What are the 2 patterns found in nature and describe their relation to Mathematics.
I suggest you look at the Fibonacci numbers, one of my favourite topics in math.
The following page will start you off and lead you to a path of discovery lasting you a lifetime.
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
Is the fibonnaci numbers are the only pattern that can be found in nature?
There are two common patterns found in nature: the Fibonacci sequence and fractals. Both of these patterns have a strong relationship with mathematics.
1. Fibonacci Sequence: The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It starts with 0 and 1, and the next number is always the sum of the previous two numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, and so on). This sequence can be observed in various natural phenomena such as flower petals, pinecones, and the arrangement of leaves on a stem.
The relation to mathematics: The Fibonacci sequence has many interesting mathematical properties. For example, if you divide any number in the sequence by its preceding number, the ratio approaches a value known as the "Golden Ratio" (~1.61803). This ratio is considered aesthetically pleasing and is found in art, architecture, and even the human body proportions. Fibonacci numbers also play a role in mathematical theories, such as the study of Fibonacci polynomials and the analysis of spiral growth patterns.
2. Fractals: Fractals are complex, infinitely repeating patterns that can be seen at different scales. They are created by mathematical algorithms and can be found in various natural structures like mountains, clouds, trees, and coastlines. Fractals exhibit self-similarity, meaning that they possess similar patterns when zoomed in or out.
The relation to mathematics: Fractals are deeply rooted in mathematics, specifically in the field of chaos theory and iterative functions. They can be generated using mathematical equations and computer algorithms. The study of fractals involves concepts like recursion, self-similarity, and the Mandelbrot set. Fractals have applications in areas such as computer graphics, data compression, and the modeling of natural phenomena.
In summary, both the Fibonacci sequence and fractals showcase the strong connection between nature and mathematics. They demonstrate how mathematical principles and patterns are prevalent in the world around us.