## Turkey - Fractal Structures

• PI DAY ACTIVITY

In the math world, the symbol π (Pi) appears regularly. As a refresher, Pi is the ratio of  circle’s circumference to its diameter. But why is this symbol used to represent this irrational number of 3.1415926…… ?

The earliest reports to the origin of this symbol date back to 250 BC when Greek mathematician Archimedes decided to calcuate pi by using regular polygons with more and more sides, he needed a letter to represent what he just found.  He noticed that increasing the number of equal length sides of a polygon, the polygon more closely represented a circle. So he used the letter Pi, (perifereia), meaning periphery or perimeter, describing the circumference of a circle.  Similar to the way we use h for the height a triangle, Archimedes used Pi. In fact, Pi is often referred to as “Archimedes constant”.

Although Archimedes used Pi, the symbol was introduced by an English mathetmatician in the early 1700’s.   This has been regularly used for only the past 250 years, however in a mathematical sense. The symbol was adopted by Euler in 1737 to represent the value.

Looking beyond the pure numerical value for pi for which the symbol π represents, according to Live Science, it discusses Pi as it pertains to nature, specifically a river.  What kind of association is possible between a river and π ?

According to the website,

“A river’s windiness is determined by its ‘meandering ratio,’ or the ratio of the river’s actual length to the distance from its source to its mouth as the crow flies,” the site says. “Rivers that flow straight from source to mouth have small meandering ratios, while ones that lollygag along the way have high ones. Turns out, the average meandering ratio of rivers approaches — you guessed it — Pi”

I suppose there is a proof somewhere verifying the claim from this website, however if does make sense that something as random as the flow of the river could relate to the irrational number Pi, which never repeats digits and never ends.

Just as mathematicians have increasingly able to obtain the value of Pi through advanced technology, more and more examples in nature or other real world settings are likely to relate to the symbol π.

One aspect of mathematics that is great is that a concept can be simple, beautiful and complex all at the same time. Pi is one such concept.

Our school activities video:

## Turkey - Fractal Structures

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

First of all, we developed a memory game by searching the fractal models on the internet in order to recognize the examples of daily life related to fractal.  Then we created 3-dimensional fractal structures.        • Do you know what a fractal is?
YES