Overview
This lecture introduces geometric patterns, discussing how shapes and transformations create sequences and highlighting the use of geometric patterns in prediction and mathematics.
Geometric Patterns and Shapes
- Geometric patterns are formed by arranging lines and curves to make shapes like circles, triangles, and polygons.
- Patterns often emerge from repeating or alternating different geometric figures (e.g., lines, circles, squares).
- Predicting the next figure in a sequence can be done using mathematical formulas and recognizing repeating patterns.
- Triangles have three sides, squares four, hexagons six, and so on, forming the basis for pattern sequences.
Sequence Prediction Examples
- Patterns can involve alternating colors (e.g., black, white, black, white) or alternating shapes (e.g., square, circle, star).
- Identifying the rule behind a pattern helps predict the next figure in the sequence.
Isometric Transformations
- Isometric transformations are linear changes that do not alter the distance between points in a figure.
- Types of isometric transformations include reflection (mirror image), translation (sliding), and rotation (turning the figure).
- Glide reflection combines reflection and translation.
Key Terms & Definitions
- Geometric Pattern — a repeated arrangement of shapes or figures based on geometric rules.
- Polygon — a closed figure with straight sides (e.g., triangle, square, hexagon).
- Isometric Transformation — a movement of a figure that preserves distances (reflection, translation, rotation).
- Reflection — flipping a shape over a line to produce a mirror image.
- Translation — sliding a shape without rotating or flipping it.
- Rotation — turning a shape around a fixed point.
- Glide Reflection — a combination of reflection and translation.
Action Items / Next Steps
- Practice identifying and predicting the next element in geometric pattern sequences.
- Review polygons and isometric transformations for upcoming discussions on mathematics in nature.