Curious Cases – Details, episodes & analysis

There is a bizarre number in maths referred to simply as ‘i’. It appears to break the rules of arithmetic - but turns out to be utterly essential for applications across engineering and physics. We’re talking about the square root of -1. WHICH MAKES NO SENSE.

Professor Fry waxes lyrical about the beauty and power of this so-called ‘imaginary’ number to a sceptical Dr Rutherford. Dr Michael Brooks tells the surprising story of the duelling Italian mathematicians who gave birth to this strange idea, and shares how Silicon Valley turned it into cold hard cash. It's all about oscillations, Professor Jeff O’Connell demonstrates. And finally, Dr Eleanor Knox reveals that imaginary numbers are indispensable for the most fundamental physics of all: quantum mechanics.

Imaginary, impossible…but essential!

Contributors: Professor Jeff O’Connell, Ohlone College California, Dr Michael Brooks, Author of 'The Maths That Made Us', and Dr Eleanor Knox, Philosopher of Physics at KCL and a Senior Visiting Fellow at the University of Pittsburgh.

Producer: Ilan Goodman

Hungry for pi? Chow down on this!

Pi is the ratio between a circle’s diameter and its circumference. Sounds dull – but pi turns out to have astonishing properties and crop up in places you would never expect. For a start, it goes on forever and never repeats, meaning it probably contains your name, date of birth, and the complete works of Shakespeare written in its digits.

Maths comedian Matt Parker stuns Adam with his ‘pie-endulum’ experiment, in which a chicken and mushroom pie is dangled 2.45m to form a pendulum which takes *exactly* 3.14 seconds per swing.

Mathematician Dr Vicky Neale explains how we can be sure that the number pi continues forever and never repeats - despite the fact we can never write down all its digits to check! She also makes the case that aliens would probably measure angles using pi because it’s a fundamental constant of the universe.

NASA mission director Dr Marc Rayman drops in to explain how pi is used to navigate spacecraft around the solar system. And philosopher of physics Dr Eleanor Knox serves up some philoso-pi, revealing why some thinkers have found pi’s ubiquity so deeply mysterious.

Hannah grins with delight for most of show. It’s all maths!

Producer: Ilan Goodman

Contributors: Matt Parker, Dr Vicky Neale, Dr Marc Rayman, Dr Eleanor Knox

"Why don't children like vegetables?" asks Penny Young from Croydon, and every parent ever.

This week Rutherford and Fry dig into the science of taste and discover that there may be more to this question than meets the eye.

Children and adults have a different taste experience when they eat the same foods. When you're young, foods can taste saltier and more bitter. What's more, as Jackie Blisset, Professor of Childhood Eating Behaviour explains, there are even evolutionary reasons why toddlers avoid vegetables.

For most children it's a phase, but a minority of adults are also labelled as fussy eaters. According to food psychologist Linda Bartoshuk, they are probably what's known as 'supertasters'.

Supertasters live in a neon taste world where vegetables are more bitter, and chillies are unbearably hot.

Adam sets out on a quest to find potential supertasters in the Radio 4 offices. First stop, the Today programme where Nick Robinson and Sarah Montague become his experimental guinea pigs, with surprising results.

Send your questions for consideration to: curiouscases@bbc.co.uk

Presenters: Hannah Fry, Adam Rutherford Producer: Michelle Martin.

"Why don't thousands of bats in a cave get confused? How do they differentiate their own location echoes from those of other bats?" This puzzling problem was sent in to curiouscases@bbc.co.uk by Tim Beard from Hamburg in Germany.

Since ecolocation was first discovered, this question has perplexed biologists. Hannah turns bat detective to try and track down these elusive creatures at The Queen Elizabeth Olympic Park in East London. This is where zoologist Kate Jones from University College London is using a network of smart sensors to find, identify and track wild bats.

John Ratcliffe from Toronto University chats bats and sonar with Adam to try and locate the answer. It's an unlikely tale involving gruesome early experiments, cunning electric fish and some surprising bat maths.

Send your Curious Cases for consideration to: curiouscases@bbc.co.uk

Presenters: Adam Rutherford, Hannah Fry Producer: Michelle Martin.

"Why do we dream and why do we repeat dreams?" asks Mila O'Dea, aged 9, from Panama.

Hannah and Adam delve into the science of sleep. From a pioneering experiment on rapid eye movement sleep, to a brand new 'dream signature' found in the brain, they discover how scientists are investigating our hidden dreamworld.

Featuring sociologist Bill Domhoff from the University of California Santa Cruz, sleep psychologist Mark Blagrove from the University of Swansea, and neurologist Francesca Siclari from the University of Lausanne.

Presenters: Adam Rutherford, Hannah Fry Producer: Michelle Martin.

Why do we get static shocks?

Jose Chavez Mendez from Guatemala asks, "Some years ago, in the dry season, I used to be very susceptible to static electricity. I want to know - why do static shocks happen?"

The team uncover some slightly unethical science experiments on static electricity from the 1700s. Hannah Fry uses a Leyden Jar to demonstrate how static electricity works with help from her glamorous assistant, Adam Rutherford. Spoiler Alert: it doesn't end well for Adam.

They discover what makes some people more susceptible to static shocks, and how bees and spiders have harnessed the awesome power of electricity.

Featuring electromagnetism scientist Rhys Phillips and physicist Helen Czerski, author of 'Storm in a Teacup: The Physics of Everyday Life'.

Presenters: Adam Rutherford, Hannah Fry Producer: Michelle Martin.

Why do songs get stuck in our heads? And what makes some tunes stickier than others?

Drs Rutherford and Fry investigate 'earworms', those musical refrains that infect our brains for days. Every morning 6Music DJ Shaun Keaveney asks his listeners for their earworms, and Hannah finds out which tunes keep coming back.

Adam asks Dr Lauren Stewart, from Goldsmiths University, to reveal the musical features that make some songs catchier than others.

And they find out why, in times of crisis, an earworm may just save your life.

Producer: Michelle Martin.

No one knows why the Earth's magnetic North and South poles swap. But polar reversals have happened hundreds of times over the history of the Earth.

So, asks John Turk, when is the next pole swap due and what will happen to us?

Hannah turns to astronomer Lucie Green from Mullard Space Science Laboratory to discover how the earth's magnetic field protects us from the ravages of space. And Adam consults geophysicist Phil Livermore from the University of Leeds to find out if, and when, we're facing a global apocalypse.

Plus astronaut Terry Virts, author of The View from Above, describes his experiences of a strange magnetic glitch in the earth's magnetic field, known as The Bermuda Triangle of Space, which could help us prepare for the next event.

Presenters: Hannah Fry, Adam Rutherford Producer: Michelle Martin.

Can chemistry help us bake the perfect cake?

Listener Helena McGinty aged 69 from Malaga in Spain asks, "'I have always used my mother's sponge cake recipe. But is there a noticeable difference in the outcome if you vary some of the ingredients, or the method?"

In this episode Hannah and Adam go head to head in a competition to create the perfect cake using the power of science.

They are aided by materials scientist Mark Miodownik, from University College London, with tips on how to combine the ideal ingredients and trusted techniques to construct a structurally sound sponge.

Jay Rayner, food critic and presenter of Radio 4's The Kitchen Cabinet, is on hand to judge the results. But who will emerge victorious in this messy baking battle?

Presenters: Hannah Fry, Adam Rutherford Producer: Michelle Martin.

"It started while listening to the excellent Experiment IV by Kate Bush. The premise of the song is of a band who secretly work for the military to create a 'sound that could kill someone'. Is it scientifically possible to do this?" asks Paul Goodfield.

Hannah consults acoustic engineer Trevor Cox to ask if sonic weapons could kill. And Adam delves into subsonic frequencies with parapsychologist Chris French to investigate their spooky effects.

You can send your everyday mysteries for the team to investigate to: curiouscases@bbc.co.uk

Presenters: Adam Rutherford, Hannah Fry Producer: Michelle Martin.