We can accomplish this with parametric functions. How can we imitate the radially-extending petals of real-life flowers? One way is to “wrap” a wavy function graph around a circle so its waves oscillate orthogonally to the tangent line of the circle at any given angle. Wrapping a wave around a circleĮnough waiting – it’s time to get to the actual math. Some of them look like they curl about the center – this is definitely a characteristic that would be nice to capture in the parametrics. Here, the petals do not extend straight out from the center as in the previous two images. The layers appear to be spaced roughly so that the maximum petal area is exposed to overhead sunlight. That purple one is pretty simple as well, but note how there are now two to three layers of petals that are offset from one another by rotation. The petals extend directly away from the center and there is only one layer of petals. That is about the most simple-looking flower you can find. Let’s take a look at some reference images and note some characteristics we want to include in our designs. Flowers come in all shapes, sizes, patterns, and colors. “Flower design” is an extremely broad term. That’s a good thing – I encourage you to experiment with different numbers and equations to see what you find. Since math class focuses primarily on questions with right/wrong answers, this artistic freedom may be uncharted math territory for some of you. The approach in this post is tailored to what I find aesthetically pleasing, so it is by no means objectively the best. Before starting, note that there is no right or wrong way to go about this. We’ll create flower designs with a large degree of artistic control using parametric curves. The goal of this post is to give an example of how math can be beautiful in a more accessible and universal way: the creation of art. That certainly sounds appealing to those who are already immersed in math, but it’s not clear how such a result is “beautiful” in the general sense of the word. “Mathematical beauty” usually refers to the elegance of a proof, that is, how cleanly some mathematical result is proven with a convincing argument.
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