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Pi as a Parameter

If we like, we can ever be quantitative about the degree of curvature of our embedded hypersurface. Picture the following construction: attach a string of length r to a fixed centre and tie a pencil to the other end. Keeping the string tight, draw a circle around the centre with radius r. Now take out a measuring device and run it around the perimeter to measure the circumference of the circle, . The ratio can be defined to be . If the hypersurface to which we are confined is "flat," then will be equal to the value we know, ; but if we are on a curved (or "warped") hypersurface then we will get a "wrong" answer, .


Jess H. Brewer - Last modified: Mon Nov 23 16:39:22 PST 2015