Long Diagonal Of Unicursal Hexagram Given Medium Section Of Short Diagonal Calculator

Formula Used:

\[ d_{Long} = \frac{6 \times d'_{Medium(Short Diagonal)}}{\sqrt{3}} \]

Long Diagonal of Unicursal Hexagram:

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1. What is 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 is an important geometric property of this unique six-pointed star shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Long} = \frac{6 \times d'_{Medium(Short Diagonal)}}{\sqrt{3}} \]

Where:

\( d_{Long} \) — Long Diagonal of Unicursal Hexagram (m)
\( d'_{Medium(Short Diagonal)} \) — Medium Section of Short Diagonal of Unicursal Hexagram (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula establishes the mathematical relationship between the medium section of the short diagonal and the long diagonal of a unicursal hexagram, using the constant ratio derived from the geometric properties of the shape.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is crucial for understanding the complete geometry of unicursal hexagrams, which have applications in various fields including sacred geometry, architectural design, and mathematical research on star polygons.

4. Using the Calculator

Tips: Enter the medium section of the short diagonal in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding long diagonal length.

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 drawing instrument from the surface.

Q2: How does this differ from a regular hexagram?
A: Unlike a regular hexagram which consists of two overlapping triangles, a unicursal hexagram is drawn with a single continuous line, creating different geometric properties.

Q3: What are practical applications of this calculation?
A: This calculation is useful in geometric design, sacred geometry studies, architectural planning involving star shapes, and mathematical research on polygon properties.

Q4: Can this formula be derived from first principles?
A: Yes, the formula can be derived using trigonometric relationships and the specific angle properties (60° angles) inherent in hexagram geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input value is accurate. The result will have the same precision as your input measurement.