Curves and surfaces of constant width
#constant width#orbiform#surface of revolution#Reuleaux triangle#lambda-convexity#Meissner
Date of design: 1911
Designer: Prof. Dr. Ernst Meissner in Zürich
Title in the catalog: (de) Modell Nr. 2 ist die Rotationsfläche des Reuleaux'schen Kreisbogendreiecks.
Size: 12x12x12 cm
Price in the catalog: 40 marks (for models No. 1-3, measuring apparatus and cloth cylinders)
Surface (body) of constant width is the surface such that the distance between any two parallel tangent (supporting) planes is constant.
An intersection of three equal discs, whose centers are placed in the vertexes of a right traingle and radii equal to its side-length, is a Reuleaux triangle. It is a curve of constant width.
The model is obtained by rotating such a triangle around one of its axes.