Each number has its own archetypes and symbols that are associated with it. By internalizing the archetypes of the numbers, we can understand geometry and symbology more innately. The number three associates itself with storybook like completion, a balancing of dualities, and more. I found 9 number 3 archetype examples to look at.
The main vibe of threeness is transcendence of opposites by integration. The preceding number two sets up companionship as well as tension. The best number 3 archetype examples dissolve duality, bestowing balance and a sense of completion. “Three wishes”, “three phases”, in a past present future, and too much not enough just right.
I mention the platonic solids and knot theory a few times in going through the number 3 archetypes examples.. These will be covered more bit by bit in future articles. 🙂
#1 Number 3 Archetype Example: Curcubits and Nightshade Plants
This includes:
- Tomatoes
- Eggplant
- Cantalope
- Cucumber
- Acorn squash
- Some varieties of pumpkins
- Tomatillos
- Golden berries
- Bell peppers
Some other types of peppers, melons, and squash have threefold symmetry as well. You can usually see it when you slice perpendicular to the direction of the stem.
#2 Trefoil knots
In media and logos we see spin-offs of this quality. Trefoil knots can be made with bits of string and grass and so they were a common teaching tool when numerical archetypes were taught. It became the symbol for pagan and celtic movements, the template for the germanic valknut as well. We can also see in the Ghanan Andrika symbols a few that strongly resemble the trefoil knot. Read about the Ghanan Andrika symbols and other cultural symbols with rotational symmetry.
Make an overhand knot and join the two loose ends together and it makes a trefoil knot. One interesting property of the trefoil is that there is a left and right handed version depending on the over and under crossings. This is chirality. One handedness cannot be transformed to the other without untying the knot (ambient isotopy).
#3 Koch Snowflake
Swedish mathematician Helge von Koch first described this simple example of recursive geometry. You start with an equilateral (60-60-60) triangle, add a triangle with side lengths one third as long as the original to each side, and keep repeating. The outline increases by a factor of 4/3 each time, and the area converges to 8/5 (Mario Livio, The Golden Ratio). The Koch snowflake not only exemplifies threeness, but blends the archetype of threeness with fractality.
#4 Borrehemean Rings
Borromean rings are a lovely example of layered symmetry. Every ring has two over and two under alternating crossings. When drawn as triangles rather than circles, it makes the Valknut symbol.
Borromean rings are an example of how something simple at first, can have intricate complexities. As people describe all the features there are to describe of this configuration, it fits into many categorizations. Especially in knot theory and symmetry categorizations, the study of Borromean rings goes deep. Invariants and isometries abound. Another realization of the rings is connecting the vertices of a regular icosahedron.
#5 Number 3 archetype example: Braids
If you try to make a braid with two strands, it will instantly untwirl. A braid with three strands perfectly stays put. With four strands you can make the braid by pretending two different strands are one every turn, essentially it’s still a three-braid. This can be likened to the stability of triangles. Braids unify 3 separate entities.
#6 The Numeral 3
If you look at a number three there are three extrema points when drawing it. Many Arabic numerals have this quality, like 4 as well, creating 4 right angles in the middle of it.
#7 Number 3 Archetype of Triptychs
Triptychs tell the beginning middle and end, or otherwise allow the artist to express in three-ness. Past, present, and future is another common theme with triptychs. One of the strongest ways to connect with three is completion, a beginning, a middle, and an end. 4 grounds this into a system, and five creates regeneration.
#8 Iris Flowers (and more)
Trilliums like pawpaw have triangular flowers too. Most edible flowers have 5 petals, but the three petaled flowers have a very raw beauty to them. Orchids even though they have five petals they have a triangular shape that many feel a threeness from.
#9 Tribar and Knot Symbolism
The Penrose triangle is said to be impossible to really exist, yet the human mind tries to wrap itself around the idea. Try to visualize and understand the Penrose triangle, and you may convince yourself it does exist. Some 3D printer models are considered to be “pretty good” approximations of it.
Which Number 3 Archetype Examples Are Strongest?
So three is still a very young number, but the first with a real semblance of maturity about it. Been there, done that, and finished it. For over 40 additional number 3 archetype examples you can read my main post on numerical archetype Three!
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