30 July 2014
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Paper Information

Families of plane curves with a constant arc length

Author(s): Tilak de Alwis

Abstract:
In this paper, we will consider envelopes of several types of one parameter families of curves in the first quadrant with a constant arc length.

One can use Mathematica to get various information on these envelopes. 1 Introduction We will consider several types of one parameter families of curves in the first quadrant with a constant arc length.

Each member of the family we are considering, will have a unique ^-intercept and a ^-intercept.

We assume that each member of the family has a fixed arc length k between those two intercepts.

The different types of families under discussion include, families of straight lines, parabolas, ellipses, and square root functions. Using Mathematica, one can plot various members of such families, and obtain parametrizations for their envelopes.

One can also use Mathematica to obtain certain conjectures about the envelopes.

The reader can...

Pages: 8
Size: 564 kb
Paper DOI: 10.2495/IMS970061

 

 

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Innovation in Mathematics

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