Importing Things From the Real World Into the Territory of Mathematics!
The goal is to find some valuable mathematical objects that look like real things such as continents, animals, etc. Such figures may encourage young people’s interest in mathematics.
The fractal Africa is created by an Africa-like octagon and its lateral inversion. From my point of view, it is the most similar octagon to the map of Africa:
The structure of this fractal is very similar to the rabbits family tree which was introduced by the Italian mathematician Leonardo Fibonacci (1170-1250). In this fractal, the number of the octagons of each size is related to the Fibonacci numbers. The fractal determines an infinite number of isosceles triangles in the plane. The number of the isosceles triangles of each size is related to the Fibonacci numbers too. The height of the biggest octagon in this fractal is φ times longer than the height of the second (or third) octagon; where φ is the golden ratio (φ=1.618…). The fractal Africa is exactly similar to an infinite number of its parts. Therefore it is a self-similar pattern.
South America & Africa Tessellations
Millions of years ago, Africa and South America were joined together. They were parts of the Pangaea supercontinent. Alfred Wegener (1880-1930) was the first person who discovered this fact. The following images show two Africa and South America tessellations which are inspired by Pangaea. Each of these two tessellations is created by an Africa-like octagon and a South America-like hexagon. The octagon of the first tessellation is mathematically similar to the octagon of the second tessellation. But the hexagon of the first tessellation is not mathematically similar to the hexagon of the second tessellation.
South America & Northern America Tessellations
The following images are two tessellations inspired —> Read More