This orange is a terrific source of both vitamin C and symmetry. Though some 'slices' seem to be further segmented, there are ten main slices, as well as an even distribution of the fruits pith and rind around the outer edge of this rosette's perspective. Any way it is cut straight across by it's diameter will produce two equal halves.
The pattern is preserved under a rotation by certain angles corresponding to the number of slices. It has has approximate isometry, in that if any of the ten slices are rotated around the center point of 36n degrees (360 degrees divided by the ten halves; n meaning any multiple of 36 degrees by which one can rotate the slice) this bisected fruit, it will correctly map onto and continue the general pattern of this rosette. Also, any portion of this perspective of the orange reflected over its center point would result in symmetry.
As a rosette is by definition, this fruit's pattern has symmetries only rotated about a single point and reflections through that point, and there are no translations nor glide reflections. Its repetition is in its slices around its center column and it highly decreases the likelihood of falling victim to scurvy. Orange you glad it has such nice symmetry?... okay I'm done.
As the orange has reflectional symmetry, it would be classified as a dihedral rosette (dn), rather than a cyclic rosette (cn), which are rosettes without reflectional symmetry.
This orange is a terrific source of both vitamin C and symmetry. Though some 'slices' seem to be further segmented, there are ten main slices, as well as an even distribution of the fruits pith and rind around the outer edge of this rosette's perspective. Any way it is cut straight across by it's diameter will produce two equal halves.
ReplyDeleteThe pattern is preserved under a rotation by certain angles corresponding to the number of slices. It has has approximate isometry, in that if any of the ten slices are rotated around the center point of 36n degrees (360 degrees divided by the ten halves; n meaning any multiple of 36 degrees by which one can rotate the slice) this bisected fruit, it will correctly map onto and continue the general pattern of this rosette. Also, any portion of this perspective of the orange reflected over its center point would result in symmetry.
As a rosette is by definition, this fruit's pattern has symmetries only rotated about a single point and reflections through that point, and there are no translations nor glide reflections. Its repetition is in its slices around its center column and it highly decreases the likelihood of falling victim to scurvy. Orange you glad it has such nice symmetry?... okay I'm done.
As the orange has reflectional symmetry, it would be classified as a dihedral rosette (dn), rather than a cyclic rosette (cn), which are rosettes without reflectional symmetry.
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