week 9 post 2

Something that every human can appreciate is beauty, and beauty is generally associated with goodness. It is a mystery why we find some things beautiful and others not, but regardless w are programed to recognize it for our survival. In specific, one common quality of beauty is symmetry seeing that it cues good health and prosperity. In addition, there is overwhelming evidence that beauty improves cognitive and physical health. An experiment involving artwork was conducted where people were asked to observe sets of two very similar paintings and report which one they felt was more beautiful and meaningful. The difference in the paintings was that one was painted with intent and the other was an unoriginal imitation. A majority of the time, people chose the painting that was full of intent as the more beautiful one. Furthermore, beauty cultivates positive emotions, and even better health. For example when meaningful art is placed hospitals, patients report feeling happier, more comfortable and required less pain medication.

Objects or organisms that people commonly consider beautiful are things that follow the Fibonacci sequence. The Golden ratio comes in many forms, and experts are puzzles as to why both animates and inanimate objects obey it. It is most easily identifiable in plants. The YouTuber MathLogger has a video named "The fabulous Fibonacci flower formula". In it, the math logger explains how the shape flowers take is the most efficient, and conveniently the most beautiful. Take the sunflower, and notice the symmetries:


Waves or movement in the water is often mistaken as the water molecules physically changing it's position over long stretches in the body. While that is true in some sense, waves are just energized water. As this video from Potato Imaginer shows, the circles, which represent the water do not move, rather the blue and orange bar that mimic the shape of a sound or light wave are moving along the line. 


In a large body water, this occurs constantly and over the entire are
as one wave will always causes other waves (or ripples). Sometimes, the ripples or waves run into each other and create curious patterns that resemble the seeds of a sunflower:


Lastly, the Mandelbrot set is a set of complex numbers that create a significant and infinite pattern:

Besides looking really cool, the Mandelbrot set is far more than that. It is deeply inter connected to the Fibbionacci sequence and similarly seen all over nature. As the math logger again explains in "Times Tables, Mandelbrot and the Heart of Mathematics", the primary cardioid (heart shape) represents a times table. Interestingly enough, it also represents how light is reflected: 

The Fourier transform is a way of breaking frequencies into its pure constituents. When you have a pure frequency, and chart it around a circle, then measure it's cycles/second. When the cycles per second match the beat/second or frequency, a cardioid appears. 

Photo from 3brown1blue 
Furthermore, when a cardio is split in half symmetrically, you see a perfect golden ratio spiral 



https://www.youtube.com/watch?v=3zbG8GUD8l4&feature=youtu.be

https://www.youtube.com/watch?v=_GkxCIW46to

https://www.youtube.com/watch?v=FFftmWSzgmk

https://www.youtube.com/watch?v=spUNpyF58BY

https://www.youtube.com/watch?v=qhbuKbxJsk8

Comments

  1. Ms. DunleyJanuary 25, 2021 at 8:32 AM

    Do you have any other examples of where this is found in nature? How would you like to see this taught to students?

    ReplyDelete

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