Consider the spiral with polar equation r = va0 where a is constant. This spiral occurs frequently in flowers because it allows seeds to be arranged in the most efficient way possible. This highly structured natural phenonomen contains many mathematical ideas, including the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, . . .. Sunflower Fibonacci of Pisa 1170 - 1250 ADThe position of the n'th seed on a sunflower is given in polar coordinates r = V2mon, 0 = 2min where y V5-1 2 ~ 0.618033988 . . . is the golden ratio, and 0 is specified in radians (not degrees). The location of the first 21 sunflower seeds are circled in red in the spiral below. The location of seed numbers 8 and 13 have a cross in the middle. 3 1 4 5 x 3 IT 2 Find the Cartesian coordinates (to two decimal places) for . seed number 8 : (5.24,-1.91) seed number 13 : (6.94,1.53) seed number 2584 : (85.24, 15.83) In fact, all of the seeds corresponding to Fibonacci numbers (such as 8, 13 and 2584) occur near the positive c-axis, which in polar form has the equation: 0 = 0