Podcast
Questions and Answers
Which of the following best describes the Fibonacci sequence?
Which of the following best describes the Fibonacci sequence?
- A sequence of numbers in which each number is the sum of the two numbers before it (correct)
- A sequence of numbers in which each number is the product of the two numbers before it
- A sequence of numbers in which each number is a random number
- A sequence of numbers in which each number is the difference of the two numbers before it
What is the golden ratio?
What is the golden ratio?
- A ratio of two quantities that have a ratio equal to the ratio of their difference to the larger quantity
- A ratio of two quantities that have a ratio equal to the ratio of their sum to the smaller quantity
- A ratio of two quantities that have a ratio equal to the ratio of their sum to the larger quantity (correct)
- A ratio of two quantities that have a ratio equal to the ratio of their difference to the smaller quantity
In what natural phenomena can the golden spiral be found?
In what natural phenomena can the golden spiral be found?
- Volcanoes
- Seashells (correct)
- Rainbows
- Tornadoes
Flashcards
Fibonacci sequence
Fibonacci sequence
A sequence where each number is the sum of the two preceding numbers.
Golden Ratio
Golden Ratio
A ratio where the ratio of two quantities is the same as the ratio of their sum to the larger quantity.
Golden Spiral
Golden Spiral
A logarithmic spiral whose growth factor equals the golden ratio, often seen in nature.
Study Notes
The Fascinating Fibonacci Sequence and Golden Ratio
- Many flowers, cacti leaves, and sunflower seeds have numbers of petals or arrangements that follow the Fibonacci sequence.
- The human hand has five fingers with three parts each, and the lengths of bones in the hand are also Fibonacci numbers.
- The Fibonacci sequence is a series of numbers in which each number is the sum of the two numbers before it.
- The sequence begins with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.
- The sequence is named after Leonardo Pisano, aka Fibonacci, who introduced the Hindu-Arabic numeral system to the Western world.
- The Fibonacci sequence has been discovered in various forms in nature and everyday life.
- The golden ratio is a ratio of two quantities that have a ratio equal to the ratio of their sum to the larger quantity.
- The golden ratio is represented by the Greek letter phi (ϕ) and has a value close to 1.618033…
- All Fibonacci numbers have the golden ratio.
- The golden spiral is a special kind of logarithmic spiral that gets wider by a factor of phi for every quarter turn it makes.
- The golden ratio and golden spirals can be found in seashells, ocean waves, hurricanes, flower buds, spider webs, and many other naturally occurring phenomena.
- Architects and artists often use the golden ratio in their designs and creations, such as Le Corbusier's Modulor system and Salvador Dali's The Sacrament of the Last Supper.
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