Triangle — The First Shape
The triangle is the first polygon — the first two-dimensional shape. Two points connected by a line create only one dimension. But once we connect three points, we gain both height and width — and with that, we enter the world of shapes. My focus is mainly on regular forms, as they serve as the foundation for unfolding patterns and ornamental systems. Sacred geometry, in turn, explains why these forms are considered the building blocks of the universe. I’ll return to this idea often as the blog unfolds.
Facts About the Regular Triangle:
• A regular triangle has all interior angles (i) equal to 60°
• The sum of interior angles in any triangle (regular or not) is always 180°
• The exterior angles (i) of a regular triangle are 120°
• For any polygon, the sum of exterior angles is always 360°
• The regular triangle can tile space on its own (think of triangular mosaics). Only three regular shapes can do this: the triangle, square, and hexagon
• Three of the five Platonic solids are made entirely of regular triangles: the Tetrahedron, Octahedron, and Icosahedron — more on these soon
Symbolic Meanings:
• A triangle in its static position (base down) symbolizes fire, stability, and the masculine principle
• In its dynamic position (pointing down), it represents water and the feminine nature
• With its three sides and three angles, the triangle often stands for trinity — sky-earth-human, body-soul-spirit, past-present-future, or the Holy Trinity
• In alchemy, an upright triangle represents fire (and air when crossed with a line), while the downward triangle symbolizes water (and earth when crossed) — I’ll explore this more in a future post
• The triangle in a circle is the alpha and omega of regular geometric forms — why, will become clear in the article about the Circle
• The triangle with an eye is the Christian symbol of God’s omniscience
• The Radiant Delta, or triangle with a shining eye, is a Masonic symbol representing the Great Architect of the Universe
• I’ll also write separately about the Triquetra (three-lobed knot), another triangle-based symbol
In the Videos:
Video 1: How to construct a regular triangle using a circle, compass, and straightedge
Video 2: How to build a triangular grid
In the next post, we’ll construct the Reuleaux triangle and begin exploring the world of “rounded” geometric figures.
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