Mathematics: Mathematical Modelling With Sequences & Series – Leaning Block Towers & The Harmonic Series – University Tutorial With Dr Robert Whittaker From University of East Anglia

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In this live interactive Mathematics tutorial, we will be joined by Dr Robert Whittaker, Lecturer in Applied Mathematics in the School of Engineering, Mathematics and Physics at University of East Anglia, who will present Mathematical Modelling with Sequences & Series: Leaning Block Towers & The Harmonic Series.

The full context/introduction to this live and interactive discussion is provided in a Headliner recorded resource (see below). This recording can be watched as a class activity or independently in preparation for the discussion.

In this Headliner, we’ll consider a simple physical problem of making a leaning stack of identical cuboidal blocks. We want to know what is the largest lean/overhang that can be achieved with different numbers of blocks. Using mathematical modelling, we’ll see that the solution turns out to involve the harmonic series (1 + 1/2 + 1/3 + 1/4 + …). 

In the pre-recorded video, I’ll introduce the problem and suggest some things to explore before the live session. In the live session, we’ll first derive the mathematical expression for the overhang of each block. We’ll then look at the properties of the harmonic series, and see what this means for the stacks of blocks. We’ll also talk a bit about convergent and divergent series (infinite sums) more generally, and see how something we take for granted about finite sums is no longer true when infinitely many numbers are involved.

It would be useful if participants have access to a set of 6 or more identical cuboidal blocks to play with (a giant Jenga set is ideal, but dominoes or other solid wooden bricks would also work). It would also be useful if viewers had time to pause the video half-way through to try some things with these blocks before continuing.

Lecturer Profile: Dr Robert Whittaker

Our events are designed so that a group of students can take part from a classroom, or students and teachers can take part as individuals, either from school or from home. There is no charge for taking part.

As a live, participative event, this session will not be recorded but access to the Headliner recording will continue to be accessible.

Suitable for: Aged 16+ pre-university students studying, or with a possible interest in studying, Mathematics. Teachers and members of school staff, as always, are welcome too and participants can join as individuals from school/college or home, or as a group from school/college.

Preparation/Pre-Reading: Students are asked to watch the Headliner recording and consider some of the key issues and any questions raised. It would be useful if participants have access to a set of 6 or more identical cuboidal blocks to play with (a giant Jenga set is ideal, but dominoes or other solid wooden bricks would also work). It would also be useful if viewers had time to pause the video half-way through to try some things with these blocks before continuing.

The IT Setup: The event will be run on Zoom and participants will be able to join using laptops, tablets, and mobile devices. If you are joining as a school group, we recommend connecting with one device and projecting on to a whiteboard. You will be able to interact with the university via typed comments and questions and/or via a microphone. Full details will be sent to those who have registered (see below) prior to the event.

Booking a Place: This is free for schools and colleges. If you would like to take part in this event, please register your interest using the link to the registration form below:

Register here