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The reuleaux triangle is made when circles are drawn from the vertices of equilateral traingles. Its constant width and curved edges make it appropriate for many applications.
Aside from a circle, what other shapes can a manhole be so that it won’t fall through the hole? One of the answers to this question is a Reuleaux triangle.
A Reuleaux triangle, also called a spherical triangle, is a shape made with intersecting curves when circles are drawn from the vertices of an equilateral triangle. This shape has a constant width when rotated, which makes it useful for many purposes. Studied by the legendary likes of Leonardo da Vinci and Leonhard Euler, it is used in various applications, such as mechanical motors, architectural windows, guitar picks and graphical signages, among others.
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Construction Of Reuleaux Triangle
The Reuleaux Triangle is named after Franz Reuleaux, the 19th-century German engineer who advanced the study of machines by converting one form of energy into another. He used this specialized triangle in many of his designs.
The construction of the Reuleaux Triangle is fairly straightforward:
- Make an equilateral triangle
- Using a compass, draw a circle, taking one of the vertexes as the midpoint and connecting the other two vertices on the edge of the circle being drawn.
- Repeat step 2 by taking the other points as the center, respectively.
Mathematical Properties Of Reuleaux Triangle
Curve With A Constant Width
The first clear property that the Reuleaux Triangle shows is its constant width when two parallel supporting lines are drawn from any surface, regardless of the orientation of the lines. The distance between the parallel lines is the radius of the circle drawn from the vertices to make the Reuleaux Triangle.
In Nature
The structure of soap bubbles has intrigued scientists for centuries, as it forms a fractal-like arrangement of varying sizes of bubbles.
In Closing
The Reuleaux Triangle has been used in many ways and in many things. Its three equal curved side and constant curve width make it desirable for many applications. Its structural stability and the small perimeter have seen its application in architecture and mechanical design as well. To this day, many new approaches to its application are being explored on new products.
