Math 10 Presentation (Fibonacci Sequence and Frieze Patterns).pptx

Fibonacci Sequence and Frieze Patterns

1. Fibonacci Sequence and Frieze Patterns

2. What is the Fibonacci Sequence? The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8… It appears in nature, art, and math, linking to the golden ratio (≈1.618).

3. What is the Fibonacci Sequence? The pinna resembles a logarithmic spiral, which is closely related to the Fibonacci sequence.

4. Fibonacci Sequence and the Golden Ratio Flowers Snail shells Tree Crowns Other examples Source: National Geographic Source: National Geographic Source: Urban Gardening Mom

5. What are Frieze Patterns? A repeating design that extends in a straight line, like a border or a decorative strip. You can see them in everyday life, such as on building walls, fences, clothing, wallpaper borders and tile patterns.

6. Frieze Patterns 7 Types of Frieze Patterns Translational Symmetry (T) when a shape moves a certain distance equally, over and over. Glide Reflections and Translations (TG) when a shape mirrors itself over a horizontal line, and then translates (or moves) a certain distance over.

7. Frieze Patterns 7 Types of Frieze Patterns Vertical Mirror Symmetry appears as though there is a mirror placed between each shape Vertical reflection lines and Translations Horizontal Mirror Symmetry appears as though a mirror is placed below a string of identical shapes Translations, Horizontal reflections, Glide reflections

8. Frieze Patterns 7 Types of Frieze Patterns 180 Degree Rotational Symmetry you can turn the pattern 180 degrees and it will look the same as if it were never turned at all Translations and 180° Rotations Glide Reflection with Vertical Mirrors generated by a glide reflection and either a rotation or a vertical reflection

9. Frieze Patterns Vertical and Horizontal Mirror Symmetry requires three generators, with one generating set consisting of a translation, the reflection in the horizontal axis and a reflection across a vertical axis Horizontal and Vertical reflection lines, Translations and 180° Rotations 7 Types of Frieze Patterns

10. Frieze Patterns The leaves grow in an alternating and rhythmic sequence, creating a continuous, structured pattern that extends in one direction. A metal truss structure with a repeating triangular pattern, a part of a roof or overhead support beam

11. Patterns Frieze Logo Reflectional Symmetry Radial Symmetry Translational Symmetry

12. Any Questions? Thank you for listening