The questions raised are i) what do you get when you make a slice parralel to the plane or line but not containing the plane or line? or ii) what do you get when you make a slice at an angle to the plane or line? or iii), can you slice the four dimensional wave fronts of the plane using two dimensional planes rather than hyperplanes to give two dimensional slices of a point's wave front? You surely can slice it to give wave fronts of a line in the plane, just remove one of the dimensions of the hyperplane that gave you the lines wave fronts in three dimensions.Īnother interesting idea to explore, which is of vital importance in electricity and magnetism in physics, is the wave fronts of non-closed or non-infinite figures. The phenomenon of slicing a line's waves in three space to give either i) the wave fronts for a point in 2 space when sliced perpundicular to the line, or ii) the wave fronts for a line in 2 space when the slice contains the line, is very interesting and can be expanded dimensionally: the wave fronts of a plane in four dimensions can be sliced i) by a perpundicular hyperplane to give the three dimensional wave fronts of a line, or ii) containing the plane to give the three dimensioal wave fronts of the plane. Specifically, the waves of two dimensional objects in three space are quite interesting. This chapter seems like an introduction to the large number of ideas that can be examined concerning these waves.Įspecially interesting aspects are uncovered when we move things out of their dimensional constrains.
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