Jesús de la Peña Hernández
21.2 CYCLIC SECTIONS DEFORMABLE ELLIPSOID (CYCLIC ELLIPSOID)
Cyclic sections of an ellipsoid are those produced in it by planes whose intersections are
circumferences.
Fig. 1 shows the horizontal main elliptical section of the ellipsoid with its horizontal
axes a = OA; b = OB. Let the steps to give, in order to get the third half-axis c, being c > b:- To draw any tangent t; its point of contact will be the umbilical point U.
- To trace any secant 11 parallel to t, outside OA.
- Within segment OU, divide OV in n equal parts. We have made n = 3 for the sake of
simplicity. - To find the figure that is homothetic to OVU11 with center O and ratio 1.
- To divide OV ́ in three equal parts as done for segment OV.
- Through these intersection points (besides O and V ́), draw parallels to t within the
ellipse. - Fig. 2 shows two pencils of parallel secants: the one obtained in step 6, plus its
symmetric with respect to axis OX.
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