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
• Edge Length — The length of the side of the Reuleaux Triangle

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

3. Importance of Arc Length Calculation

Details: Calculating the arc length is essential in engineering applications, particularly in designing objects of constant width such as drill bits, coins, and mechanical components that require smooth rolling motion.

4. Using the Calculator

Tips: Enter the edge length of the Reuleaux Triangle in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Reuleaux Triangle?
A: A Reuleaux Triangle is a curved triangle with constant width, formed by the intersection of three circular disks.

Q2: Why is the arc length exactly π×edge/3?
A: Because each arc is a 60° segment (1/6 of a circle) of a circle whose radius equals the edge length, making the arc length (π×edge)/3.

Q3: What are practical applications of Reuleaux Triangles?
A: They are used in manufacturing drill bits that can drill square holes, in coin design, and in various mechanical engineering applications.

Q4: Does the Reuleaux Triangle have constant width?
A: Yes, like all Reuleaux polygons, it has constant width equal to its edge length.

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