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Gnomon Dimensions

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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What Is the Question?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

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Factorising with Multilink

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Building Gnomons

Stage: 4 Challenge Level: Challenge Level:1

This screenshot shows you how to use the Cellular resource to build gnomons from scratch. Alternatively, you can choose the "build gnomons" starter drawing and manipulate them in the same way.

How to build gnomons


Here are the perimeters of $G_6$.


Here are the perimeters of $G_6$ rewritten in terms of their Fibonacci numbers ($F_1 = 1, F_2 = 1, F_3 = 2, F_4 =3$ and so on).

Can you draw a diagram showing what happens more generally?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.