Or will they have you in pieces?

Today’s puzzles are all geometrical, and all from the mind of the UK’s most enduring and eloquent popular maths writer, Ian Stewart.

1. Bonnie Tiler

Child in a critical condition in hospital after being pulled from the water in Vaucluse at about 4.20pm Sunday

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A boy has been attacked by a shark in Sydney’s east and is in a critical condition after suffering serious injuries to both legs.

The boy, believed to be aged about 12, was pulled from the water at Shark beach at Neilsen Park, in the eastern suburb of Vaucluse, on Sunday afternoon.

Newly appointed Cambridge professor says feat would accelerate scientific knowledge by an order of magnitude

Dark, hungry and inescapable: black holes are often portrayed as the ultimate cosmic villains.

But now astronomers are preparing to capture a movie of a supermassive black hole in action for the first time, in observations that could help reveal another side to these elusive – and perhaps misunderstood – space objects.

Pioneering scheme hopes species that thrived for thousands of years in Irish waters can do so again

The dinghy slowed to a stop at a long line of black bobbing baskets and David Lawlor reached out to inspect the first one.

Inside lay 60 oysters, all with their shells closed, shielding the life within. “They look great,” beamed Lawlor. So did their neighbours in the next basket and the ones after that, all down the line of 300 baskets, totalling 18,000 oysters.

Our reviewer loved this wake-up light more than any other he’s tested – it’s even knocked his previous best sunrise alarm off the top spot

• Read the full ranking in our sunrise alarm clock test

Since I first tested sunrise alarm clocks last winter, I’ve come to suspect that there’s no such thing as getting up on the wrong side of bed. What we ought to be worried about is waking up on the wrong side of dawn.

During summer (and other times of the year, for late risers), the sunrise begins to rouse us before we wake up. The brain kicks into gear and sends signals to initiate all sorts of bodily processes, from metabolism to hormone release, which helps us to feel ready for the day. It’s a fundament of our circadian rhythm – and we miss out on it whenever we wake before it gets light.

With tens of thousands thought to be arriving each year, the ‘southern route’ is becoming more perilous and extortionary

On the evening of 5 January, residents driving through the suburb of Mulbarton in south Johannesburg saw five young men in the street dressed only in underwear.

They were later picked up along with seven other young men by South African police. Police said two were in a car involved in a high-speed chase. A 47-year-old Ethiopian man was arrested and charged with kidnapping and failing to stop when police instructed him to. The 12 men, originally thought to be teenagers but said by police to be 22 to 33, were charged with being in South Africa illegally.

Food produce and other waste has been littering Sussex coastline as capsized shipping containers wash ashore

Coral Evans was walking along the beach in Brighton on Tuesday evening when she came across an unfamiliar sight.

“Hundreds of dust masks had washed up, along with single-use plastic gloves and cans of dried milk,” she said. “It was odd to see in winter – because nothing surprises us in summertime with the amount of people on the beach.”

Tony Cholerton created Robovacc to inoculate a timid tiger at London zoo – but says it could administer jabs to badgers

It began with the tiger who wouldn’t come to tea. Cinta was so shy that she refused to feed when keepers at London zoo were around, and staff wondered how they would ever administer the young animal’s vaccinations without traumatising her.

So Tony Cholerton, a zookeeper who had been a motorcycle engineer for many years, invented Robovacc – a machine to quickly administer vital jabs without the presence of people.

Call for UK state to step in after Gupta-owned Dalzell works in Scotland unable to produce metal for three new warships

A shipbuilder for the Royal Navy faces an uncertain wait for the steel to build three warships because of a shortage of cash at the Scottish steel mill that has won the contract.

Liberty Steel Dalzell in Scotland has been unable to start production in earnest because there is “no cashflow to buy slab”, despite an order to supply 34,000 tonnes of metal plates to build fleet solid support (FSS) ships for the navy, according to two sources with knowledge of the situation.

• 23-year-old dismantles unwell Italian 7-6 (1), 6-4, 6-1

• First Grand Slam appearance as a direct qualifying entrant

For a few fleeting moments inside the vast John Cain Arena, it seemed like Arthur Fery had missed his opportunity. The 23-year-old’s attempts to serve out an excellent set against, the 20th seed at the Australian Open, Flavio Cobolli, had ended painfully. He quickly found himself serving down 5-6 against one of the best players in the world with his back to the wall.

These circumstances often do not favour the more inexperienced, lower-ranked players, but in one of the biggest matches of his career Fery made his own luck as he rose to the occasion and delivered the first great upset of the Australian Open, dismantling Cobolli 7-6 (1), 6-4, 6-1 to reach the second round for the first time.

Royal will join a group of notable figures in his action against the tabloid and its stablemate, the Mail on Sunday, in a trial expected to last nine weeks

On Monday morning, Prince Harry’s legal war with the Daily Mail, one of the British media’s most formidable forces, will finally come to trial in court 76 of the high court in London.

The prince is joined in his action by some of the most recognisable figures in British life: the singer and songwriter Elton John and his husband, David Furnish; actors Liz Hurley and Sadie Frost; Doreen Lawrence, a Labour peer whose son Stephen was murdered in a racist attack; and former politician Simon Hughes, who once ran to lead the Liberal Democrats.

Donald Trump will lead the largest US delegation ever at the World Economic Forum, as others plan a fightback against his policies

“A Spirit of Dialogue”: the theme for this year’s World Economic Forum, the gathering of the global elite in the sparkling Alpine air of Davos, seems a heroic stretch, when star guest Donald Trump has spent the past year smashing up the world order.

The president will touch down alongside the snowcapped Swiss mountains with the largest US delegation ever seen at the WEF, including the secretary of state, Marco Rubio, the treasury secretary, Scott Bessent, the commerce secretary, Howard Lutnick, and the special envoy Steve Witkoff.

Couples not sharing religious beliefs or going to each other’s places of worship isn’t unusual, but perhaps there’s something else going on here

When I met my husband eight years ago, I knew he was churchy, but as a low-church Protestant, I thought this wouldn’t be a problem. Outside church, I am comfortable with our religious differences. I sort of believe in God, and find immense spirituality in nature, but think Christ was simply a good man, whereas my husband believes it. He respects my beliefs and has never imposed his on me.

The problem I have is with the church we attend. I often feel a fraud as I don’t share the beliefs of the rest of the congregation. I feel alienated by the emphasis on theology over Christ’s teachings, and the hymns and rituals. I resent having to sacrifice my Sundays mouthing words I do not believe.

My experience of court was eye-opening. And when I sat in on other cases, I realised how often mothers are vilified

It’s 1836 and the French writer George Sand is swimming in the River Indre with her clothes on, weighed down by layers of ankle-length fabric. To anyone passing by, she must look mad or worse – driven by a death wish. But for her there is the relief of cool water sluicing hot skin, after walking for hours in 30C heat. She’s been moving all day because if she stops she’ll remember how frightened she is: she’s about to go to court to fight for her children against a husband driven by punitive anger.

Custodire. To care. To look after. To guard. To restrain. Maternal care is, we are constantly told, the most natural of functions. But for century after century, women who transgress the expected norms of what a mother should be have battled for their children and been found wanting. Maternal care comes at a price when the law is involved. And all too often custody can be more a question of restraint than care.

Government extends grip on north after stalled efforts under Ahmed al-Sharaa to reach accommodation with Kurds and fold their forces into national army

Syria’s army has taken control of swathes of the country’s north, dislodging Kurdish forces from territory over which they held effective autonomy for more than a decade.

State media said on Saturday that the army took over the northern city of Tabqa and its adjacent dam, as well as the major Freedom dam, formerly known as the Baath, west of the Syrian city of Raqaa. It came despite US calls to halt the advance.

Prime minister and opposition politicians condemn threat to impose 10% tariff unless deal reached to buy the Arctic island

Keir Starmer has said Donald Trump’s decision to impose 10% tariffs on the UK and seven other European countries over Greenland was “completely wrong”.

The US president said on Saturday that the levies would apply from 1 February to Nato members – including the UK, France and Germany – who have deployed troops to the territory in response to growing uncertainty over its future.

Many believed a US president would – for the first time – rescue them but now people can only despair after mass arrests and brutality

When Donald Trump, said he would “rescue” protesters if Iranian authorities started shooting, Siavash Shirzad believed the US president.

The 38-year-old father had seen protests rise up before, only to be brutally crushed by authorities.

But this was the first time in his life that the president of the United States had promised to help demonstrators. Reassured, Shirzad took to the streets, ignoring his family’s warnings and joining the growing crowds.

Hormones impact almost all of our bodily functions, from skin, to the gut, to our moods. Here, experts on hormonal and metabolic health explain how to stay well

“Most people would like to have more energy and be leaner,” says Prof David Ray, an endocrinologist at the University of Oxford who also provides NHS services. “There is a connection between how we choose to live, what our bodies look and feel like, and the hormones that are going around the body. What endocrinologists deal with is disorders of either a lack of hormones, or too much of a hormone.”

• Vance to represent US at Olympic opening ceremony

• Ceremony spans Milan and three mountain venues

• Former US Olympic champions set to join delegation

US vice-president JD Vance will head the American presidential delegation to the opening ceremony of the 2026 Winter Olympics in Italy, the White House confirmed Saturday.

Vance is scheduled to attend the ceremony on 6 February, when the Milan-Cortina Games officially get underway. He will be accompanied by second lady Usha Vance, secretary of state Marco Rubio and US ambassador to Italy Tilman Fertitta.

Three Czech skiers swept away in Murtal district while five killed in Pongau area near Salzburg

An avalanche killed three Czech skiers in central Austria, police said, bringing the total to eight killed in the country’s Alps on Saturday.

Avalanches across the Alps have claimed victims since last week after heavy snowfall.

• Nix to undergo surgery after breaking ankle in OT

• Season-ending injury suffered late in playoff win

• Denver advance despite injury to second-year QB

Bo Nix broke his right ankle late in overtime of the Denver Broncos’ divisional-round victory over Buffalo on Saturday and will have surgery that will sideline him for the rest of the playoffs.

Coach Sean Payton delivered the stunning news about his second-year quarterback in the aftermath of Denver’s biggest win in a decade. Backup quarterback Jarrett Stidham will start the AFC championship game next weekend.

Kyrylo Budanov arrives in US heading delegation for further talks on peace proposals. What we know on day 1,425

Russia is taking aim at Ukraine’s nuclear power system, Volodymyr Zelenskyy said on Sunday, as the Kremlin continues to try to freeze Ukraine into submission by crippling its energy grid. “We do not see any willingness on the part of the aggressor to comply with any agreements or end the war,” the Ukrainian president said. “Instead, there is ample information about preparations for further Russian strikes on our energy sector and infrastructure, including facilities and networks that serve our nuclear power plants. Each such Russian strike on the energy sector amid such a harsh winter weakens and undermines the efforts of key states – in particular the United States – to end this war.”

Zelenskyy spoke after a briefing from Ukraine’s chief of defence intelligence, Oleh Ivashchenko – the recent replacement for Kyrylo Budanov, who was made head of the president’s office. Budanov on Saturday confirmed his own arrival in the US to discuss peace proposals. He and Ukrainian negotiators Rustem Umerov and Davyd Arakhamia would meet with US envoy Steve Witkoff, Jared Kushner and the US army secretary, Dan Driscoll, Budanov said. Zelenskyy has tasked his delegation at the Miami talks with finalising proposals about security guarantees and economic recovery. If American officials approve the proposals, the US and Ukraine could sign a deal next week at the World Economic Forum in Davos, Switzerland, according to Zelenskyy. However Russia has given no indication it will accept any peace deal without Ukraine’s entire Donbas region being handed over for a start.

Russian attacks left at least two people dead and others injured in Kharkiv oblast on Saturday, regional authorities said. A strike that damaged a critical infrastructure facility in Kharkiv city’s industrial district could seriously affect power and heating, said the mayor, Ihor Terekhov, with the energy system “constantly operating at its limits”. One person was wounded in the attack. An attack on a house in Kharkiv city killed a woman aged 20 and wounded others. In the village of Borivske, a 52-year-old woman was killed when a drone hit a public transport stop, prosecutors said. In the Sumy region, emergency services said an airstrike on a residential neighbourhood wounded three women and a seven-year-old child, and left 15 residential buildings damaged.

Russia struck energy infrastructure in Ukraine’s Kyiv and Odesa regions overnight into Saturday, the ministry of energy said. More than 20 settlements in the Kyiv region were left without power. Zelenskyy said Ukraine needed to ramp up the importation of electricity and the acquisition of additional equipment from partners. Officials have instructed state energy companies Ukrzaliznytsia, Naftogaz and Ukroboronprom to urgently purchase imported electricity covering at least 50% of their own consumption, according to Denys Shmyhal, the energy minister.

Shmyhal announced that Lithuania would be providing Ukraine with more energy generating equipment for Kyiv and the most critically affected regions, after already supplying equipment for emergency repairs on coal and nuclear power plants. “In addition we have received over 2,000 solar panels, various equipment and machinery from our Lithuanian friends,” Shmyhal said. “Lithuania has contributed €5.7m euros to the energy support fund of Ukraine … There is not a single power plant left in Ukraine that has not been hit by Russian strikes. Ukrainian energy workers continue to repair around the clock and return electricity to people.”

Brisbane Entertainment Centre
Solo songs and Talking Heads classics mingle in a spectacular performance that doesn’t pull any punches

Dressed from head to foot in iridescent orange, David Byrne and his 12-piece backing band look as if they’re about to burst into flames. On a vast, empty stage – uncluttered by amplifiers, microphones or any of the usual things that anchor a live performance – the former Talking Heads frontman is still full of twitchy energy.

Thankfully, there’s no spontaneous combustion. The template for tonight’s spectacle remains the legendary Stop Making Sense tour of 1984 – via American Utopia – where the show is built in increments. It starts slowly with Heaven, from Talking Heads’ 1979 album Fear of Music, a song that has lost none of its existential power.

• Valentino Guseli takes bronze and NZ’s Campbell Melville Ives silver

• More medals in bobsleigh and snowboard cross ahead of Milan-Cortina Games

Snowboard king Scotty James has dazzled to reign supreme in the last World Cup halfpipe event before the Olympics, where he’ll be seeking an elusive gold medal.

On a big day for Australia’s Olympic hopes, James sent a clear message to rivals as he won the prestigious Laax Open in Switzerland for a third consecutive time and fifth time in total, while young countryman Valentino Guseli was third.