Contents
Golden Ratio
Local Pentagonal Symmetry:
Real-World Applications:
The golden ratio isn’t just used in the field of mathematics; it is often used in history and in modern contexts, sometimes unconsciously, and can be found in front of us almost every day.
Many of our everyday designs, ranging from credit cards to television screens, to historical designs like medieval manuscripts, follow the golden ratio and form golden rectangles.
Some of the Egyptian pyramids closely follow current mathematical pyramids, the latter of which can be taken apart to show the relationship between the sides of the square base, the height, and $ \phi $.
In nature, flowers often follow the golden spiral with the arrangement of their leaves (see Introduction for picture). This is also why seeds have to planted in a certain way (in a line) so they have space to grow in a spiral[1].
Many 20th century artists and architects proportioned their works to the golden ratio, often using the golden rectangle when positioning the features of their works. This was named divine proportion in the 16th century, and it led to artists tying the golden ratio to religious works (such as Salvador Dali with his The Sacrament of the Last Supper). One such alleged example is the Mona Lisa, which shows the proportions of the lady’s eyes and face matching the Fibonacci sequence’s numbers.
Further Readings:
- http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden_Ratio/golden.html --> This is a very good source for exploring the real-world applications of golden ratio.
- Robinson triangles are not the only shape that is related to the golden ratio. Here are some sites that explain golden rectangles, golden spirals, and golden stars (pentagram) and where they show up in our everyday lives:
