of flying boomerangs, with two ("multiple V") variations included:

The Aussie
Running Man
The Running Man
Four Pull
The four pull

--- BVD' Rangs Boomerang Catalog ---

By adding the example of the triangular (inverted V-shaped) pine tree used for Christmas, it is of further value to note that there is an associated linear- circular- triangular pattern to be witnessed with respect to overall tree growth in varying locations:

Three Trees

While many people can see the above three forms, they have difficulty in seeing distinct divisions due to the presence of overlapping circumstances of growth. This is further complicated by the fact that many species of trees (and plants) are successfully transplanted by humans (and other means) into different terrains than the trees initially developed. Additionally, the human definitions of Low~ Medium~ High with regards to the Linear~ Circular~ Triangular generalization, may be better expressed with respect to variations of growth in a single locality instead of a global assessment.

The following image is a generalized representation of the Linear~ Circular~ Triangular formula as it relates to differences in terrain (location):

3 terrain divisions

In thinking about what might have influenced the V-shaped flight formation as well as the multitude of variations and their attendant labels, I had wondered whether or not there might have been an environmental influence which inscribed this pattern on various species within the context of species-specific susceptibility during particular stages of development, which might include impressions made on biological substrates such as cells, genes, or even DNA.

Such an environmental influence must satisfy certain requirements:

  • It must have been present for millions of years.
  • It must have a sustained intensity.
  • It must be widespread and have a "V"-shaped expression.

The only thing I could come up with that is still present today in order to observe, is the path of the Sun (and Moon) from rise to set. The rotation of the Earth assists the formation of this particular type of image which would have varied with respect to the speed of the Earth's rotation. This rotation was faster in the past and will be slower in the future. The V-pattern of the Sun would have acted as a type of branding iron on the "hide" (genetics/biology/physiology) of a particular organism in a particular way depending on environmental/nutritional circumstances over the evolutionary development of the species.

Sun and Moon along triangular pathways


In 1947, the English physicists George D. Rochester and Clifford C. Butler observed new particles which were a thousand times more massive than the electron. These particles were often associated with V-shaped tracks; they were at first called V particles. Their origin and purpose were an entire mystery. For the following six years, the V particles were observed, and two kinds became apparent. Those whose decay products always include a proton are called hyperons or Lambda particles, and those whose decay products consist only of mesons are called K mesons or kaons. The hyperons and kaons soon became known as the strange particles because of their anomalous (strange) behavior. pp. 49-50, source A

Originally, strangeness was introduced to explain why some hadrons decay quickly by the strong nuclear force while others decay slowly by the weak force. p. 185, source A

Strange came from the fact that something "strange" was going on with a third particle that was neither an up nor a down quark. (Drasko Jovanovic) Lacking any good explanation, theorists simply dubbed them "strange" particles, a name that has survived to this day as the label for a completely new property of matter. The quark that all strange particles contain is known as the strange quark, and it is this quark that gives them their property of "strangeness."


"Strangeness" is a term, a name, for a property of matter seen only in violent collisions of subatomic particles; it has no corresponding meaning in the everyday world of our senses that language was originally developed to describe. Physicists have had to create a new nomenclature in order to begin talking with each other about the weird subatomic landscape. One way they do so is to borrow words from everyday language and use them in entirely new ways. In this case, "strangeness" is a property found in particles containing the strange quark.

Dodd, J.E. The Ideas of Particle Physics: An Introduction for Scientists. Cambridge University Press: Cambridge, 1984.

--- Physics Folklore By Lynne Zielinski ---

On some heaters/coolers two filters are used and set in a V-pattern.

The long robes worn by those in antiquity can be viewed as triangles (like wedding dresses).

Date of initial creation: Sunday, July 23, 2017, 4:07:54 AM
Latest update: Monday, March 15th, 2021... 11:07 AM

Your Questions, Comments or Additional Information are welcomed:
Herb O. Buckland