Watch Fibonacci Numbers and the Golden Ratio

2025
1 Season

Taught by Professor Arthur T. Benjamin of Harvey Mudd College, this course introduces two ubiquitous patterns in nature and human culture: the Fibonacci sequence and the golden ratio. You learn how a simple algorithm produces the Fibonacci sequence, and how this is one of many paths to the golden ratio. Professor Benjamin presents proofs, puzzles, magic tricks, games, and many amazing insights.

Fibonacci Numbers and the Golden Ratio is a series that ran for 1 seasons (12 episodes) between February 20, 2025 and on The Great Courses

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Seasons

12. Fibonacci and the Golden Ratio Everywhere

February 20, 2025

Why do the Fibonacci sequence and golden ratio appear so often in the natural world? For example, the structure of plants and flowers show a strong preference for irrational numbers, particularly phi. Consider the types of spirals in nature and refute some of the more extravagant claims for the ubiquity of the golden ratio. Professor Benjamin closes with a limerick and a poem.

11. The Golden Ratio and Benford

February 20, 2025

Many lists of numbers, such as the Fibonacci sequence and the powers of phi, follow a phenomenon called Benford

10. The Golden Ratio and Geometry

February 20, 2025

Astronomer Johannes Kepler regarded the Pythagorean theorem and golden ratio as the two greatest treasures of geometry. Find the link between them in a figure called Kepler

9. A Golden Formula for Fibonacci

February 20, 2025

How do you specify any number in the Fibonacci sequence? In 1843, Jacques Philippe Marie Binet described a formula that allows anyone to plug in the position of the desired value

8. Phi: The Most Irrational Number

February 20, 2025

The golden ratio is denoted by the Greek letter phi. See how phi can be computed by a simple, infinitely long continued fraction. When all of the terms in the continued fraction are 1, then the result is phi. Learn how this calculation relates to Fibonacci numbers.

7. The Mysterious Golden Ratio

February 20, 2025

The golden ratio is a number that even the math-averse can love. A rectangle with length to height equal to the golden ratio is widely considered the most beautifully proportioned of all quadrilaterals. Explore the golden ratio

6. Fibonacci Numbers, Lucas Numbers, and Beyond

February 20, 2025

Fibonacci

5. A Favorite Fibonacci Fact

February 20, 2025

See the professor

4. Fibonacci Numbers and Pascal

February 20, 2025

Turn to Pascal

3. Applications of Fibonacci Numbers

February 20, 2025

Arrange a strip of various lengths with squares and dominoes (which are twice the length of squares). Discover that the number of tiling combinations follows the Fibonacci sequence. This leads to the concept of combinatorial proofs, which are Professor Benjamin

2. Proving Perplexing Properties

February 20, 2025

How do we know that some of the patterns examined in the previous lecture hold up for the entire Fibonacci sequence out to infinity? Roll up your sleeves and use different mathematical techniques to prove these conjectures. In a fun diversion, Professor Benjamin, an accomplished magician, uses a remarkable property of the Fibonacci sequence called Cassini

1. Puzzling Fibonacci Patterns

February 20, 2025

Learn the simple procedure for generating the Fibonacci sequence and see how it leads to a world of intriguing patterns. Also, get to know Fibonacci himself

Description

Where to Watch Fibonacci Numbers and the Golden Ratio

Fibonacci Numbers and the Golden Ratio is available for streaming on the The Great Courses website, both individual episodes and full seasons. You can also watch Fibonacci Numbers and the Golden Ratio on demand at Amazon Prime and Amazon.