definition

With each vertex of an equilateral triangle as the center and the side length as the radius, an arc is inserted between the other two vertices, and the curved triangle surrounded by three arcs is the Leroy triangle (reuleaux? Triangle), also known as Rullo Triangle?

Leroy Triangle was first discovered by Leroy (1829 ~ 1905), a German mechanical engineer and sportsman, and was named after him.

nature

Fixed width curve and fixed width

The concept of fixed-width curve: A curve with a fixed width (similar to a circle) is called a fixed-width curve. ?

Geometrically speaking, if a circle is placed between two parallel lines and tangent to them, it can be realized that no matter how the circle moves, it is still in these two parallel lines and always tangent to them. ?

Leroy triangle is a typical fixed-width curve. ?

It is easy to prove that the width of Leroy triangle is equal to the side length of equilateral triangle. When a Leroy triangle rotates in a square whose side length is its width, the trajectory of each corner is basically a square. ?