PROPORTION · ROOT RECTANGLE
What is a
Root 3 rectangle?
A Root 3 rectangle has sides in the proportion √3:1. Its longer side is approximately 1.7320508076 times its shorter side.
The proportion can be extended with diagonals and reciprocal lines to form a compositional armature.
The example opens as an editable Construct document.
- Exact ratio
- √3 : 1
- Decimal
- 1.732050807568…
- Not the same as
- 3:2 = 1.5:1
01 · RATIO
√3 is a proportion
before it is a grid.
If the short side is 1 unit, the long side is √3 units. The value is irrational, so its decimal expansion does not terminate. In practice, software can preserve the exact expression while displaying a useful approximation.
Norma uses √3 internally and shows 1.732 only when a human-readable approximation is useful.
02 · CONSTRUCTION
Diagonal, reciprocal,
relationship.
The rectangle’s main diagonal establishes its long directional movement. Reciprocal lines intersect that diagonal and generate related subdivisions. Together they can guide alignments, scale changes and the placement of smaller fields.
03 · GEOMETRIC FAMILY
One root,
four revelations.
The √3 proportion appears naturally in the regular hexagon and vesica piscis, measures the body diagonal of a unit cube, and reproduces itself when a landscape Root 3 rectangle is divided into three equal vertical fields.
Geometric references
- John Kappraff — The Root Three System — Hexagon, vesica piscis and cube relationships.
- Wolfram MathWorld — Vesica Piscis — Circle intersections and inscribed equilateral triangles.
04 · COMPOSITION
The armature organizes.
The content communicates.
The poster uses an exact portrait Root 3 field inside its 4:5 frame. Its generated diagonals, reciprocals and color regions are visible in this preview and remain editable in Construct.
05 · COMPARE
Know every ratio
by its character.
| Frame | Exact ratio | Decimal | Character |
|---|---|---|---|
| Root 3 | √3:1 | ≈ 1.732:1 | Longer and more directional than 3:2. |
| 3:2 | 3:2 | 1.5:1 | Common, compact landscape relationship. |
| Golden | φ:1 | ≈ 1.618:1 | Between 3:2 and Root 3. |
| Root 2 | √2:1 | ≈ 1.414:1 | The ISO paper-family proportion. |
06 · QUESTIONS
Root 3, precisely.
What is the ratio of a Root 3 rectangle?
Its longer side is √3 times its shorter side, approximately 1.7320508076:1.
Is a Root 3 rectangle the same as a 3:2 rectangle?
No. 3:2 equals 1.5:1; √3:1 is approximately 1.732:1.
Why use it in composition?
Its diagonal and reciprocal constructions create related positions and directions that can support hierarchy and movement.
Does the rectangle need to be visible?
No. It can define the frame or operate as an armature inside another region.
07 · RELATED
Place the ratio in context.
Open the armature.
Change the hierarchy.
Inspect the actual Root 3 poster document, then move beyond the example.