Fractals: A Different Type of Geometry
The Dimensions in Between
The mathematics that we have learned since elementary school is a bit beautiful. A line is perfectly straight, the path of the ball thrown upward is a parabola and the shape of the earth we see in books is a sphere. The truth is, the lines, parabolas, and spheres are “flawless models” of the real world. A straight line that can be drawn using a ruler or a meter stick is not perfectly straight (try using a magnifier). The shape of the path of the ball thrown upward is not all the time a symmetric parabola. Lastly, Earth is not a perfect sphere, it bulges in the equator, it has mountains, valleys, and trenches.
Clearly, the perfect mathematics that we know is an ideal notion and it does not have a very close resemblance of reality. It also appears that the mathematics, particularly the Geometry that we have learned in school is not enough to describe the real world. The dimensions that we have talked in the last post, cannot simply apply to these types of “irregularities.” » Read more