Math Meets Art: Discovering the Sierpinski Triangle, Fibonacci and Golden Ratio: A Fascinating Trio in Mathematics
The Sierpinski Triangle
The Sierpinski triangle, named after the Polish mathematician Wacław Sierpiński, is a fractal pattern that can be generated using a simple recursive algorithm. This pattern is not only visually interesting, but it also has connections to the field of number theory, particularly with the famous Fibonacci sequence.
The Sierpinski triangle can be generated by starting with a single large triangle and repeatedly dividing it into four smaller triangles, removing the middle one each time. This process can be repeated indefinitely, creating a pattern of smaller and smaller triangles within the larger triangle. As the recursion proceeds, the number of triangles at each stage follows the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, and so on.
The Fibonacci Sequence
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. This sequence appears in many areas of mathematics and nature, such as the branching of trees and…
