Cuspidal Rosettes
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Authors
Rigge, William F., S.J.
Issue Date
1919-10
Volume
26
Issue
Type
Article
Language
en_US
Keywords
Rigge Papers , Harmonic Curves
Alternative Title
Abstract
First Paragraph:
The rose, rosette, rosace, Rosenkurve or multifolium, or whatever other name it may have, is a periodic polar curve whose equal sectors may have any angular magnitude. Its general equation, as usually given, p = a + b sin nθ,3 supposes the tracing point to move with a simple harmonic motion of n cycles along a radial line through the pole, at the same time that it makes one revolution about this pole with uniform angular speed. A simple instance of such a polar curve is the trifolium, Fig. 1 (p. 324), which is drawn by having a tracing pen move with simple harmonic motion of amplitude b in a radial line over a uniformly rotating disk in such a way that the pen just touches its centre without passing beyond, and the disk makes one revolution in three cycles of the pen. The equation is then p = a(1 — sin 3θ), as is seen by inspection in Fig. 2.
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