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Resources tagged with Fibonacci sequence similar to Euclid's Algorithm and Musical Intervals:

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Broad Topics > Sequences, Functions and Graphs > Fibonacci sequence

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Continued Fractions I

Stage: 4 and 5

An article introducing continued fractions with some simple puzzles for the reader.

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Golden Fractions

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

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Golden Mathematics

Stage: 5

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

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Golden Trail 1

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

A first trail through the mysterious world of the Golden Section.

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Farey Fibonacci

Stage: 5 Short Challenge Level: Challenge Level:1

Investigate Farey sequences of ratios of Fibonacci numbers.

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Golden Fibs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

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The Golden Ratio, Fibonacci Numbers and Continued Fractions.

Stage: 4

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

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Leonardo of Pisa and the Golden Rectangle

Stage: 2, 3 and 4

Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.

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Pythagorean Fibs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What have Fibonacci numbers got to do with Pythagorean triples?

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Whirling Fibonacci Squares

Stage: 3 and 4

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

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Fibonacci Fashion

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

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Plus or Minus

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

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Golden Powers

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

You add 1 to the golden ratio to get its square. How do you find higher powers?

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Cellular

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Cellular is an animation that helps you make geometric sequences composed of square cells.

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Building Gnomons

Stage: 4 Challenge Level: Challenge Level:1

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

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First Forward Into Logo 11: Sequences

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

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Magical Maze - 35 Activities

Stage: 4 and 5

Investigations and activities for you to enjoy on pattern in nature.

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Gnomon Dimensions

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.

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Stringing it Out

Stage: 4 Challenge Level: Challenge Level:1

Explore the transformations and comment on what you find.

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LOGO Challenge - Circles as Bugs

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

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Spirals Instead of Sunflowers

Stage: 3 and 4 Challenge Level: Challenge Level:1

Using logo to investigate spirals

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Fibonacci Factors

Stage: 5 Challenge Level: Challenge Level:1

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

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Ordered Sums

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .

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Got a Strategy for Last Biscuit?

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you beat the computer in the challenging strategy game?


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