1. What is the Arc Length of Reuleaux Triangle?

The arc length of a Reuleaux Triangle refers to the length of one of its curved sides. A Reuleaux Triangle is a shape of constant width formed by the intersection of three circular disks, each centered at the vertices of an equilateral triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \pi \) — Mathematical constant approximately equal to 3.14159
• \( r \) — Radius of the Reuleaux Triangle (m)

Explanation: Each arc of the Reuleaux Triangle is exactly one-third of a full circle's circumference, hence the division by 3.

3. Importance of Arc Length Calculation

Details: Calculating the arc length is essential in engineering applications, particularly in mechanical design where Reuleaux Triangles are used for constant-width shapes in drills, manhole covers, and other rotating mechanisms.

4. Using the Calculator

Tips: Enter the radius of the Reuleaux Triangle in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Reuleaux Triangle?
A: A Reuleaux Triangle is a curved triangle with constant width, formed by three circular arcs. It's named after Franz Reuleaux, a German engineer.

Q2: Why is the arc length πr/3?
A: Each arc is a 60° segment of a circle (360°/6), but since the triangle is formed by three intersecting circles, each arc represents 1/3 of a full circle's circumference.

Q3: What are practical applications of Reuleaux Triangles?
A: They're used in drill bits that create square holes, coin designs (UK 20p and 50p coins), and various mechanical components requiring constant width.

Q4: How does the Reuleaux Triangle maintain constant width?
A: Despite not being a circle, the distance between parallel lines tangent to the shape remains constant regardless of orientation.

Q5: Can this formula be used for other Reuleaux polygons?
A: No, this specific formula applies only to the triangular version. Other Reuleaux polygons have different arc length calculations.