Off-the-shelf Masterclass: Numbers in nature

What is the Golden Ratio and why is it interesting? Why does it crop up in nature so often? Here we explore these questions and discover the mathematics of nature.

close-up of a daisy
Image credit: Sergio Quesada via flickr

About this Masterclass

Mathematics can be used to describe many aspects of the world around us, and interesting mathematical concepts underlie many natural structures. Starting from the idea of limits of sequences, we look at the Golden Ratio, a number which has many links in nature, but is also misunderstood. We discuss why this number is interesting, and explore some examples of places it can be seen.

Note that this session overlaps to a certain extent with ‘Rabbits and Sequences’, which also covers the idea of sequences and introduces the Fibonacci sequence. However, both sessions could be covered by the same group, as this session focuses more on limits and covers the Golden Ratio.

Length: 2 hours (see the session leader notes for ideas on how to shorten the Masterclass).

Resources needed

  • Worksheets - as detailed in the Session Leader Notes
  • Calculator, one per student (doesn’t need to be a scientific calculator)
  • A pair of scissors per student
  • A bunch of flowers and a bag of pine cones (see below*) - either enough for one of each per student, or one of each per pair of students
  • Marker pens, for drawing on the pine cones (if possible, a metallic or chalk pen will show up better); pencils may work in a pinch
  • A whole pineapple and some brightly coloured electrical tape (optional)
  • Whiteboard or flipchart, for collating results
  • Glue sticks - one per student, or one per pair

*Please read instructions in Session Leader Notes about the correct type of flowers and how to prep the pine cones in advance.

Support for this Masterclass

All supporting notes, worksheets and solutions can be downloaded from this page along with the Powerpoint presentation.

The Session Leader Notes offer full notes on the activities and a detailed list of resources, including quantities needed. 

The Session Helper Sheet can be distributed amongst helpers so they can better support the students.

Ask the Ri

You can collect any student questions and email them to the Ri Masterclass team at - we will endeavour to answer them before the next Masterclass in your series.

Masterclass series support

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