Acute solution

The method sometimes works for triangular prisms too. Measuring the height of the triangle at the end of the prism packaging, doubling it and adding it to the overall length of the box gives you the perfect length of paper to cut to cover its triangular ends with paper three times for a flawless finish.

To wrap a tube of sweets or another cylindrical gift with very little waste, measure the diameter (width) of the circular end and multiply it by Pi (3.14…) to find the amount of paper needed to encircle your gift with wrap. Then measure the length of the tube and add on the diameter of one circle to calculate the minimum length of paper needed. Doing this should mean the paper meets exactly at the centre of each circular end of the gift requiring one small piece of tape to secure it. But it’s best to allow a little extra paper to ensure the shape is completely covered or risk spoiling the surprise.

Circling back

If you have bought anyone a ball, then woe – spheres are arguably the hardest shape to wrap. It’s impossible to cover a ball smoothly using a piece of paper, not only because the properties of paper stop it from being infinitely bendable, but because of the hairy ball theorem, says Sophie Maclean, a maths communicator and PhD student at King’s College London. The theorem explains it is impossible to comb hair on a ball or sphere flat without creating at least one swirl or cowlick.

“If you think about putting wrapping paper round a ball, you’re not going to be able to get it smooth all the way round,” says Maclean. “There’s going to have to be a bump or gap at some point. Personally, I quite like being creative with wrapping and this is where I would embrace it. Tie a bow around it or twist the paper to get a Christmas cracker or a present that looks like a sweet.”

If paper efficiency is your goal when wrapping a football, you may want to experiment with a triangle of foil. An international team of scientists studied how Mozartkugel confectionery – spheres of delicious marzipan encased in praline and coated in dark chocolate – are wrapped efficiently in a small piece of foil. They observed that minimising the perimeter of the shape reduces waste, making a square superior to a rectangle of foil with the same area.

SALZBURG, Austria — As you approach Salzburg’s Max Aicher Stadium on the eve of the feast of St. Nicholas, you’d be forgiven if you thought that, from a distance, there appeared to be a Chewbacca convention underway. As you got closer, though, you’d realize the few hundred mostly men dressed in furry brown costumes were not from a galaxy, far, far away, but had instead assembled for a far more traditional, Earth-bound reason: to play, en masse, the alpine character of Krampus, the monstrous horned devilish figure who, according to custom in this part of Europe, accompanies St. Nicholas as he visits children and assesses their behavior from the past year. While St. Nick rewards the good boys and girls, his hairy, demonic sidekick punishes the bad children.

“It’s basically a good cop, bad cop arrangement,” says Alexander Hueter, self-proclaimed Überkrampus of Salzburg’s annual Krampus Run, an event when hundreds of Krampuses are let loose throughout the old town of Salzburg, where they terrorize children, adults, and anyone within the range of a swat from their birch branch switches they carry.

Members of Krampus clubs throughout Austria and the German state of Bavaria gather at a local soccer stadium to change into their Krampus costumes.

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When asked to explain why people in this part of Europe take part in this centuries-old tradition, Hueter skips the centuries of Roman, Pagan and early Christian history that, together, morphed into the legend of the Krampus figure and instead cuts straight to the chase: entertainment.

“If St. Nicholas comes to town on his own, it’s nice,” says Hueter with a polite smile, “but there’s no excitement. No tension. I mean, St. Nick is all well and good, but at the end of the day, people want to see something darker. They want to see Krampus.”

And if it’s Krampus they want, it’s Krampus they’ll get, says Roy Huber, who’s come across the border from the German state of Bavaria to take part in this year’s Krampus Run. “The rest of the year, I feel like a civilian,” Huber says with a serious face, “but when the winter comes, you have the feeling under your skin. You are ready to act like a Krampus.”

Huber stands dressed in a coffee-colored yak and goat hair costume holding his mask which has a scar along the left side of its face, two horns sticking out of the scalp, and a beautifully waxed mustache that makes his monstrous avatar look like a Krampus-like version of the 1970s Major League Baseball closer Rollie Fingers.

Roy Huber, from Bavaria, holds his Krampus mask prior to the Krampus Run. “When the winter comes, you get the feeling to be Krampus,” he says.

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Behind Huber stands a Krampus with a red face and several horns that make up a mohawk. Benny Sieger is the man behind this punk version of a Krampus, and he says children are especially scared of his get-up.

“Very scared,” he says, “but if I act like a sensitive Krampus, it can go well. In fact, our hometown Krampus club hosts an event called ‘Cuddle a Krampus’ to ensure that we are not so scary.”    
       
Sieger, though, says he shows no mercy for young adults, especially young men, who he says “are basically asking to be hit” if they come to a Krampus run. He shows off a long switch made up of birch tree branches that smarts like a bee sting when hit with it.

Normally Nicklaus Bliemslieder would be one of those young adults asking for it at the Krampus run — he’s 19 years old — but his mother boasts of how her son gamed the system by playing a Krampus for 14 years straight since he was 5 years old.

“I was never scared of being a Krampus,” he says, “but I was scared of the Krampus. The first time I put the mask on, I wasn’t scared anymore.”

Blieslieder, Siger, Huber and dozens of other Krampuses pile onto a row of city buses that will take them to Salzburg’s old town, singing soccer songs on the way to rile themselves up. In the town center, they put their masks on, the bus doors swing open, and dozens of Krampuses empty into the streets of downtown Salzburg, lunging at shoppers, swatting them with switches, their cowbells a-clanging. At the front of the procession dressed in a white and gold robe is St. Nicholas, holding a staff, handing out candy with a serene smile, and blissfully oblivious of the cacophony of blood-curdling chaos behind him.

After a city bus drops off more than 200 Krampuses at the entrance to the old town of Salzburg, the Krampuses start to put their masks on and get into character.

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Salzburg resident Rene Watziker watches the Krampuses go by, his 4 1/2 year-old son Valentin perched on his shoulders, his head buried into the back of his father’s neck, and his oversized mittens covering his eyes in terror. As Valentin shakes in fear, his father tries to coax him out of it — unsuccessfully.

“He’s too scared of the Krampuses,” says Watziker, laughing. “This is great, though, because this is my childhood memory, too. I want him to have the same good memories of his childhood. He’s going to look at the video I’m shooting and then he’ll be very proud he came.”

Salzburg resident Rene Watziker watches the Krampuses go by, but his four-and-a-half year-old son Valentin perched is too scared to look at them.

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Further down the pedestrian street, Krampuses hit onlookers with handfuls of branches and smear tar on people’s faces. Onlooker Sabeine Gruber, here with her 13-year-old daughter, manages to crack a smile at the spectacle, but she says the Krampus Run has gotten tamer with time. She points to the stickers on the backs of these Krampuses exhibiting numbers in case you want to complain that a particular Krampus hit you too hard.

“When I was a child,” says Gruber, “this was far worse. You were beaten so hard that you woke up the next day with blue welts on your legs. These days the Krampus run is more like a petting zoo.”

Esme Nicholson contributed reporting.

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Published
December 13, 2025
4:00 AM PST