Surprising way maths is used in the real world

IT’S a calculation that has helped shape the world around us, even though most of us don’t understand it. Could you solve this high school maths problem?

MATHS can affect so much of the world around us but not many people understand it.

Chalmers Institute of Technology associate professor Julie Rowlett has been in Australia this week to support the Australian Mathematical Sciences Institute (AMSI) winter school and hopes to get more people excited about its potential.

“People might not always get that there is a lot of creativity involved,” Prof Rowlett told news.com.au.

“You try to solve a problem that people are interested in but that no one has solved before — it requires a new idea or approach.

“Some of the ideas don’t work out but it’s really exciting to try them out.

“And once you can prove an idea, it’s true forever.”

One example of maths in action is in the construction of bridges.

Most people may not consider the effects harmonics can have on a structure but mathematicians and engineers have.

Suspension bridges, such as the Golden Gate Bridge in San Francisco, can vibrate in a similar way to a guitar string being plucked.

A famous example where the harmonics of a suspension bridge were not adequately taken into account was the Tacoma Narrows Bridge in Washington state in 1940. This bridge broke apart after a sustained wind of about 64km/h caused the bridge to vibrate as a standing wave.

Mathematicians can predict the resonance of structures like bridges using the study of trigonometry, something that school students are taught in years 11 and 12. Other factors such as aerodynamics (the study of how the wind will behave when it passes over and under the structure) are also related to this.

These calculations help people to visualise how a string (or bridge) would look like when it’s moving.

Maths can be used to describe precisely the way a string can move when it’s plucked and there are only a certain number of patterns. The first three are shown below.

The different ways a piece of string can vibrate. Picture: AMSI

So how do you create a bridge that can accommodate these movements?

The answer is pretty simple, if you know how to get there.

If you add the heights of each curve together at the different points, this gives a snapshot of a particular moment in time. You subtract the values underneath the line because they are “pulling” the string in the opposite direction.

Add the figures above the line and subtract the figures below the line. Source: AMSI.

The numbers you end up with show the position of each part of the bridge, taking into account things like the wind and its speed as well as the material the bridge is made from (different materials have different stiffness).

Traditionally people used to calculate these numbers using pen and paper but the bridges they created were very solid structures.

“If you look at bridges 70 to 100 years old, they are really solid and heavy and overconstructed in some ways because they didn’t have time to do a lot of different calculations by hand,” AMSI schools outreach manager Michael O’Connor told news.com.au.

The more points you calculate the more precise your design will be.

Plotting each point will show how the bridge will move at a certain point in time, under specific conditions.

These days mathematicians have come up with formulas that they can program into computers so it does the calculations for many different points — leading to a more refined project.

Different formulas that can be used to predict the movement of a string. Picture: AMSI

The Golden Gate Bridge vibrates and moves when the wind blows but mathematicians have been able to predict this.