Area Of Unicursal Hexagram Given Sections Of Long Diagonal And Short Diagonal Calculator

Formula Used:

\[ A = (d'_{Long(SD)} + d'_{Short(SD)})^2 \times \sin(\pi/3) + 2 \times d'_{Short(SD)} \times d'_{Long} \]

Longest Section of SD of Unicursal Hexagram (d'Long(SD)):

Shortest Section of SD of Unicursal Hexagram (d'Short(SD)):

Section of Long Diagonal of Unicursal Hexagram (d'Long):

Area of Unicursal Hexagram (A):

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1. What is the Area of Unicursal Hexagram?

The Area of Unicursal Hexagram is defined as the total quantity of the region enclosed within the Unicursal Hexagram. It is calculated based on specific sections of the diagonals of the hexagram.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = (d'_{Long(SD)} + d'_{Short(SD)})^2 \times \sin(\pi/3) + 2 \times d'_{Short(SD)} \times d'_{Long} \]

Where:

\( A \) — Area of Unicursal Hexagram (m²)
\( d'_{Long(SD)} \) — Longest Section of SD of Unicursal Hexagram (m)
\( d'_{Short(SD)} \) — Shortest Section of SD of Unicursal Hexagram (m)
\( d'_{Long} \) — Section of Long Diagonal of Unicursal Hexagram (m)
\( \sin(\pi/3) \) — Sine of π/3 (approximately 0.866025)

Explanation: The formula combines geometric properties of the hexagram, utilizing the sum of sections of the short diagonal squared, multiplied by the sine of π/3, and added to twice the product of the shortest section of the short diagonal and the section of the long diagonal.

3. Importance of Area Calculation

Details: Calculating the area of a Unicursal Hexagram is important in geometric studies and applications, providing insight into the properties and dimensions of this specific shape.

4. Using the Calculator

Tips: Enter the longest and shortest sections of the short diagonal, and the section of the long diagonal, all in meters. Ensure all values are positive and valid.

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 line without lifting the pen from the paper.

Q2: Why use this specific formula for area calculation?
A: This formula is derived from the geometric properties of the Unicursal Hexagram, specifically relating the sections of its diagonals to the enclosed area.

Q3: What are the units of measurement for the inputs?
A: All inputs should be in meters (m), and the resulting area will be in square meters (m²).

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal inputs for more precise calculations.

Q5: Is the sine value in the formula fixed?
A: Yes, \( \sin(\pi/3) \) is a constant value approximately equal to 0.8660254037844386.