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Fractals from Triangles, Quadrilaterals, Inscribed Circles, and Squares

Fractals are self-similar objects. What does self-similarity mean? If you look carefully at a fern leaf, you will notice that every little leaf - part of the bigger one - has the same shape as the whole fern leaf. You can say that the fern leaf is self-similar.

Pascal's Prime Number Multiple Fractals: 2 (and odds),3,5,7,11,13,17

My favorite discovery in Pascal’s are the fractals first found by Sierpinski in 1915 (almost 300 years after Pascal); it is referred to as Sierpinski’s Triangle and is created by coloring in the even numbers (numbers that end in 0,2,4,6,8). It is also quite beautiful to color in the odd numbers (numbers that end in 1,3,5,7,9); you will get a negative image of Sierpinski’s Triangle. 

Pascal's Triangle Patterns (Natural, Triangular, Tetrahedral, Square, Cubic, Powers of 11, Powers of 2, Fibonacci, Hockey Sticking, and Multiplying Seeds > 1

Last week the children were introduced to Pascal’s Triangle, its history and its properties.  They created their own Pascal’s Triangle and experimented with different seed numbers (the seed number of a traditional Pascal’s Triangle is 1; 1 is placed on the left and right diagonals of the triangle). You fill each cell with the sum of the two cells above it. 

Pascal's Triangle (all digits, last digit, and combinametrics)

Pascal's Triangle is created by starting with only 1s in each of the two perimeter diagonals of a triangular array. Fill in this array by adding the two numbers above each cell. The numbers start out small such as 1 2 1 on the second row and 1 3 3 1 on the third row and 1 4 6 4 1 on the fourth row but then they explode.

Prime Pyramid

Prime Pyramid: Compete the pyramid by filling in the missing numbers on each row. Each row must contain the consecutive whole numbers from 1 to the row number but not necessarily in that order. In each row, the numbers from 1 to the row number are arranged such that the sum of any two adjacent numbers (neighboring numbers) is a prime number.