The Fibonacci Sequence and Golden Ratio Quiz

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Questions and Answers

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?

  • 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?

  • Volcanoes
  • Seashells (correct)
  • Rainbows
  • Tornadoes

Flashcards

Fibonacci sequence

A sequence where each number is the sum of the two preceding numbers.

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

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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