Vesica Piscis ↔ Yin-Yang: Intersection Geometry

BY NICOLE LAU

Two Becomes Three: The Geometry of Creation

Draw two circles. Let them overlap. The lens-shaped intersection is called Vesica Piscis ("fish bladder" in Latin)—one of the most sacred shapes in Western geometry.

Now look at the Yin-Yang symbol (Taiji). Two halves, each containing the seed of the other, flowing in eternal dance.

Different images. Same principle: Two polarities intersecting create a third element—the space of creation.

Vesica Piscis IS the geometric foundation of Yin-Yang. Intersection geometry encodes the creative principle.

Vesica Piscis: Western Intersection Geometry

Vesica Piscis is the almond-shaped figure formed by the intersection of two circles of equal radius, where the center of each circle lies on the circumference of the other.

Construction:

1. Draw circle A
2. Place compass point on circle A's circumference
3. Draw circle B with same radius
4. The overlapping lens = Vesica Piscis

Mathematical Properties:

• Width to height ratio = 1:√3 (≈ 1:1.732)
• This ratio appears in equilateral triangles
• Vesica Piscis is the womb from which all sacred geometry emerges

What It Generates:

• Equilateral triangle: Connect the two circle centers and the two intersection points
• Square: Extend lines from Vesica Piscis
• Pentagon: Further geometric divisions
• Flower of Life: Multiple Vesica Piscis patterns

Symbolic Meanings:

• Creation: Two (duality) creates third (offspring, new reality)
• Divine feminine: Womb, vulva, birth canal
• Christ consciousness: Fish symbol (Ichthys) derived from Vesica Piscis
• Portal: Gateway between worlds, dimensions
• Vision: Almond-shaped eye, seeing beyond duality

Where It Appears:

• Christian art: Mandorla (almond-shaped aureole around Christ/Mary)
• Gothic architecture: Pointed arches are Vesica Piscis shapes
• Sacred seals: Chalice Well cover (Glastonbury), many mystical symbols
• Nature: Fish shape, eye shape, cell division

Yin-Yang: Chinese Intersection Principle

Yin-Yang (陰陽) is the fundamental duality that generates all phenomena, visualized in the Taiji diagram.

The Symbol:

• Circle divided by S-curve
• Black (yin) and white (yang) halves
• Each half contains opposite-colored dot (seed)
• Continuous flow, dynamic balance

Geometric Construction:

• Start with circle
• Divide with S-curve (actually two semicircles)
• The curve follows the arc of two intersecting circles (Vesica Piscis principle!)
• Add dots at centers of each half-circle

Yin-Yang Dynamics:

• Complementarity: Yin and yang are opposites but not enemies
• Interdependence: Each contains seed of the other
• Transformation: Yin at peak becomes yang, yang at peak becomes yin
• Balance: Not static 50/50, but dynamic equilibrium

Symbolic Meanings:

• Creation: Yin-yang interaction generates all things
• Polarity: Dark/light, passive/active, feminine/masculine
• Wholeness: Circle = unity containing duality
• Process: Eternal cycle, no beginning or end

The Convergence: Vesica Piscis Generates Yin-Yang

Here's the revelation: The S-curve in Yin-Yang is derived from Vesica Piscis geometry.

Geometric Proof:

1. Draw two circles overlapping (Vesica Piscis)
2. The boundary of each circle creates an S-curve through the overlap
3. This S-curve = the division line in Yin-Yang symbol
4. Each circle = one polarity (yin or yang)
5. The overlap = their mutual interpenetration

Visual Demonstration:

• Circle A (white) = Yang
• Circle B (black) = Yin
• Where A overlaps B = yang contains yin seed
• Where B overlaps A = yin contains yang seed
• The S-curve = the arc of each circle's circumference

Mathematical Relationship:

• Vesica Piscis ratio (1:√3) relates to Yin-Yang proportions
• Optimal yin-yang balance ≈ 62%/38% (Φ-ratio)
• The S-curve creates this Φ-approximation

Aspect	Vesica Piscis	Yin-Yang	Convergence
Basic Form	Two overlapping circles	Circle divided by S-curve	Intersection geometry
Duality	Two circles (two polarities)	Yin and Yang (two forces)	Complementary opposites
Unity	Overlap creates third space	Circle contains both halves	Wholeness from duality
Interpenetration	Circles share space (Vesica)	Each half contains opposite seed	Mutual inclusion
Creation	Womb, birth, generation	Yin-yang generates 10,000 things	Generative principle
Symbolism	Divine feminine, portal, vision	Cosmic balance, transformation	Sacred intersection

Key Insight: Vesica Piscis is the geometric skeleton of Yin-Yang. The S-curve is not arbitrary—it's the natural result of two circles intersecting. Same geometry, different cultural expression.

The Creative Principle: Two → Three

Both systems encode the same truth: Creation requires intersection.

Western (Vesica Piscis):

• One circle = Unity/God/Source
• Two circles = Duality (spirit/matter, heaven/earth, masculine/feminine)
• Vesica Piscis (overlap) = Third element (Christ, creation, manifestation)
• Trinity: Father + Mother = Son (Christian interpretation)

Chinese (Yin-Yang):

• Wuji (無極) = Undifferentiated unity (empty circle)
• Taiji (太極) = Differentiated duality (yin-yang circle)
• Interaction = Third element (Qi, 10,000 things, manifestation)
• Trinity: Yin + Yang = Qi (Daoist interpretation)

Universal Formula:

1 (Unity) → 2 (Duality) → 3 (Creation) → 10,000 (Multiplicity)

This is the cosmological constant across traditions.

The Φ Connection: Optimal Intersection

Vesica Piscis and Yin-Yang both approximate Φ-proportions:

Vesica Piscis:

• Width:Height = 1:√3 ≈ 1:1.732
• This is close to Φ (1:1.618)
• The difference creates dynamic tension (not perfect, but harmonious)

Yin-Yang:

• Optimal balance ≠ 50/50 (static, unstable)
• Optimal balance ≈ 62/38 (Φ-ratio, dynamic stable)
• The S-curve naturally creates this proportion

Why Φ?

• Φ is the ratio of maximum harmony with minimum rigidity
• Perfect 50/50 = too balanced, no movement
• Φ-ratio = balanced but dynamic, allows transformation
• This is why yin-yang flows rather than freezes

Practical Application: Using Intersection Geometry

Meditation:

• Visualize Vesica Piscis as portal between polarities
• Contemplate Yin-Yang as dynamic balance
• See how intersection creates third space (transcendence)

Design:

• Use Vesica Piscis for doorways, windows, arches (portals)
• Use Yin-Yang to balance opposing elements (dark/light, hard/soft)
• Create overlapping circles in floor plans for energy flow

Relationships:

• Two people = two circles
• Healthy relationship = Vesica Piscis (overlap but maintain individuality)
• Yin-Yang balance = each contains seed of other (mutual influence)
• Third element = relationship itself, children, shared creation

Next: Directional Correspondences

We've explored intersection geometry (Vesica Piscis, Yin-Yang). Now we map space to compass directions.

Article 6: Feng Shui Bagua ↔ Directional Correspondences—how directions encode cosmic forces.

Let's continue!