Math Thematics 1st Ed. Book 3
Module 4 - Patterns and Discoveries
Section 1: Sequences
Lessons (1)
Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.
Activities (6)
Students work step-by-step through the generation of a different Hilbert-like Curve (a fractal made from deforming a line by bending it), allowing them to explore number patterns in sequences and geometric properties of fractals.
Step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, and explore number patterns in sequences and geometric properties of fractals.
Step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, and explore number patterns in sequences and geometric properties of fractals.
Step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.
Step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.
Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.