A Plane Quartic with Eight Undulations
1950 ◽
Vol 8
(4)
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pp. 147-162
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1. The chief purpose of this paper is to demonstrate the existence of a plane quartic curve with eight undulations, an “undulation” being a point at which the tangent has four-point contact. It is shown that the curvewhere (x, y, z) are homogeneous point-coordinates and f a constant, has undulations at the eight points The curve has, in addition to these undulations, eight inflections which are; in general, distinct. But there are two geometrically different possibilities of their not being distinct, and in either instance they coincide in pairs at four further undulations. Thus two types of curve arise without any ordinary inflections at all, their 24 inflections coinciding in pairs at 12 undulations.
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1935 ◽
Vol 31
(2)
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pp. 174-182
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Keyword(s):
1991 ◽
Vol 109
(3)
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pp. 419-424
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1924 ◽
Vol 22
(1)
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pp. 24-25
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2017 ◽
Vol 32
(14)
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pp. 2631-2637
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1969 ◽
Vol 27
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pp. 160-161
1983 ◽
Vol 41
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pp. 708-709
1974 ◽
Vol 32
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pp. 436-437
1978 ◽
Vol 36
(1)
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pp. 548-549
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1978 ◽
Vol 36
(1)
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pp. 540-541