This was the first piece of art I created. Rose graphs can be created using the r=asinbtheta. I utilized this equation along with the slider function on Desmos to create this pretty flower design. The best part? It's completely math-powered! Here is the function I used:
Moving the "a" slider left and right adjusts the size of the graph. Both positive and negative numbers yield the same results - if I had used 3.3 for "a" rather than -3.3, the graph would have been the same size.
Moving the "b" slider left and right adjusts the number of petals and the design of the rose.
For example, here is the graph where b=1.1:
Here, b=2.5:
And here, b=3:
Each graph is drastically different depending on the value of "b."
Rose graphs were just one of the types of graphs we explored using Desmos. We also learned about limacon graphs and "Spiral of Archimedes" graphs. Limacon graphs use the equation r=a+bsin theta and create two interlocking circles. The "Spiral of Archimedes" can be created using the equation r=theta.
I then used all of the polar graphs we learned and combined them into one crazy graph!
I used the following equations to create this graph.
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