equal to the chord BC.

This is the

[Seggern, p. 88], [Booth, II, p. 163].

Considering arbitrary values for the parameter in the last equation and taking in particular s=sqrt(2) we obtain the

Another view of this curve and some additional remarks are presented in Hippopede2.html .

is that it has basis DE of length twice the length of BC. The hippopede can be considered as the path described by

vertices {D,E} as the trapezium changes position by requiring:

a) that BC passes through the fixed A,

b) that DE passes through the fixed O,

c) that DE has double the length of BC.

What about an isosceles trapezium varies satisfying conditions {a,b,c} but allowing in (c) more general than k=2

for the ratio k=DE/BC? The interesting cases occur when O is not the center of DE. In fact, it is easily seen that

for this particular case the resulting curve is homothetic to an hippopede. A figure illustrating the general case in

which point O is not the middle of DE can be seen in Hippopede_Gen.html .

Hippopede_Gen.html

[Lockwood] Lockwood, E. H.

[Mathcurve] Robert Ferreol

[Seggern] David von Seggern

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