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 points in this geometric shape.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( d_{Long} \) — Long Diagonal of Unicursal Hexagram (m)
• \( l_e \) — Edge Length of Unicursal Hexagram (m)

Explanation: The long diagonal is exactly twice the length of any edge in a unicursal hexagram, making this a straightforward geometric relationship.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is essential for understanding the complete geometry of the unicursal hexagram, determining its overall dimensions, and for various applications in geometric design and mathematical analysis.

4. Using the Calculator

Tips: Enter the edge length of the unicursal hexagram in meters. The value must be positive and valid for accurate calculation.

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.

Q2: How does the long diagonal relate to other dimensions?
A: The long diagonal is the largest dimension of the hexagram and is exactly twice the length of any individual edge.

Q3: Can this formula be used for any size hexagram?
A: Yes, this geometric relationship holds true for unicursal hexagrams of any size, as long as the shape maintains its proportional geometry.

Q4: What are practical applications of this calculation?
A: This calculation is useful in geometric design, architectural planning, artistic compositions, and mathematical studies of geometric properties.

Q5: Is the long diagonal always exactly twice the edge length?
A: Yes, in a perfect unicursal hexagram, this mathematical relationship is consistent and reliable for calculation purposes.