The one thing that people who love math and people who hate math tend to agree on is this: You're only really doing math if you sit down and write formal equations. This idea is so widely embraced that to suggest otherwise is "to start a fight," says Maria Droujkova, math educator and founder of Natural Math, a site for kids and parents who want to incorporate math into their daily lives. Mathematicians cherish their formal proofs, considering them the best expression of their profession, while the anti-math don't believe that much of the math they studied in school applies to "real life."
But in reality, "we do an awful lot of things in our daily lives that are profoundly mathematical, but that may not look that way on the surface," Christopher Danielson, a Minnesota-based math educator and author of a number of books, including Common Core Math for Parents for Dummies, tells Mental Floss. Our mathematical thinking includes not just algebra or geometry, but trigonometry, calculus, probability, statistics, and any of the at least 60 types [PDF] of math out there. Here are five examples.
1. COOKING // ALGEBRA
Of all the maths, algebra seems to draw the most ire, with some people even writing entire books on why college students shouldn't have to endure it because, they claim, it holds the students back from graduating. But if you cook, you're likely doing algebra. When preparing a meal, you often have to think proportionally, and "reasoning with proportions is one of the cornerstones of algebraic thinking," Droujkova tells Mental Floss.
You're also thinking algebraically whenever you're adjusting a recipe, whether for a larger crowd or because you have to substitute or reduce ingredients. Say, for example, you want to make pancakes, but you only have two eggs left and the recipe calls for three. How much flour should you use when the original recipe calls for one cup? Since one cup is 8 ounces, you can figure this out using the following algebra equation: n/8 : 2/3.
However, when thinking proportionally, you can just reason that since you have one-third less eggs, you should just use one-third less flour.
You're also doing that proportional thinking when you consider the cooking times of the various courses of your meal and plan accordingly so all the elements of your dinner are ready at the same time. For example, it will usually take three times as long to cook rice as it will a flattened chicken breast, so starting the rice first makes sense.
"People do mathematics in their own way," Droujkova says, "even if they cannot do it in a very formalized way."
2. LISTENING TO MUSIC // PATTERN THEORY AND SYMMETRY
The making of music involves many different types of math, from algebra and geometry to group theory and pattern theory and beyond, and a number of mathematicians (including Pythagoras and Galileo) and musicians have connected the two disciplines (Stravinsky claimed that music is "something like mathematical thinking").
But simply listening to music can make you think mathematically too. When you recognize a piece of music, you are identifying a pattern of sound. Patterns are a fundamental part of math; the branch known as pattern theory is applied to everything from statistics to machine learning.
Danielson, who teaches kids about patterns in his math classes, says figuring out the structure of a pattern is vital for understanding math at higher levels, so music is a great gateway: "If you're thinking about how two songs have similar beats, or time signatures, or you're creating harmonies, you're working on the structure of a pattern and doing some really important mathematical thinking along the way."
So maybe you weren't doing math on paper if you were debating with your friends about whether Tom Petty was right to sue Sam Smith in 2015 over "Stay With Me" sounding a lot like "I Won't Back Down," but you were still thinking mathematically when you compared the songs. And that earworm you can't get out of your head? It follows a pattern: intro, verse, chorus, bridge, end.
When you recognize these kinds of patterns, you're also recognizing symmetry (which in a pop song tends to involve the chorus and the hook, because both repeat). Symmetry [PDF] is the focus of group theory, but it's also key to geometry, algebra, and many other maths.
3. KNITTING AND CROCHETING // GEOMETRIC THINKING
Droujkova, an avid crocheter, she says she is often intrigued by the very mathematical discussions fellow crafters have online about the best patterns for their projects, even if they will often insist they are awful at math or uninterested in it. And yet, such crafts cannot be done without geometric thinking: When you knit or crochet a hat, you're creating a half sphere, which follows a geometric formula.
Droujkova isn't the only math lover who has made the connection between geometry and crocheting. Cornell mathematician Daina Taimina found crocheting to be the perfect way to illustrate the geometry of a hyperbolic plane, or a surface that has a constant negative curvature, like a lettuce leaf. Hyperbolic geometry is also used in navigation apps, and explains why flat maps distort the size of landforms, making Greenland, for example, look far larger on most maps than it actually is.
4. PLAYING POOL // TRIGONOMETRY
If you play billiards, pool, or snooker, it's very likely that you are using trigonometric reasoning. Sinking a ball into a pocket by using another ball involves understanding not just how to measure angles by sight but triangulation, which is the cornerstone of trigonometry. (Triangulation is a surprisingly accurate way to measure distance. Long before powered flight was possible, surveyors used triangulation to measure the heights of mountains from their bases and were off by only a matter of feet.)
In a 2010 paper [PDF], Louisiana mathematician Rick Mabry studied the trigonometry (and basic calculus) of pool, focusing on the straight-in shot. In a bar in Shreveport, Louisiana, he scribbled equations on napkins for each shot, and he calculated the most difficult straight-in shot of all. Most experienced pool players would say it’s one where the target ball is halfway between the pocket and the cue ball. But that, according to Mabry’s equations, turned out not to be true. The hardest shot of all had a surprising feature: The distance from the cue ball to the pocket was exactly 1.618 times the distance from the target ball to the pocket. That number is the golden ratio, which is found everywhere in nature—and, apparently, on pool tables.
Do you need to consider the golden ratio when deciding where to place the cue ball? Nope, unless you want to prove a point, or set someone else up to lose. You're doing the trig automatically. The pool sharks at the bar must have known this, because someone threw away Mabry's math napkins.
5. RE-TILING THE BATHROOM // CALCULUS
Many students don't get to calculus in high school, or even in college, but a cornerstone of that branch of math is optimization—or figuring out how to get the most precise use of a space or chunk of time.
Consider a home improvement project where you're confronted with tiling around something whose shape doesn't fit a geometric formula like a circle or rectangle, such as the asymmetric base of a toilet or freestanding sink. This is where the fundamental theorem of calculus—which can be used to calculate the precise area of an irregular object—comes in handy. When thinking about how those tiles will best fit around the curve of that sink or toilet, and how much of each tile needs to be cut off or added, you're employing the kind of reasoning done in a Riemann sum.
Riemann sums (named after a 19th-century German mathematician) are crucial to explaining integration in calculus, as tangible introductions to the more precise fundamental theorem. A graph of a Riemann sum shows how the area of a curve can be found by building rectangles along the x, or horizontal axis, first up to the curve, and then over it, and then averaging the distance between the over- and underlap to get a more precise measurement.
Though he’s most often linked to his role as the Tenth Doctor on the legendary sci-fi series Doctor Who, David Tennant is much more than that, as audiences around the world are beginning to discover. Born David John McDonald in West Lothian, Scotland on April 18, 1971, the man who would become David Tennant has spent the past 30-plus years carving out a very particular niche for himself—both on the stage and screen in England and, increasingly more, as a staple of the big screen in Hollywood. To celebrate the award-winning actor’s birthday, here are 15 things you might not know about David Tennant.
1. HE TOOK HIS NAME FROM THE PET SHOP BOYS.
As a teenager, the budding actor learned that because there was already a David McDonald in the actors’ union, he needed to come up with an alternate moniker to pursue a professional acting career. Right around the same time, he read an interview in Smash Hits with Neil Tennant, lead vocalist for the Pet Shop Boys, and "David Tennant" was born.
Today, he legally is David Tennant. “I am now actually Tennant—have been for a few years,” he said in 2013. “It was an issue with the Screen Actors' Guild in the U.S., who wouldn't let me keep my stage name unless it was my legal name. Faced with the prospect of working under two different names on either side of the globe, I had to take the plunge and rename myself! So although I always liked the name, I'm now more intimately associated with it than I had ever imagined. Thank you, Neil Tennant.”
2. HE BECAME AN ACTOR WITH THE SPECIFIC GOAL OF STARRING ON DOCTOR WHO.
While a lot of young kids dream of growing up to become astronauts or professional athletes, Tennant set his own career goal at the tender age of three: to star on Doctor Who. It was Tom Baker’s version of The Doctor in particular that inspired Tennant to become an actor. He carried around a Doctor Who doll and wrote Who-inspired essays at school. "Doctor Who was a massive influence," Tennant told Rolling Stone. "I think it was for everyone in my generation; growing up, it was just part of the cultural furniture in Britain in the '70s and '80s.”
On April 16, 2004, just two days before his 34th birthday, Tennant achieved that goal when he was officially named The Tenth Doctor, taking over for Christopher Eccleston. “I am delighted, excited, and honored to be the Tenth Doctor,” Tennant said at the time. “I grew up loving Doctor Who and it has been a lifelong dream to get my very own TARDIS.”
3. THOUGH BECOMING THE DOCTOR WAS A LIFELONG DREAM, THERE WAS SOME TREPIDATION.
Though landing the lead in Doctor Who was a lifelong dream come true for Tennant, the initial excitement was followed by a little trepidation. When asked by The Scotsman whether he worried about being typecast, Tennant admitted: “I did remember being thrilled to bits when I got asked and then a few days later thinking, ‘Oh, is this a terrible idea?’ … But that didn't last very long. Time will tell. The only option is you don't take these jobs when they come up. You've got to just roll with the punches.”
4. HE MADE HIS PROFESSIONAL DEBUT IN A PSA.
While most actors have some early roles they’d prefer to forget, Tennant’s first professional gig didn’t come in some otherwise forgettable movie, TV series, or play. When he was 16 years old, he booked a role in an anti-smoking PSA for the Glasgow Health Board, which played on television and was shown in schools. Thanks to the power of the internet, you can watch his performance above.
5. HE MARRIED THE FIFTH DOCTOR’S DAUGHTER, WHO ONCE PLAYED THE TENTH DOCTOR’S DAUGHTER.
Confused? In 2011, Tennant married Georgia Moffett, who played his artificially created daughter, Jenny, in the 2008 Doctor Who episode “The Doctor’s Daughter.” In real life, Moffett really is The Doctor’s daughter; her father is Peter Davison, who played the Fifth Doctor from 1981 to 1984.
6. HIS FIRST MOVIE ROLE HAD HIM ACTING OPPOSITE CHRISTOPHER ECCLESTON.
In 1996, Tennant landed his first movie role in Michael Winterbottom’s Jude, where he played the very descriptive “Drunk Undergraduate.” His big scene had him acting opposite Christopher Eccleston—the man who, less than a decade later, would hand over the keys to the TARDIS to Tennant.
7. HE AVOIDS READING REVIEWS OF HIS WORK.
While it’s hard to imagine that Tennant has ever had to deal with too many scathing reviews, it doesn’t really matter to the actor: good or bad, he avoids reading them. When asked during a livechat with The Guardian about one particularly negative review, and whether he reads and reacts to them, Tennant replied: “The bad review to which you refer was actually for a German expressionist piece about the Round Table called Merlin. It was the first extensive review I'd ever had, and it was absolutely appalling. Not that it's scarred into my memory in any way whatsoever. I try not to read them, these days. Reviews aren't really for the people who are performing, and—good or bad—they don't help. You always get a sense if something you're in has been well received or not, that's unavoidable. But beyond that, details are best avoided.”
8. HE HOSTED MASTERPIECE THEATRE.
In 2007, Masterpiece Theatre reinvented itself. In addition to dropping the “Theatre” from its title, the series announced that it was splintering into three different seasons—Masterpiece Classic, Masterpiece Mystery!, and Masterpiece Contemporary. Unlike the days of the past, when Alistair Cooke held court, each of the new series had its own host, Tennant among them. (He was in charge of Masterpiece Contemporary.)
9. HE GOT A LOT OF YOUNGER AUDIENCES INTERESTED IN SHAKESPEARE.
Tennant has logged a lot of hours with the Royal Shakespeare Company over the years. In 2008, while still starring in Doctor Who, he took on the role that every actor wants in the RSC’s production of Hamlet, which ended up being one of London’s hottest (and hardest to get) tickets. The Guardian reported that hundreds of people were lined up to buy tickets, with some even camping out overnight outside the West End theater. Within three hours of the tickets going on sale, all 6000 of them were sold out.
“Hamlet is a very popular play,” a RSC spokesperson said at the time. “It's the most famous. But obviously there's the factor that David Tennant is in it and the good news is that he's bringing a lot of younger audiences to Shakespeare."
10. HE WAS ON A ROYAL MAIL STAMP.
In 2011, the Royal Mail paid tribute to Royal Shakespeare Company’s 50th anniversary with a series of stamps featuring images from a handful of the RSC’s productions, including Tennant as Hamlet.
11. HE ALMOST PLAYED HANNIBAL LECTER.
Though it’s easy to see why Bryan Fuller cast Mads Mikkelsen in the title role of his television adaptation of Hannibal, Tennant came pretty close to playing the fava bean-and-chianti-loving, flesh-eating serial killer at the heart of Thomas Harris’s novels. Fuller was so impressed with Tennant’s dark side that he tried to make a guest appearance happen during the series’ run.
“I’m a huge fan of David Tennant, and we’ve been trying to get him on the show for quite some time,” Fuller said. “He’s such a spectacular actor. He brings such an effervescence to every performance. I would love to have David on the show. Or just write for David! I would kill and eat somebody to work with David! He’s my favorite Doctor.”
12. HE’S JODIE WHITTAKER’S FAVORITE DOCTOR.
Fuller isn’t the only one who puts Tennant at the top of their Favorite Doctor list. Jodie Whittaker, who recently made her debut as the Thirteenth Doctor—and is the first woman to take on the role—recently told The Sunday Times that “David [is my favorite Doctor] of course, because I know him.” (The two spent three seasons co-starring in the British crime drama Broadchurch.)
When asked about Whittaker’s casting at the New Orleans Wizard World Comic Con, and whether he had given her any words of advice, Tennant said that, “We had a wee chat, yes. It is quite a unique job, because it's a show that has so much history to it. And it has a reach that's quite unlike other things. It's a bit of a kind of cultural thing—Who's going to be the Doctor?—it's a news story, really. So to find yourself in the middle of that is a bit overwhelming. I think inevitably, you sort of look to people who'd been there before to go, 'What is this like? What is this madness I entered into?' And that's certainly been the case with Matt and Peter, and now with Jodie. I know that Jodie's talked to Peter, and she's talked to Matt. You just for a little support group. You go, 'What is this madness? Tell me about it.' And of course, you know, she 's a little trepidatious, but she's basically really excited. She's such a fantastic choice for it. You see it in just those 30 seconds that she did at the end of the last episode. You just go, 'Oh my god, she's all over it. Brilliant. It's great.’”
13. HE’S DYING TO WORK WITH AARON SORKIN.
When asked by Collider if there’s ever been a television show he’s watched and wished he was a part of, Tennant copped to being a huge fan of The West Wing.
“The West Wing is finished now [but] that’s the one that I would have loved to have been part of," he said. "I’d love to work with Aaron Sorkin on something. Just the way he writes, he has no fear in writing people that are fiercely intelligent, and I love that. I love the speed of his stuff, and the way people free-associate and interact. That kind of writing is very exciting. It’s hard to have that kind of clarity of voice, especially in a world where there’s a million executives listening to everything you do and having an opinion and trying to drive everything towards the lowest common denominator because that’s what happens when things are made by committee. So, to have someone who’s got a strong individual voice that is allowed to be heard is quite increasingly rare. These people need to be cherished.”
14. HE HAS EARNED A LOT OF FAN ACCOLADES, INCLUDING “COOLEST MAN ON TV.”
In addition to his many professional acting accolades—including a couple of BAFTAs and a Daytime Emmy and an Olivier Award nomination—Tennant has earned a number of less official “awards” over the years. In 2007, a Radio Times survey named him the Coolest Man on TV. The National Television Awards named him Most Popular Actor of 2006, 2007, 2008, and 2010. In 2008, he was one of Cosmopolitan’s Sexiest Men in the World. In 2012, British GQ readers named him the third Best Dressed Man (behind Tom Hiddleston and Robert Pattinson).
15. YOU CAN BUY HIS PANTS.
On April 17, 2018, as part of the Royal Shakespeare Company’s Stitch in Time fundraiser, the organization began auctioning off more than 50 original costumes worn during RSC performances. Among the items that you can bid on? The black trousers Tennant wore in Hamlet, and the white robe he wore in Richard II.