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Date: 16-9-2021
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Date: 7-10-2021
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Date: 21-8-2021
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A curve named after James Watt (1736-1819), the Scottish engineer who developed the steam engine (MacTutor Archive). The curve is produced by a linkage of rods connecting two wheels of equal diameter. Let the two wheels have radius and let their centers be located a distance
apart. Further suppose that a rod of length
is fixed at each end to the circumference of the two wheels. Let
be the midpoint of the rod. Then Watt's curve
is the locus of
.
The polar equation of Watt's curve is
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(1) |
The areas of one of the inner lenses, heart-shaped half-region, and entire enclosed region (which resembles a lemniscate are
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(2) |
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(3) |
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(4) |
If , then
is a circle of radius
with a figure of eight inside it.
REFERENCES:
Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 162, 1967.
MacTutor History of Mathematics Archive. "Watt's Curve." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Watts.html.
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