The Conics of Ludwig Kiepert:

If a visitor from Mars desired to leam the geometry of the triangle but could stay in the earth' s relatively dense atmosphere only long enough for a single lesson, earthling mathematicians would, no doubt, be hard-pressed to meet this request. In this paper, we believe that we have an optimum solution to the problem. The Kiepert conics, though seemingly unknown today, constitute a significant part of the geometry of the triangle and to study them one has to deal with many fundamental concepts related to this geometry such as the Euler line, Brocard axis, circumcircle, Brocard angle, and the Lemoine line in addition to weIl-known points including the centroid, circumcentre, orthocentre, and the isogonic centres. In the process, one comes into contact with not so weIl known, but no less important concepts, such as the Steiner point, the isodynamie points and the Spieker circle. In this paper, we show how the Kiepert' s conics are derived using both analytic and projective arguments and discuss their main properties, which we have drawn together from several sourees. We have applied some modem technology, in this case computer graphics, to produce aseries of pictures that should serve to increase the reader' s appreciation for this interesting pair of conics. In addition, we have derived some results that we were unable to locate in the available literature.