## An interview with...Mirinda Carfrae

Mirinda Carfrae is an amazing Australia Ironman who has achieved incredible international success over the last 10 years. In 2006 she came 3rd in the Ironman 70.3 World Championships (Half-ironman). The following year (2007) she came first. From 2009, she progressed to the full Ironman course, the World Championships at Kailua-Kona, which involves a 3.86km swim, a 180.25km bike ride and then a full marathon 42.195km run. Since 2009, Mirinda has finished 3rd once (2012), come second twice (2009, 2011) and won the gold medal twice (2010, 2013). Mirinda currently holds the women's record for fastest overall time and also fastest running leg.

And then there are the other numerous events throughout the year that she competes in (and wins!).

You can imagine what her training schedule must be like. So I was really pleased when Mirinda agreed to answer a few questions for me about how maths relates to her sport.

Here is what she had to say.

Describe what maths lessons were like for you at school.
I didn’t mind math class in school, it certainly wasn’t my favorite but it was far from my least favorite.  Wasn’t too fond of the advanced math class I took in Year 11 & 12 because I didn’t see the point of it and mostly didn’t quite get it (only took it because it was a prerequisite for the course I wanted to get into in university).

When you left school, did you expect to be using any of the maths that you were taught ever again?
Certainly didn’t expect to be using advanced math (and haven’t) but could clearly see that simple math would be used in everyday life.

How good do you need to be at mental arithmetic to do calculations in your head as you train for and participate in a race?
I think it’s helpful to be quick with your calculations during training and races. It’s sometimes a little harder to do the math in your head the more fatigued you get but it’s nice to be able to occupy your mind with something other than the pain during a race.

How aware are you of angles in your technique – angle of body in water, angle of body on the bike, angle of a corner etc?
I don’t think I am all that aware at all. I mostly race to feel and move my body accordingly.

When you are racing, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?
I spend a lot of the race doing the math, especially the latter part of the race. I occupy my mind with figuring out my pace and what pace I need to be holding to catch the next person or take the lead. I think I only do that to keep my mind occupied though because I am still going to race to the finish line as fast as I can regardless or whether I am in the hunt or in the lead.

Is estimation good enough or do you rely on accurate measurement of distances and times?
The more accurate the better but since the splits you receive out on course come at such random times and are generally quite varied you kind of have to be ok with estimates.

Do you keep an eye on the times of other competitors as you prepare for a race?
Absolutely, it’s a little different in triathlon since every race is different, on different courses and under different conditions.  But I like to see how people are racing leading up to a big event.

Thanks Mirinda for participating in the Maths in Sport project and for taking the time to answer these questions. Good luck for 2014!

Website - http://mirindacarfrae.com

## An interview with Mathew Belcher

Mat Belcher is an Australian sailor who competes in the 470 class where he has been World Champion for several years - 2010, 2011 and 2012 with Malcolm Page and 2013 with WIll Ryan. He was also Olympic gold medalist with Malcolm Page in London 2012. Prior to this, Mat had also been World Champion with Daniel Belcher in the 420 class in 2000. In 2013, Belcher and Ryan were named the Australian Institute of Sport Team of the Year.

Belcher and Ryan are currently leading the World Cup point score with an unbeaten run in World Cup events this season.  He is currently in Miami preparing for the next World Cup event that starts tomorrow but he kindly took some time out to answer some questions about how maths relates to the sport of sailing. Here is what he had to say.

Describe what maths lessons were like for you at school. (Please be honest – not all of us loved maths at school)
I actually didn't mind maths compared to many other subjects I took. I knew the fundamentals we were learning were practical and useful. In today's world you can't get away without knowing basic maths and its applications.

When you left school, did you expect to be using any of the maths that you were taught ever again?
Actually yes, I think the curriculum we were taught was very practical to today's world.

How good do you need to be at mental arithmetic to do calculations in your head as you train and compete?
One of the key things to be successful in our sport is making quick decisions. Start line angles compared to wind angle, line bias, velocity made good (VMG) calculations, judging the fastest angle to the next mark.

How aware are you of angles in your sport?
Angles in our sport are critical, probably one of the most important aspects to our sport. Being able to judge the angle of wind approaching, heading of the boat compared to angle towards the top mark. Not to mention the 50 other boats on the course with you, crossing back and forward at different angles to the wind.

When you are racing, how much is “mathematical thinking and calculating” and how much is acting from instinct – “go as fast as you can”?
I would probably say acting from observation mainly, with a combination of mathematical thinking and instinct. Mathematical thinking relates to areas such as differences in true wind relative to current on the course, and the effects the current has in changing the angle of the breeze. Basic calculations, such as angle of start line compared to wind direction, which will allow us to determine if one end of the line is closer to the top mark than the other, allowing us to take an advantage (Sail a shorter distance).

Is estimation good enough or do you rely on accurate measurement of distances and times?
It really depends on the type of classes. In Olympic sailing we have quite a lot of restrictions in what digital instruments we are allowed. Usually estimation is good enough.

Do you keep an eye on the results of other competitors as you prepare for a race in competitions?
I try not too but it usual means I have a little look. Always nice to know how your competitors are going. However, as we race together (sometimes 50 boats on the same course) you can usually tell who is doing well.

Have your coaches ever used mathematics and physics to explain your style and movement?
Not really, but this is probably more from our side. It hasn't been a priority area for us. Certainly their are areas in bio-mechanics and pumping techniques that would help but we haven't invested the time in this area, only on on-water testing in this area.

Do you look at statistics much to analyse your training and performance?
Actually not so much on a day to day basis. We have the ability to analyse angle of heel, rudder movement to the degree and hull speed as outputs to determine how accurate we were with steering the boat positioning but it tends to be pretty blunt in our sport. You know very quickly if you are doing something wrong or not as we have so many indicators on the course that you can gauge from.

Do you have any other insights to offer into how you use mathematics in your sport?
You covered it pretty well.

Thanks Mat for taking the time out of your busy schedule to participate in the Maths in Sport project. Good luck with the event in Miami (tomorrow) and all the best for the rest of the season!

## An interview with Stacey Lewis

Stacey Lewis is an American golfer. She was 2013 British Women's Open Champion and LPGA Player of the Year in 2012. In March 2013, Stacey held the #1 world ranking. In 2013 she also won the LPGA Vare Trophy for the woman with the lowest scoring average for the season.

Stacey took some time out of her schedule to answer some questions that I sent her, asking about how mathematics relates to her sport.

Here is what she had to say.

When you left school, did you expect to be using any of the maths that you were taught ever again?
I did know that I would be using math as I was an accounting major.  I did not know that I would be using it in golf for elevations, yardages and expenses, but I did think I would be using it.

How good do you need to be at mental arithmetic to do calculations in your head as you go around the course?
It takes practice and I play a lot so I think that makes me pretty good at it.

How aware are you of angles when preparing for a shot?
I do think of angles depending upon the lie of my ball.  The upslope or downslope will impact my yardages.

When you are putting, how much is "mathematical thinking" and how much is "feel"?
I use the Aimpoint putting method and it has a lot of math.  The math is done to prepare for the putt and once I line up over the ball, it is all feel.

Is estimation of distances good enough?
It is important to be able to look at a shot and estimate the yardage, but I do want exact yardages before hitting the shot.

Do you keep an eye on the scoreboard as you go around in a tournament?
Yes, I do like to know how the course is playing.  I want to know where I stand among the other competitors.

Have your coaches ever used maths and physics to explain your swing?
There are a lot of different ways to coach.  My coach works on a right arm angle at the top of my backswing.  I need to make that angle small.

Do you look at statistics much to analyze your game?
Yes, I evaluate where I am doing well and where I need to improve.

Do you have any other insights to offer into how you use maths when playing golf?
Math is used in golf more than other sports.  You have the time to calculate and analyze where other sports happen a bit faster.

Thank you Stacey for being a part of the Maths in Sport project. I really appreciate your contribution. Good luck for 2014.

Website - http://www.stacysback.com

## An Interview with Ashton Eaton

Most people on the planet would struggle to compete in a single event at the Olympic level. Ashton Eaton is a decathlete and so he has to complete 10 events in 2 days, an awesome and inspiring achievement.

Ashton is the current (2013) World Champion in decathlon and Olympic gold medalist (2012). He also won the heptathlon at the 2012 Indoor World Championships. He holds the world record for decathlon (9039 points) and the heptathlon (6645 points).

And tomorrow (21st January) is his birthday!

I asked Ashton 10 questions about how mathematics relates to his events. Here is what he had to say.

Describe what maths lessons were like for you at school.
In my early years math was fun and easy.  We’d use objects to practice adding and subtracting (you have one bottle cap, add one bottle cap, now you have 2) and there was never “homework.”  It was like running a 60 second 400m.  As I got older the teachers started using projection screens and white boards and just doing example problems for the class then we’d be left with the book and our notes and minds to figure it out some other time outside of class.  Algebra, calculus, and physics became the big three.  At this point it was like trying to throw the shot put 15m.  I could only do it sometimes and when I did it was difficult.

When you left school, did you expect to be using any of the maths that you were taught ever again?
After college I never thought I’d be doing math again.  Maybe a plus or minus here and there but nothing more complex.

How good do you need to be at mental arithmetic to do calculations in your head as you compete in each event of the decathlon?
It really depends on what situation you’re in.  For example, I could be in between events with a little bit of free time and if I want to estimate what position I’m in and how many points I need to move into the next place I could be moderately good at using some mental math and have no problem.  But, what if I’m getting ready to throw the javelin and it’s my last throw?  I only get a minute to throw it.  Say, before, when I was in-between events and I figured out that I was 56 points behind first place and I know that in javelin you get 6 points every meter (not actually sure points per meter) and I have to figure out how many meters I have to beat this person by.  It could get pretty stressful and that calculation is important.  I’ve lost by 3 points once.

How aware are you of angles in throwing events, such as angle of arms, angle at release, angle of javelin etc?
I’m somewhat aware of angles during competition.  I know that if I’m “flat” during a long jump take-off that next time I jump if I just increase my angle I’ll get more distance.  I’d say the javelin is the event where we pay the most attention and even then it’s just a guess as to what is optimal.  I’m sure if someone threw or jumped to mathematic perfection they’d have an advantage over others.

When you are running, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?
When running I split these thoughts probably 50/50.  I’ll look up at the clock during the 1500m and see how fast the previous 200m was to determine if I’m on pace or not.  Then, I’ll take stock of how I feel to determine if I can go fast the next 200m or if I need to conserve for the end of the race.  The shorter the races the less this takes place and shift more 10/90 for calculation vs feel.

Is estimation good enough or do you need to measure things accurately?
The beauty of track and field is its measurability and accuracy.  I’ve seen people win races by .001 of a second!  You have to remember, when someone wins by that much, someone also lost by that much, imagine how important accuracy is to them.  Accuracy is also crucial because in track and field we’re always trying to better ourselves.  If I’ve run 10.21 seconds in the 100m before and I race again and the timer says it was around 10.2 that’s not good enough for me.  I want to know, did I run 10.20 or 10.22?

Do you keep an eye on the scoreboard throughout the decathlon?
Always.

Have your coaches ever used maths and physics to explain your performance?
They’ve used physics in the pole vault mostly.  General additions and subtraction to figure out what I need to score in the next event or events.

How do you use statistics to analyse your results?
I’ve never personally done this but I’ve seen it done on various track and field websites.  People love to figure out what percentile you’re in for the “best runners of decathlon history” or “height to weight ratio of speed compared to Olympic sprinters.”  The list goes on lim x —> a f(x) = f(a).  Haha.

Do you have any other insights to offer into how you use maths when competing in a decathlon?
This is the extent of my math knowledge concerning the decathlon.

Thanks you Ashton for taking the time to be a part of the Maths in Sport project - and I love the little maths joke in there too! I really appreciate your thoughtful and interesting answers. Good luck for the 2014 season!

Website - http://doylemanagement.com

## An interview with... Etienne Daille

Etienne Daille is a French kayaker who competes in the K1 slalom. He was overall individual World Champion in 2012 as well as being part of the French team that came first in the 2012 European Championships and third in the 2013 World Championships.

Etienne kindly agreed to answer some questions about how maths relates to his sport of kayak slalom. Here is what he had to say.

Describe what maths lessons were like for you at school.
I studied math until university. It wasn’t the matter that interested me the most because, it was sometimes too abstract.

When you left school, did you expect to be using any of the maths that you were taught ever again?
Some things yes, because I study in a ‘’Sport University’’

How good do you need to be at mental arithmetic to do calculations in your head as you race?
During the race, you need memories, skills, openness, adaptability, quick thinking... But, sometimes during the race, you can listen to the speaker say intermediate times. You can calculate your differences with the best. See if you lose or gain time at every ¨split time¨. To know if you need to take more risks to win the race...Just after the race (the finish line), the mental arithmetic can help you to calculate different rankings.

How aware are you of angles in your technique – angle of approach into a corner, angles in the course, angle of arms, angle of body etc?
The approach angle of the gates is very important, including upstream gates. There is a lot of perspective effect, it’s difficult to take good benchmarks. It’s important also to have a good proprioception of your body so you don’t touch the slalom gates.

When you are racing, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?
I'm focused on the trajectory and speed of the boat. If it goes well, then the time will be good.

Is estimation good enough or do you rely on accurate measurement of distances and times?
For the time, I need a stopwatch. And for distances, often a camera to compare the trajectories on the computer.

Do you keep an eye on the clock as you go around a course in training and in races?
There are many things to manage: I rather focus on what I have to do on the water when I paddling. I have a look on the clock when I finish the course.

Have your coaches ever used mathematics and physics to explain your style and movement?
Slalom is a sport that uses ‘’open skill’’. There are very different morphologies of kayakers. The courses are different for each competition. So there are many different styles of kayakers. You must understand your style and the track to choose the best movement to go as fast as possible. This requires to use also mathematics and physics not only for the race but also to choose the best equipment for you.

Do you look at statistics much to analyse your training and races?
Yes, to analyze the regularity of performance, penalties, the choice of trajectories...

Do you have any other insights to offer into how you use mathematics in racing?
Yes, when you developing and testing a new shape of kayak. For example, you need to compare the new shape with any other kayak. To do it, you make lot of different tests. And to analyse these tests, you use for sure mathematics, statistics...

Thanks Etienne for being a part of the Maths in Sport project. Good luck for the 2014 season!

## An Interview with Jonathan Brownlee

Jonathan Brownlee is an amazing triathlete. Winner of the World Championship in 2012 and runner up in 2013, bronze medalist at the 2012 Olympic games, and currently ranked #2 in the ITU world rankings by a mere 25 points, Jonathan agreed to answer a few questions about how maths relates to his sport.

Here is what he had to say.

Describe what maths lessons were like for you at school.
They were OK, mostly I enjoyed them. I enjoyed most of my lessons at school, good school, good teachers. If I had to choose a favourite subject though, it would have been History.

When you left school, did you expect to be using any of the maths that you were taught ever again?
I think you rarely make the connection to what you were taught in school to what you use day to day. Definitely don’t use any of the complicated stuff but I’m always calculating split times when swimming and running.

How good do you need to be at mental arithmetic to do calculations in your head as you race in a triathlon?
Now the World Champion is decided by a Series rather than a one off race, it’s much more relevant. For example, when I won the World title in 2012, I knew as soon as we were down to three in the lead group I had won it.

How aware are you of angles in your technique – angle of approach into a corner, angle of arms when swimming, angle of body on a bike etc?
Most of it is natural now but when I was learning to swim it was very important. It made things much easier to communicate with the coaches because you could understand what they were telling us. Also, when riding -  cornering on the bike – I don’t think anyone mentioned mathematics but of course it is all about the angle of the turn.

When you are racing, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?
It’s definitely always go as fast as you can, the numbers come into it when you can’t go any faster and need to think about damage limitation. Best example is of what lap I was to take my 15 second penalty at the Olympics, I was working out all the time how much of a lead I had on the French lads.

Is estimation good enough or do you rely on accurate measurement of distances and times?
In training it’s very important as it gives you an accurate measure of your progress.

Do you keep an eye on the clock as you go around a course in training and in races?
I like to wear a watch in training so I can. Also, the coaches shout out split times to us. That’s harder when you are racing but we get information at different places on the course.

Have your coaches ever used mathematics and physics to explain your style and movement?
Maybe when I was younger but I don’t remember. I can’t think of anything recently but I know they are always studying biomechanics to try and help us improve.

Do you look at statistics much to analyse your training and races?
Statistics are always kept for us, training and racing, but I only would look at them if something goes wrong.

Do you have any other insights to offer into how you use mathematics in triathlons?
I use maths a lot in triathlon. As per my Olympic example, I’m always working out how far ahead or behind I am  judging on the time difference. There’s normally a dead turn somewhere on the run course which is another way of working out what you need to do to take the win/get on the podium.

Thank you Jonathan for being a part of the Maths in Sport project. We all appreciate your thoughtful and considered comments.

Website - currently under construction