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Hailstones

Hailstones revisited

"Mathematics is not yet ready for such problems." This is what the mathematician John Conway reportedly said about the Collatz conjecture, a simple-looking, yet unsolved mathematical mystery. This week Plus hosted two intrepid work experience students, Sabrina Qian and Joe Dickens, who decided to have a go at this fiendish problem nevertheless. And they made some intriguing discoveries. Here is what they came up with.
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How do insects find their way home?

When insects go foraging, they zoom off from their nest in complex zig-zag paths. How do they manage to find their way back home? And how do they manage to do so along a straight path? These questions are explored in an exhibit at the Royal Society Summer Science Exhibition, currently taking place at the Southbank Centre in London.
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A molecule's eye view of water

Water is essential for life on Earth, and it is a resource we all take for granted. Yet it has many surprising properties that have baffled scientists for centuries. Seemingly simple ideas such as how water freezes are not understood because of water's unique properties. Now scientists are utilising increased computer power and novel algorithms to accurately simulate the properties of water on the nanoscale, allowing complex structures of hundreds or thousands of molecules to be seen and understood.
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Shining a light on gold

People have been using gold particles dispersed in water — gold hydrosols — for medical purposes for over 1000 years. Recently, hydrosols containing gold nanoparticles have become particularly popular because they have exciting potential in cancer therapies, pregnancy tests and blood sugar monitoring.
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Fat body slim

Obesity has reached epidemic proportions and the World Health Organisation estimates that, by 2015, about 3 billion adults will be overweight or obese worldwide. These individuals will be at increased risk of cardiovascular disease, type 2 diabetes, cancer and osteoarthritis.
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The serious mathematics of cereal, socialising and starlings

What have muesli, social networking sites and flocks of birds got to do with mathematics? Scientists and students from the University of Bath will be explaining all at the Royal Society's prestigious Summer Science Exhibition, which opens today.
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The maths inside

This year the Royal Society celebrates its 350th anniversary and Plus is joining in the celebrations. The annual Royal Society Summer Science Exhibition is this year part of a festival called See Further: The Festival of Science + Arts, which explores the links between science and the arts. The festival is taking place at the Southbank Centre in London from the 25th of June to the 4th of July 2010.
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Martin Garner with his hands behind his head

Is the magic over?

The shadow of the late Martin Gardner looms large in Manchester this week as the workshop How to talk maths in public, organised by the Institute of Mathematics and its Applications, draws to a close. The question on everyone's mind is "who will fill the enormous hole left by his absence"?
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Pi

Pi day magic revealed

On March 14 2010 a mathematician and a magician teamed up to perform what they believed to be the world's largest live magic trick. The trick involved a thousand volunteers from the around the world who, using free choice, each came up with a number that was only known to themselves. And although the volunteer might be on the other side of the globe, the mathematician and the magician were able to read their mind and tell them which number they had chosen.

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Win money with magic squares

Magic squares have been known and studied for many centuries, but there are still surprisingly many unanswered questions about them. In an effort to make progress on these unsolved problems, twelve prizes totalling €8,000 and twelve bottles of champagne have now been offered for the solutions to twelve magic square enigmas.