# Resources tagged with: Fibonacci sequence

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### There are 21 results

Broad Topics > Patterns, Sequences and Structure > Fibonacci sequence

### Fibonacci Factors

##### Age 16 to 18Challenge Level

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

### Plus or Minus

##### Age 16 to 18Challenge Level

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

### Pythagorean Fibs

##### Age 16 to 18Challenge Level

What have Fibonacci numbers got to do with Pythagorean triples?

### Fibonacci Fashion

##### Age 16 to 18Challenge Level

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

### Golden Fractions

##### Age 16 to 18Challenge Level

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

### Last Biscuit

##### Age 11 to 18Challenge Level

Can you find a strategy that ensures you get to take the last biscuit in this game?

### Golden Fibs

##### Age 16 to 18Challenge Level

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

### Farey Fibonacci

##### Age 16 to 18 ShortChallenge Level

Investigate Farey sequences of ratios of Fibonacci numbers.

### Golden Powers

##### Age 16 to 18Challenge Level

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

### Ordered Sums

##### Age 14 to 16Challenge Level

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. . . .

### The Golden Ratio, Fibonacci Numbers and Continued Fractions.

##### Age 14 to 16

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.

### Golden Mathematics

##### Age 16 to 18

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

### Gnomon Dimensions

##### Age 14 to 16Challenge Level

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

### Building Gnomons

##### Age 14 to 16Challenge Level

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

### Continued Fractions I

##### Age 14 to 18

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

### Leonardo of Pisa and the Golden Rectangle

##### Age 7 to 16

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

### Stringing it Out

##### Age 14 to 16Challenge Level

Explore the transformations and comment on what you find.

### Whirling Fibonacci Squares

##### Age 11 to 16

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

##### Age 11 to 16Challenge Level

Using logo to investigate spirals

### LOGO Challenge - Circles as Bugs

##### Age 11 to 16Challenge Level

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

### First Forward Into Logo 11: Sequences

##### Age 11 to 18Challenge Level

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