Back to the Circle

Reviewers of Beauty for Truth's Sake have been kind, but even the most ecstatic would admit that there are weak and even silly patches in the book, especially in the chapter called "The Golden Circle", where I play with some ideas relating theology and mathematics (inspired by Simone Weil's work and Vance Morgan's excellent book on her). Apart from anything else, I came up with a concept called "the Golden Circle" and wasn't able to develop it properly, since I lack the mathematical ability to do so. The "Circle" was simply a Golden Rectangle inscribed in a circle, which I thought one could use to explore the relations of Pi to Phi (Φ and π are connected together by the fact that the Golden Rectangle’s diagonal forms the diameter of the circle).

But my conception of the Golden Circle has evolved, and Michael Schneider has kindly redrawn it for me on the right (an intermediate stage was discussed in an earlier post). The Golden Circle itself is now a Golden Ring, shown in yellow. There are in fact three circles, one inscribed within the short sides of a Golden Rectangle, one inside the long sides, and one through the corners of the rectangle. On the basis of Pythagoras's Theorem, a large number of relationships can be established between areas and lengths in this figure, since we know that the circumference of a circle is Pi multiplied by the diameter, and the area is Pi multiplied by the radius squared. For example, the circumference of the middle-sized circle (the outside of the yellow ring) is Pi times Phi. But I'll leave you to work out what the rest of them are. Let me know sometime. It might make a nice exercise for a geometry class. The theology can wait.