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# rose

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A curve consisting of a number of loops meeting at the origin, which resemble the petals of a flower like the rose. In polar co-ordinates the equation is of the form r=a cos (nθ) or r=a sin (nθ) where a determines the distance from the origin to the tip of each loop. The polar axis is always an axis of symmetry for curves of this form with cos, while for curves with sin the perpendicular to the polar axis is an axis of symmetry. If n is even, then there will be 2n loops, while if n is odd there are only n loops with gaps between the loops. The reason for this discrepancy is that when n is odd, and r returns a negative value, it traces over a loop created 180° out of phase, where r returned a positive value. When n is even, the value of r returned for any two angles which are 180° different is necessarily the same sign, and a new loop is created.

The rose created by r=1.5 cos (2θ).

The rose created by r =1.5 cos (3θ).

Subjects: Mathematics.

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