1. What is the Long Diagonal of Unicursal Hexagram?

The Long Diagonal of Unicursal Hexagram is defined as the longest straight line joining two opposite corners of a Unicursal Hexagram through its vertex. It represents the maximum distance between two vertices in this geometric configuration.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( Short Diagonal \) — The shortest straight line joining two opposite corners of the Unicursal Hexagram (in meters)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula establishes the precise mathematical relationship between the short and long diagonals in a unicursal hexagram, derived from geometric properties and trigonometric relationships.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is essential for geometric analysis, architectural design involving hexagram patterns, and understanding the proportional relationships within unicursal hexagrams. It helps in determining the overall dimensions and spatial requirements for designs incorporating this geometric shape.

4. Using the Calculator

Tips: Enter the short diagonal value in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding long diagonal using the mathematical relationship between these two dimensions.

5. Frequently Asked Questions (FAQ)

Q1: What is a unicursal hexagram?
A: A unicursal hexagram is a six-pointed star that can be drawn in one continuous movement without lifting the pen from the paper, unlike the traditional Star of David which requires two overlapping triangles.

Q2: Why is the square root of 3 used in the formula?
A: The square root of 3 appears naturally in equilateral triangles and regular hexagrams due to the 60-degree angles and trigonometric relationships inherent in these geometric shapes.

Q3: Can this formula be used for any size of unicursal hexagram?
A: Yes, the formula maintains the same proportional relationship regardless of the hexagram's size, as it's based on the geometric properties of the shape.

Q4: What are practical applications of this calculation?
A: This calculation is useful in geometric design, architecture, sacred geometry studies, artistic compositions, and any application requiring precise dimensional relationships in hexagram-based patterns.

Q5: How accurate is the calculated result?
A: The result is mathematically exact based on the input value, with the calculation performed to six decimal places for precision in most practical applications.