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The Long Diagonal of an Octagon is the longest straight line that can be drawn between two opposite vertices of a regular octagon. It passes through the center of the octagon and is an important geometric property used in various mathematical and engineering applications.
The calculator uses the formula:
Where:
Explanation: This formula calculates the long diagonal length based on the inradius of a regular octagon, using mathematical constants derived from the octagon's geometric properties.
Details: Calculating the long diagonal is essential in geometry, architecture, and engineering for determining the maximum span across an octagonal structure, designing octagonal components, and solving geometric problems involving regular octagons.
Tips: Enter the inradius of the octagon in meters. The value must be positive and greater than zero. The calculator will compute the corresponding long diagonal length.
Q1: What is a regular octagon?
A: A regular octagon is an eight-sided polygon where all sides are equal in length and all interior angles are equal (135 degrees each).
Q2: How is inradius different from circumradius?
A: Inradius is the radius of the inscribed circle (touching all sides), while circumradius is the radius of the circumscribed circle (passing through all vertices).
Q3: Can this formula be used for irregular octagons?
A: No, this formula applies only to regular octagons where all sides and angles are equal.
Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, mechanical engineering, carpentry, and any field dealing with octagonal shapes and structures.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octagons, with accuracy depending on the precision of the input value.