The Convex Sets Of Constant Width Besed On The Top Fan For Artifacts

The convex sets of constant width have been the focus of attention because of the special nature of other convex set does not. They have a wide range of applications in mechanical engineering, architecture, medicine and other fields, so there is very important practical application value structuring and studying convex sets of constant width.First, This article will convex sets of constant width click can guide on the side of the convex set number, divided into angular point, first order point is three categories, such as second order point and study of these three point on the boundary.Let x be a angular point on the boundary of some convex sets K of constant width w,then there exists a arc of circle of radius w width center x on the boundary of the convex sets K of constant width w;There is a curvature radius at any point on the boundary of some convex setsK of constant width w, and r(x)=w0,then the curvature radius of the pointy=x-w·v on the boundary of some convex sets K of constant width w is r(y)=w- w0.Second, this paper constructed a new class of convex sets of constant width Based on the top fan for artifacts, and gives the specific ruler gauge drawing method. Such convex bodies of constant width includes Reuleaux polygon and isosceles trapezoid of constant width structured.