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A smooth curve that is not closed is often referred to as a smooth arc. [6] The parametrization of a curve provides a natural ordering of points on the curve: () comes before () if <. This leads to the notion of a directed smooth curve. It is most useful to consider curves independent of the specific parametrization.
Jansen's linkage is a planar leg mechanism designed by the kinetic sculptor Theo Jansen to generate a smooth walking motion. [1] Jansen has used his mechanism in a variety of kinetic sculptures which are known as Strandbeesten ( Dutch for "beach beasts").
SketchUp is a 3D modeling software that is used to create and manipulate 3D models. It is used in architecture and interior design.. SketchUp is owned by Trimble Inc. The software has a free web-based version, and three paid subscriptions to gain access to applications for Windows and macOS.
Every bounded convex curve is a rectifiable curve, meaning that it has a well-defined finite arc length, and can be approximated in length by a sequence of inscribed polygonal chains. For closed convex curves, the length may be given by a form of the Crofton formula as times the average length of its projections onto lines. [8]
Any regular curve may be parametrized by the arc length (the natural parametrization). From the point of view of a theoretical point particle on the curve that does not know anything about the ambient space, all curves would appear the same. Different space curves are only distinguished by how they bend and twist.
It is used in manual drafting and in fashion design to draw smooth curves of varying radii. The curve is placed on the drawing material, and a pencil , knife or other implement is traced around its curves to produce the desired result.
Before the full formal development of calculus, the basis for the modern integral form for arc length was independently discovered by Hendrik van Heuraet and Pierre de Fermat. In 1659 van Heuraet published a construction showing that the problem of determining arc length could be transformed into the problem of determining the area under a ...
For a curve C given by a sufficiently smooth parametric equations (twice continuously differentiable), the osculating circle may be obtained by a limiting procedure: it is the limit of the circles passing through three distinct points on C as these points approach P. [3]