oval of Cassini

oval of Cassini

[′ō·vəl əv kə′sē·nē]
(mathematics)
An ovallike curve similar to a lemniscate obtained as the locus corresponding to a general type of quadratic equation in two variables x and y; it is expressed as [(x + a)2+ y 2] [(x-a)2+ y 2] = k 4, where a and k are constants. Also known as Cassinian oval.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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denotes the (i, j)-th Brauer oval of Cassini for A, then similarly
In this case, as each Brauer oval of Cassini [K.sub.i,j](A), i [not equal to] j, corresponds to a circuit (of length 2) in B(A), it follows from (2.7) that K(A) _ B(A), but as the reverse inclusion holds in (3.1), then