Identify repeating patterns in geometric shapes and map geometric properties to numerical sequences.
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Introduction to geometry and shape sequences.
Other important and basic patterns that occur in mathematics are patterns of shapes. These shapes may be in one, two, or three dimensions (1D, 2D, or 3D)—or in even more dimensions. The branch of mathematics that studies patterns in shapes is called geometry.
Key insight that counting shape elements yields familiar number sequences.
Key mathematical shape sequences including regular polygons, complete graphs, stacked shapes, and the Koch Snowflake.
Explanation of how line segments multiply in the Koch snowflake.
The Koch Snowflake is a fascinating shape sequence that creates complex geometric borders. To get from one shape to the next in the sequence, you simply replace each straight line segment with a shape that looks like a "speed bump" (a small triangle pushing outward).
Matching exercise linking geometric properties to number sequences.
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