Crcles V Ellipses

Many years ago when Gavin first got involved in what we then called Witchcraft, we became interested in the confusion that reigned over the size of the Circle within which religious services should be performed. There seemed to be two general opinions: 1. A circle with a diameter of nine (9) feet 2. A circle with a diameter of eleven (11) feet. Neither dimension fitted the dimensions of the ancient stone circles that dominate the landscape all over Europe, from Shetland/Orkney to Malta. When Professor Alexander Thom went out and measured many of those circles, he came to the conclusion that they were all built to a standard that he called the Megalithic Yard: 2.71 feet in the English measure of today. Four times that dimension gave him (and us) a circle with a diameter of 10.84 feet. Thus Gavin decided to use that dimension as part of the Church of Wicca's teaching. Later popular thought said that the dimension of the outermost circle, the one designed to keep back the abyss, should have a dimension of an indivisible number of units, ie 17 Ft. and that circles cast within that outer circle should be representative of the earthplane and the spiritual plane respectively as the worshippers who met at the circle site moved from the outermost circumference toward the center. A conclusion became fairly obvious: that those two circles should have circumferences of 16 Ft and 15 Ft respectively, because with circles of such dimensions it would be easy to construct a square representing the earthplane and a pentacle representing the spiritual plane. Such an approach equates nicely with the idea that the hearthstone (Welsh pentanfaen) also represents earth and spirit. In the 1970s further reflection led to the idea that for modern Wicca a "circle" should in fact be an ellipse, because that would give two foci: one for the male flamen and one for the female flamenca. It became a mathematical nightmare when we tried to make the circumferences of the ellipses 17, 16, and 15 MY. Indeed, we are hereby setting this out as a problem for you to solve. Drawing an ellipse is easy: Drive two stakes into the ground. Take a rope loop around them and out to a marker. By simply keeping the rope loop taut you can draw an ellipse. Let us suppose it would be nice to include the Megalithic Yard in your construction. We (the Church of Wicca) hereby offer a free Advanced Course (value $220) to the person who can come up with a workable mathematical solution to this challenge. To summarize: If you put two stakes into the ground separated by a distance of two Megalithic Yards (5.44 English feet), how long must the cord be to cast ellipses with circumferences of 17, 16, and 15 MY? Practically, you can do it by actually taking a rope and some pegs and changing the length of the rope a little at a time until you get an answer. What we're asking for here is a mathematical expression of the solution. Good luck. Send your solution to PO Box 297, Hinton, WV 25951.