The-Fibonacci-Sequence-and-Golden-Ratio.pptx

Fibonacci sequence

1. The Fibonacci Sequence and Golden Ratio The Fibonacci sequence is a fascinating mathematical pattern found throughout nature, art, and even finance. This presentation will explore the applications of the Fibonacci sequence and the related golden ratio. by Ethan,Josh,dean, carlos

2. Introduction to the Fibonacci Sequence 1 What is the Fibonacci Sequence? A series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. 2 Historical Origins Introduced by Italian mathematician Leonardo of Pisa, also known as Fibonacci, in the 13th century. 3 Mathematical Properties The sequence exhibits unique mathematical patterns and relationships, such as the golden ratio.

3. Understanding the Fibonacci Sequence 1 Starting Point The sequence begins with 0 and 1 as the first two numbers. 2 Next Numbers Each subsequent number is the sum of the previous two numbers. (0,1,1,2,3,5,8,13,21,34) 3 Growing Pattern The sequence continues to grow, with each number becoming larger than the previous two.

4. The Golden Ratio and its Connection to the Fibonacci Sequence What is the Golden Ratio? A mathematical ratio, approximately 1.618, that is found in many natural and man-made structures. Fibonacci Connection The ratio between consecutive Fibonacci numbers approaches the golden ratio as the numbers get larger. Aesthetic Appeal The golden ratio is considered aesthetically pleasing and is often used in art, architecture, and design.

5. Fibonacci Sequence in Nature Sunflowers The arrangement of seeds in a sunflower head follows the Fibonacci sequence. Seashells The spiral patterns of many seashells, like the nautilus, are based on the Fibonacci sequence. Tree Branches The branching patterns of many trees exhibit Fibonacci-like arrangements. DNA Structures The double-helix structure of DNA molecules contains Fibonacci-related patterns.

6. Fibonacci Sequence in Art and Architecture Parthenon The ancient Greek temple's design is based on the golden ratio. Mona Lisa Leonardo da Vinci's famous painting follows the golden ratio in its composition. Spiral Staircases Many iconic spiral staircases, like the one in the Louvre, are inspired by Fibonacci patterns.

7. Fibonacci Sequence in Finance and Economics Technical Analysis Traders use Fibonacci ratios to identify potential support and resistance levels in financial markets. Economic Indicators Fibonacci patterns can be observed in economic growth, stock market trends, and other financial data. Portfolio Management Investors may incorporate Fibonacci-based strategies to time market entries and exits.

8. Fibonacci Sequence in Biology and Science 1 Plant Growth The branching patterns of plants often follow the Fibonacci sequence. 2 Animal Structures The spiral patterns in seashells, horns, and even the human body exhibit Fibonacci-like forms. 3 Quantum Physics Fibonacci-related sequences have been observed in the behavior of subatomic particles.

9. Conclusion and Key Takeaways 1 Widespread influence The Fibonacci sequence and golden ratio are found in a wide range of natural, artistic, and scientific phenomena. 2 Mathematical patterns/sequence The patterns and relationships within the Fibonacci sequence exhibit a remarkable mathematical elegance. 3 Practical Applications Understanding the Fibonacci sequence can provide insights and inform decision-making in fields like finance, design, and engineering.