In this text we will limit ourselves to the latter. Two mathematical fields are particularly apt for describing such occurrences: the theory of fractals and non-Euclidean geometry, (especially hyperbolic geometry). They found suggestive models useful in understanding such patterns and discovered new applications. Over the last few decades a growing number of mathematicians worked on making theoretical advances in the study of patterns similar to the ones pictured above. The beauty embedded in these naturally occurring patterns is not only pleasurable but also intriguing. You might see arrangements no less interesting than the ones discernable in the vegetables. Or walk over to the floral department and search for flowers with sophisticated conformations. Look, for instance, at the Romanesco broccoli, at kale and lettuce, and at the pineapple. Next time you are in the produce section of a supermarket, take a close look at some fruits and vegetables with particularly interesting configurations. We are not always well served by the millennia-long mathematical acculturation that pervades even our best available instruction in school geometry.Ĭurious geometrical patterns are ubiquitous.
Some of these deceptively “clear” terms remain more ambiguous than a cursory view accords them. Similarly, delimitating enclosures, building shelters, and accommodating small hierarchical or egalitarian communities must have presupposed an appreciation for the notions of center, equidistance, length, area, volume, straightness. Building a good hunting bow and getting the best arrows for it surely involved some intuitive appreciation of space, direction, distance, and kinematics. Geometry must be as old as humans’ struggle for survival.
Non euclidean geometry in geography pdf#
There are also three instructional modules inserted as PDF files they can be used in the classroom. The aim of this text is to offer a pleasant guide through the many online resources on non-Euclidean geometry (and a bit more). Good expository introductions to non-Euclidean geometry in book form are easy to obtain, with a fairly small investment. Non-Euclidean Geometry Online: a Guide to Resources
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