Geometry Patterns and Meanders
Children love to discover patterns in the world around them. Patterns help kids understand that things occur over a period of time and that patterns are repeatable. Patterns can be simple things, such as stripes on a sweater, or complex images, such as circles printed on fabric. Whatever pattern a child is looking at, they can usually identify a repeating pattern.
As children develop their sense of math skills, they are able to create patterns with numbers. For example, if you draw a line connecting two points, you can follow a series of numbers that repeat infinitely. When these repeating numbers go together, you can figure out the distance between the two points by finding the sum of the first number and the second. This is the basic definition of addition, subtraction, and multiplication and it applies to most math classes.
However, there is much more to patterns in math than just addition, subtraction, and multiplication. It is possible to make use of the repeating patterns to create new math equations. For instance, by working with the well-known Fibonacci calculator, you can solve for x using the Fibonacci formula. You can even solve for x by finding the minimum (or maximum) value of the function. In addition, you can create your own patterns by taking advantage of the fuzzy logic rule of computing.
Fractals are patterns where the shape or size of a shape is repeating itself. These patterns are especially useful in mathematics. For instance, the elliptic curve forms a repeating pattern when graphed; and the Mandelbrot set is a shape that repeats infinitely when created from a set of straight lines. By finding the areas of a given shape and repeating the segments of that shape, you can form a new pattern that determines the area of the area and the meaning of the shape.
Patterns can also be used in other fields such as engineering, chemistry, and physics. A popular application is the sorting of different types of liquids by their boiling points. By determining the boiling point of different types of liquids using a series of mathematical calculations, engineers can design new machines or weapons. Also, chemists can determine the number of different types of molecules in different types of matter, which can be useful for identifying the different types of cancer cells.
There are many other applications of patterns and meanders in mathematics and other fields. Learning about patterns and meanders can lead to impressive mathematical patterns and insights into the world around us. The main article in this series focuses on the application of meanders and sequences in geometry.