Consider the maps [0, 1] R given as g(t) = (cos 4t, sin 4t). f(t)...

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Consider the maps [0, 1] › R² given as g(t) = (cos 4πt, sin 4πt). f(t) = (cos 2πt, sin 2πt), Describe the maps f and g geometrically. (b) Illustrate a homotopy between f and g. (c) Viwed as a family of maps, describe the maps appearing in the homotopy you constructed in item (b). Consider the maps [0, 1] › R² given as g(t) = (cos 4πt, sin 4πt). f(t) = (cos 2πt, sin 2πt), Describe the maps f and g geometrically. (b) Illustrate a homotopy between f and g. (c) Viwed as a family of maps, describe the maps appearing in the homotopy you constructed in item (b).

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