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

Fibonacci Numbers and the Golden Ratio
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Seasons
Fibonacci and the Golden Ratio Everywhere
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.
The Golden Ratio and Benford
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
The Golden Ratio and Geometry
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
A Golden Formula for Fibonacci
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
Phi: The Most Irrational Number
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.
The Mysterious Golden Ratio
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
Fibonacci Numbers, Lucas Numbers, and Beyond
6. Fibonacci Numbers, Lucas Numbers, and Beyond
February 20, 2025
Fibonacci
A Favorite Fibonacci Fact
5. A Favorite Fibonacci Fact
February 20, 2025
See the professor
Fibonacci Numbers and Pascal
4. Fibonacci Numbers and Pascal
February 20, 2025
Turn to Pascal
Applications of Fibonacci Numbers
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
Proving Perplexing Properties
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
Puzzling Fibonacci Patterns
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

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

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.
  • Premiere Date
    February 20, 2025
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