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If p differs little from cz/2, the waist is hardly noticeable, and for p equal to or greater than cz/2 the waist disappears completely and the lemniscate takes the form of an oval (Fig. 35; the figure also shows some other lemniscates for comparison). 18. The Lenmiscate with Arbitrary Number of F oci Take an arbitrary number of points F1, F2, F ,, in the plane and make a point M move so that the product of its distances from all the points taken is always constant. , F ,, and the value of the constant product.

G SE 3S >~ 0 cn EE 3 c: ¤ Smh ·•-· Q. E =·—. ¤¤ E ¤ Lu CU ¤E0 <: 8¢é·°$ n. ‘~ 2 iii? ‘* gs -DL•.. “;-'13 2é*E¤%$.

38), and number these positions thus 0, I, 2, 3, 4, 5, 6 I n order to go from one position to the next one the loop has to rotate one—sixth of the whole revolution (as the distance between two neighbouring points is equal to one-sixth of the circumference of the circle). , A, OI23456 Figure 38 Thus, if in position O the chalk is at the point M 0, in position I it will be at the point M 1 (at one·sixth of the circumference from the point of tangency), in position 2 at the point M 2 (at two·sixths of the circumference from the point of tangency), and so on.

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A Handbook for Designing Mathematics Laboratory in Schools by Hukum Singh


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