Dec 17th / Last Friday, some of the students in Year 10 attended Mathematics and Physics lectures at the Institute of Education in London.  In the following report Jeannie Leung explains what she and her fellow students all learned about.

Maths day 1

The lectures were given by professors from a range of Universities, providing the students with insights into the fields of Maths and Physics.

Dr Hannah Fry: The Human Herd

Maths = Hannah Fry

The first lecture was led by Dr Hannah Fry from the University College of London [UCL], who is researching ‘Consumer behaviour’ and also has a pHd in ‘food dynamics’.  She began the lecture with a game: we were asked to guess the number of sweets that were inside a jar. The audience gave a range of answers from 21 to 360. Dr Fry finally revealed that the answer was ‘117’.  However this was not the point of the game.  From this exercise, Dr Fry added the guesses and found the average of these group of numbers and the average was ‘117.9’, which was extremely close to the actual number.  This proves the theory of the Wisdom of the Crowd suggested by ‘Francis Galton.’ The theory shows that the number of people who overestimate the answer balances out the number of people who under estimate, so the average of these collected numbers is an accurate estimate of the actual answer.

Have you ever wondered why we can clap in synchronization within a big crowd? You probably didn’t realise this but when we all clapping in a crowd, we automatically clap at the same rate as the person next to us and this continues all around the room, creating a synchronized clap. This is what we explain as ‘Herd-like behaviour’, since we are matching the movements of those around us – like a ‘herd’.  Mathematical models like these can be used to predict how human/living things will react in different situations. For example, architects use these to help them design a building that is safe, since with a Mathematical model we can predict the movements of people during a fire, so with this data architects can design buildings that can lead people to safety as efficiently as possible.

Just like life, Wikipedia is a network which is connected to many different things. For example, if you were to begin on a page [any page] and you were to click on the first link that is not in italics/bold or in brackets, there is a 94.52% chance for you to end up at the page ‘Philosophy.” From any page such as ‘One Direction,’ you would eventually end up at the page ‘Philosophy.’ From this experiment we can see that some pages are well connected [Philosophy] and other pages are less connected [One Direction].

We can see that in many situations, people are one big herd.

Dr Hugh Hunt: Boomerangs, Bouncing balls and other Spinning things

Maths = Hugh Hunt

The second lecture was led by Dr Hugh Hunt from the University of Cambridge, who works in the Engineering department [which involves a lot of maths].  Do bouncing balls help us to understand the particle theory of light?  No!  Light does not behave in this way. When light is reflected off the ground and a mirror [one above the other] it always goes to the opposite direction from which it was shone. Unlike light, a bouncing ball always returns the way it came.  Why is this? This is because as the ball hits the ground it spins turning it back in the direction it came.  The backspin on a ball will always return the way it came. A topspin will go in the opposite direction. The famous bouncing bombs of the Dambusters Raid reflect the theory of spinning.

Why does a spinning top stay up? The theory of the ‘Gyroscopic effect’ [Gyroscopic precession] is what keeps it up. For this theory to work, you need a ‘couple’ [a pair of two equal forces]. In many ways a spinning top and a bike wheel are very similar.

Linear momentum = mass x velocity

Force = mass x acceleration

You can tell when something is accelerating since a force will be present. Dr Hunt performed a demonstration to show this. He had a tennis ball, string, a steel pipe and a carton of 2 litres of water.  The string was then attached to the ball and the carton with the steel pipe in between. Surely, it is not possible for a spinning tennis ball to lift a carton of water? Wrong, it is entirely possible! With the accelerating speed of the tennis ball a force was created and soon enough the carton began to rise.

Similarly with ballet dancers and ice skaters when their arms are out, they feel heavy and they spin slowly however as soon as the arms are moved closer to the body the speed of the spin begins to accelerate. With cats, it is the same idea. They always land on their feet because they can turn their bodies whilst they are falling to ensure that they land on their feet.