Spike Height of Polygram Calculator

Spike Height of Polygram Formula:

\[ h_{Spike} = \sqrt{\frac{(4 \times l_e^2) - l_{Base}^2}{4}} \]

Spike Height of Polygram (hSpike):

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1. What is the Spike Height of Polygram?

The Spike Height of Polygram is the height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes. It represents the perpendicular distance from the base to the apex of the triangular spikes.

2. How Does the Calculator Work?

The calculator uses the Spike Height of Polygram formula:

\[ h_{Spike} = \sqrt{\frac{(4 \times l_e^2) - l_{Base}^2}{4}} \]

Where:

\( h_{Spike} \) — Spike Height of Polygram (m)
\( l_e \) — Edge Length of Polygram (m)
\( l_{Base} \) — Base Length of Polygram (m)

Explanation: This formula calculates the height of the isosceles triangles that form the spikes of a polygram, derived from the Pythagorean theorem applied to the triangular geometry.

3. Importance of Spike Height Calculation

Details: Calculating the spike height is essential for determining the overall dimensions and proportions of polygram shapes, which is important in geometric design, architecture, and various mathematical applications involving polygrams.

4. Using the Calculator

Tips: Enter the edge length and base length of the polygram in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a polygram?
A: A polygram is a star-shaped polygon formed by connecting non-adjacent vertices of a regular polygon, creating spikes or star points.

Q2: How is the spike height related to the polygram?
A: The spike height determines how far the triangular spikes extend from the base polygon, affecting the overall appearance and dimensions of the polygram.

Q3: Can this formula be used for all types of polygrams?
A: This specific formula applies to polygrams where the spikes are isosceles triangles with the given edge and base length relationships.

Q4: What units should be used for the inputs?
A: The calculator uses meters as the default unit, but any consistent unit of length can be used as long as both inputs are in the same unit.

Q5: What if I get a negative value inside the square root?
A: A negative value indicates that the given edge and base lengths cannot form a valid triangle according to the triangle inequality theorem. Please check your input values.