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Worksheet on Hyperbolic Geometry The formula for the circumference of a circle of radius r, in the ‘hyperbolic’ plane is _____________________________ . The growth of the circumference is _________ on the sphere, _________ in the plane and ___________ in the ‘hyperbolic’ geometry. The program KaleidoTile can be found at the website _______________________. Since triangles are ‘thin’ in the hyperbolic geometry setting the symmetry to _____ will put you into the tiling. For a binary tree (part of the hyperbolic plane) each parent has ____ daughters. This means the number of descendents in the nth generation is __________. Most bacteria grow in ___________, one example is plaque. From the graph of the neocortex, the hyperbolic structure allows for messages to ______________________________________. In the true circle model as beautifully displayed by Escher, geodesics inside the painting are _________________________. True or False, through any point P not on a line L, there is a unique parallel line to L?