July 19, 2010

Of Thinking beyond flat lines and surfaces !

We always think in terms of lines, circles and all kinds of euclidean geometric shapes. But the world we live in is far from those perfect rules of Euclidean Geometry. Is it always true that given a line and a point, you can only draw one line through that point parallel to the given line ?
Try this simple experiment, find a free space in your garden or somewhere, fix a point as centre, and then walk around the point in a circular path while tracing the path. Now fix five equidistant points on the circular path, join each of these points to the centre, measure the angle subtended by each of the five segments of the circular path at the centre, what will be the sum of these angles ? should it not be 360 degrees ? why am I even asking this question ??. Think Again !, if  it is not the standard value you expected, can you explain why it is not ? Check out the terms Curvature , Geodesic, Riemannian Geometry, Tensors.

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