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Friday, April 3, 2015

HP 50g - Graphing Rose Petals - Polar Graphs

Graphing Rose Petals - HP50g

Written by: Larsha Johnson

How to graph a rose petal on the HP50g. Rose curve equations have two forms: 
  1. r = a cos(nθ) and 
  2. r = a sin(nθ) 
where a ≠ 0 and n is a positive integer. Petals have length determined by a. If n is odd, the number of petals is n. However, if n is even, the number of petals is 2n.

The simplicity and symmetry of Rhodonea or rose curves have fascinated mathematicians since they were first named by the Italian mathematician Guido Grandi in the 1700s. We were fascinated by an interesting pattern created by counting the number of petals of these curves.

In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates. This concept is studied in Precalculus or Calculus.

Students will understand the role of the values of a and n in the equation r = asin(nθ).
Students will be able to predict the number of petals and their length by examining the polar equation.
Student will understand the relationship between the equation of a rose curve and the equation of a sinusoidal function.

rose curve
sinusoidal function

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