Fibonacci sequence

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

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

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

Investigate Farey sequences of ratios of Fibonacci numbers.

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

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

Using logo to investigate spirals

Explore the transformations and comment on what you find.