Final Assignment

By: Olamide Alli

*Part One: Ceva’s Theorem*

*Part Two*

Rhombus: Prepare a GSP Sketch with script tool for a Rhombus in each of the following three situations.

i. Given one side and one angle

ii. Given one angle and a diagonal

iii. Given the altitude and one diagonal

*Part Three*

Select one additional item from the assignments from the explorations presented in class that you have not written up. Submit a write up about it.

__Obsession with Floral Designs in Graphing Calculator__

I’ve chosen to write up another exploration from assignment 11. My interest was piqued with the n-leaf rose, due to my obsession with floral designs, so I wanted to explore some other polar equations in order to produce floral images.

Step 1: Let’s use the polar equations of the form r = a(sin(kq))+b and r=a(cos(kq))+b

From the Picture above the only difference when using cosine and sine is the 90 degree shift.

a = the length of the petals

k = the number of petals in one circumference of the flower

b = determines whether or not the petals of the flower will move in or out.

For example if k = 4, we get four petals. By adding 1m we keep the function from ever being negative. If we add to 2, we get further away from the origin. When use cosine instead of sine, the graph is rotated.

Step 2: The flower we’ve produced is just taking a sine function, adding a constant (to make the values positive) and increasing the frequency by using the value of k and changing it into a circle by changing x to theta.

Step 3: If we input various values for a, k, b, we can produce some pretty cool floral arrangements.

Please feel free to email me if you come up with any cool designs using polar equations.