Maths in Dance - Drew Hedditch

Interview with Drew Hedditch

Drew was born in Canberra and started tap classes at the age of five; he started ballet at the age of eight. He studied at the Lisa Clark Dance Centre and the Australian Ballet School. He toured with The Dancers Company in 2012 and 2013, and joined The Australian Ballet in 2014.

Drew is a keen rugby player and once harboured ambitions of

becoming Australia's first tap-dancing Wallaby.

Drew kindly agreed to answer some questions about how he sees the relationship between mathematics and dance.

Photo by James Braund

The Questions and Answers

Describe what math lessons were like for you at school. 

I loved maths at school, I always preferred maths and science to English etc.

When you left school, did you expect to be using any of the math that you were taught ever again?

I expected to be using percentages in relation to shopping (sales!) and also number patterns, eg patterns with music.

Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions?

Yes, for example you might repeat a step four times within a musical bar of eight, therefore each movement has a value of two musical counts, the fraction being ¼.

How aware are you of angles in your technique – angle of body, angle of arms and legs, angle of movements?

Angles are strongly used in relation to positions of the legs. Angles often describe the height of the leg in relation to the supporting leg and floor eg. A 90 degree arabesque has the back leg raised parallel to the floor.

When you are moving in a performance, how much is “mathematical thinking and calculating where the space is” and how much is “feel for the space”?

When performing we have a strong sense of the eight quarter and centre stage marks that are specifically measured and marked by our stage management crew.

Is estimation good enough or do you rely on accurate measurement of distances and times?

Estimation is not good enough, particularly in the corps de ballet, but that’s also why we rehearse. Each travelling movement has a value of how far it is meant to travel, if you estimate this you could possibly ruin the overall shape.

How aware are you of timing and beat when you are dancing?

I am very aware of timing – if movements are out of time, it looks wrong. The music is not always a constant rhythm either, for example you could have three bars of eight, one bar of twelve, and a bar of nine – you need to be aware of this when dancing.

Have your teachers or choreographers ever used math and physics to explain your technique?

The angles of legs are a key factor in the positions within your technique. Physics is strongly used particularly with weight placement. You need to be very accurate with this, otherwise you can fall over when lifting your leg, during a pirouette or landing from a jump!

Do you look at statistics much to analyse your training and performance?

Yes, if eight out of ten people are doing one arm and two are doing a different arm – this needs to be fixed.

Do you have any other insights to offer into how you use mathematics in dance?

With all our Pilates and strength training, we need to be particular with the amount of weight/resistance we use as we want this to benefit our dancing and not our physical shape.

Photo by Luis Ferriero

Thank you Drew for taking time out to be a part of the "Maths in Dance" project.

Maths in Dance - Tommy Franzen

An Interview with Tommy Franzen

Tommy started his dance training in Sweden, where he is originally from. Initially he was only taking streetdance classes but soon his eyes opened for other dance styles as well. Tommy began working professionally soon after that at the age of 14 in the musical “Joseph”. He stayed in Sweden until the age of 19 going from musical to musical before he got a scholarship for a 3-year performing arts diploma course at the Urdang Academy in London. 

Tommy is probably mostly recognised as the runner-up of BBC 1’s “So You Think You Can Dance” 2010 but some might have seen him in "Mamma Mia – The Movie", "Some Like It Hop Hop" at Peacock Theatre, "The Five" and "The Prophecy of Prana" at Barbican etc. 

Tommy is also an active choreographer. He has choreographed for "Some Like It Hip Hop" and "Blaze" (Peacock Theatre and world tour) and Cher Lloyd’s music video and the live performances of her UK charts #1 hit single “Swagger Jagger” etc. Last year Tommy won an award for “Outstanding Performance in Modern Dance (male)” by the Critics’ Circle “National Dance Awards” for his efforts in “Some Like It Hip Hop “ and “The Rodin Project” with Russell Maliphant Company. He was nominated for the same award in 2010 for “Goldberg” with Tamara Rojo at The Royal Opera House and “Blaze”. This year he co- hosted the awards alongside Bennet Gartside. Other nominations Tommy has had are Laurence Olivier Awards 2012 for “Outstanding Achievement in Dance” and South Bank Sky Arts Awards 2013 for “The Times Breakthrough Award ”. 

Tommy kindly agreed to answer some questions for me about how mathematics relates to dance.

 

The Questions and the Answers

1. Describe what math lessons were like for you at school.

I really enjoyed maths in school. I did pretty well in it and it was something I wanted to be good at.

2. When you left school, did you expect to be using any of the math that you were taught ever again?

I expected to be using it a lot more than I have. It's starting to come in handy in the last few years as I've gone in to business as well. I use it for my accounts and also creating spreadsheet calculations to analyse numbers etc.

3. Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions?

There is a trick called a 540 due to the amount of degrees you turn around. We also count dance normally in counts of 8. So when we learn new choreography we break down the phrases into fraction of maybe 1, 2 and 4 for example.

4. How aware are you of angles in your technique – angle of body, angle of arms and legs, angle of movements?

I'm very aware. It's important in certain dance style to have your arms for example horizontally to the sides or elbow bent by 90 degrees. In ballet you are aiming to get 180 degrees of rotation of your legs when heals are touching each other. I've got about 90 degrees so I'm clearly not built for ballet. 

5. When you are moving in a performance, how much is “mathematical thinking and calculating where the space is” and how much is “feel for the space”?

It starts off as mathematical when you make the spacing and then it's more a feel for the space when you perform. In some shows I've done we've had numbers at the front stage left matching stage right. That makes it easy when you are initially spacing it to see if your opposite is on the same number for example.

6. Is estimation good enough or do you rely on accurate measurement of distances and times?

Estimations are normally fine.

7. How aware are you of timing and beat when you are dancing?

Timing is very important. In some styles like hip hop dance styles your timing has to be impeccable as you are dancing to every little sound in the music. Contemporary dance can float a bit more over the top and then just pick up some key moment in the music.

8. Have your teachers or choreographers ever used math and physics to explain your technique?

One choreographer I've worked with called Russell Maliphant is trained in Rolfing and is seeing the movement in a very anatomical and physics kind a of way. Otherwise I haven't come across it a lot.

9. Do you look at statistics much to analyse your training and performance?

No not really.

Thank you Tommy for your participation in the "Maths in Dance" project. 

We really appreciate your generosity with your time and thoughts.

Website - http://www.tommyfranzen.com

 

100 000

Thank you everyone who has 

visited the blog 

in the last 2 years.

This morning we had the

100 000th view.

Thank you for your support.

Bruce

And if I had $1 for every view, that would be...

 

Maths in Dance - Corey Herbert

Corey Herbert - photo by James Braund

An Interview with Corey Herbert

Corey was born in Melbourne, and began dance classes at the age of seven. She studied at the Victorian College of the Arts Secondary School and at The Australian Ballet School. She toured with The Dancers Company in 2013, and joined The Australian Ballet in 2014. As a final-year student at The Australian Ballet School, Corey danced as part of the swan corps in The Australian Ballet’s Brisbane season of Stephen Baynes’ Swan Lake.  
 (from http://www.australianballet.com.au/about_us/dancers/dancer_bio/corey_herbert)

Corey kindly agreed to answer some questions about how mathematics relates to her art as a dancer in the Australian Ballet.

The Questions and Answers

1. Describe what math lessons were like for you at school.

I was always better at maths than English at school, I enjoyed solving problems and working with numbers. I advanced early into algebra in my final year of primary school and always enjoyed the advanced maths classes from year 7 - 10.

2. When you left school, did you expect to be using any of the math that you were taught ever again?

I always knew that I would need basic maths in everyday life. I must admit I would not be able to tell you how algebra or any of those harder equations work anymore, as I haven't needed to use them. Obviously simple maths is handy when dealing with money and those sorts of things, but there is also a lot of mathematics in dancing. Although we don't necessarily always think mathematically in our minds when we are dancing or on stage the math elements are still there.

3. Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions?

During performances we always have intervals. A ballet might be split into two halves or three thirds depending what work you’re doing. In each section I will usually be aware of how many times I enter the stage. Say I enter three times I will think about each third of the ballet separately. The stage is also set with marks in eights. The red marks usually represent the quarters so you can find centre or be on quarter mark on stage. The green marks are then your eights. These marks help us stay in line.

4. How aware are you of angles in your technique – angle of body, angle of arms and legs, angle of movements?

In ballet we often refer to our line of leg through angles. Certain steps require us to lift our leg to a certain height. Eg grand battement is referred to 90 degrees and above (creating a 90 degree angle between the legs . Jete is 45 degrees off the floor. If in a certain ballet the choreographer wants the arabesque (leg lifted being body) going straight across at a right angle they will asks the dances to have their legs at ninety degrees.

5. When you are moving in a performance, how much is “mathematical thinking and calculating where the space is” and how much is “feel for the space”?

When we are on stage we do use the quarter and eighth marks on stage to place ourselves. But as a dancer you are not always able to see the marks or you won’t be on a specific mark so you have to be very spatially aware of your movements and consider where everyone is around you. Being part of the Corps De Ballet it is extremely important to stay in line and be aware of those around you. I do this more by having a feel for the space and the people more so than thinking mathematically.

6. Is estimation good enough or do you rely on accurate measurement of distances and times?

Our movements aren't specifically measured. Unless we have a certain mark on the stage we have to travel to and from with a certain amount of steps our movement otherwise is quite free. We just have to be aware of travelling in the space we are in. Travel and measurements of the ballets will always depend what theatre we are performing in as some stages are smaller than others. In this case our length of travelling and movement will differ.

7. How aware are you of timing and beat when you are dancing? 

As a dancer timing and dancing on the music is crucial. When we are taught a ballet each movement is set on a specific count. In ballet we usually count 1-8 or 1-16 but obviously this can vary.

8. Have your teachers or choreographers ever used math and physics to explain your technique?

When we are being taught choreography finding patterns in our counts of music helps a lot. Eg we could be holding a pose on the side for 2 sets of 8 counts and a four, and then dancing for 4 sets of 8 counts and a 6 before pose again. Recognising these sorts of patterns in the music help us to learn the choreography. As dancers we are also very aware of the space around us and the shapes and dimensions we form and create within the space.

9. Do you look at statistics much to analyse your training and performance?

I personally don't refer to statistics to analyse my training, but I'm sure a lot of the medical staff would. Statistics would be very relevant towards injury prevention amongst our physios and strengthening team.

10. Do you have any other insights to offer into how you use mathematics in dance?

With all our Pilates and strength training, we need to be particular with the amount of weight/resistance we use as we want this to benefit our dancing and not our physical shape.

Thank you Corey for your answers and comments about maths in dance. Your insights are greatly appreciated!

 Photo by Luis Ferreiro

Maths in Dance - Elena Grinenko

Biography

Elena was born in Russia and began ballroom dancing at the age of 7. In 1994, while still at school, she won the Latin title at both the Moscow and Russian championships.

In 1998, Elena emigrated to America to pursue her dancing career. After turning professional, Elena won several awards and competitions in the "Rising Star" category, including the 2002 Closed American National Rising Star Championship with Maksim Chmerkovshiy.     

With Tony Dovolani, she was to become national and world champion in the American Rhythm section in two consecutive years (2005-6). Elena also appeared as one of the professional dancers in "Dancing with the Stars US" (series 3 and 4). 

As well as competing in Dancesport championships, Elena has worked in many professional dance performances and productions as a dancer and choreographer including stage shows, TV and live performances, worked with major pop musicians and entertainers and also adjudicated at professional dance competitions.

A truly dedicated and passionate dancer, Elena kindly agreed to answer some questions about how mathematics relates to dance. Here is what she had to say.

Elena with Tony Dovolani, 2006

The Questions and Answers

1. Describe what math lessons were like for you at school.

I actually finished high school with an emphasis on high math and geometry. In Russia after 8th grade you can actually choose your sort of major, like in college here. My school had: Literature and History, Math and Geometry and Physics
  

2. When you left school, did you expect to be using any of the math that you were taught ever again?

Yes always in my dancing. But not in college. I finished "Performance Art Academy" that had to do with dance and stage production. 



3. ­ Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions?

Absolutely. When we talk about rhythms and very much about full bit, half bit and even quarters. Each dance has unique rhythms.
Example:
Cha Cha
Slow, slow, slow, quick, quick = full, full, full, half half
Samba:
slow a slow
3/4 1/4 full
and so on

The more advanced a student is, the more intricate timing becomes. I say when you get to the high quality dancing, you control the music, not the music controls you, by the way you express that movement though your body rhythms.
 

4. How aware are you of angles in your technique ­ angle of body, angle of arms and legs, angle of movements?

Yes, yes, yes. We have very specific ways of how much you can turn and which direction you go after that turn, especially in basics. Which angle your arm can go in order to get the right look and where to place your feet. In the book of technique you can find descriptions on how much the turn is, and which direction to move after.

We use words like parallel or perpendicular to the wall or your partner, diagonal to the corner or inside of the line of dance and set.


5. When you are moving in a performance, how much is "mathematical thinking and calculating where the space is" and how much is "feel for the space"?

This one for me is more connected to the feeling and the story we want to show vs calculating it. We are not machines and cannot be in the perfect position all the time and if I practice that I have a certain amount of space calculated and my partner is too close or too far, that will lead to all kinds of problems. So in this situation you adjust immediately based on what is in front of you and where you need to be, in order to make it work vs. make it right.
 
I guess it also can be calculating but it's instant and based on the situation. It's like driving a car and reacting to everything around you. I don't think people really think they are calculating - they just react.  



6. Is estimation good enough or do you rely on accurate
measurement of distances and times?

Estimation for sure, it can never be exact because when we compete we have other couples with us at the same time on the floor. Plus the floors can always be different sizes. So you map out your choreography when you practice and the places you ideally want to be but on the day and time of the actual performance it might not happen because you have to make adjustments based on what is going on around you. If you're dancing show case numbers. which means you're the only couple on the floor, then you have a very clear idea of distance and directions you want to move to, but again it's never the same. For example the floor can be slippery or sticky and that will affect your movement for sure.
 

7. How aware are you of timing and beat when you are dancing?

This is very similar to fractions that I mentioned earlier. That is definitely very calculated in advance and rehearsed a lot so that it becomes second nature. At high level dancing it changes to freedom to choose right at the moment based on the music and how you feel that particular split second to express the music. It becomes even more rewarding if your partner is in tune with what you are doing and reacts on those charges that just happened in your body. We do that a lot though practicing lean and follow, when two people can fell though connection what happens in the other person's body.
 

8. Have your teachers or choreographers ever used math and physics to explain your technique?

Of course people have different styles of teaching but technique is technique and does not change. So yes in the beginning it comes with instruction of timing, directions and amounts of turns. Good technique makes good dancers. Once you pass that level it take the whole new form of what you're learning. It become about story, relationship, acting, expressing your feeling though your body. Those are very emotional things that cannot be calculated or measured. That's what makes good dancers, great dancers, unique dances or even admired dancers. If dance can grab you emotionally and you can't take your eyes off the couple, it's not because they have perfect technique, it's because of all those other aspects of dance. 

 
9. Do you look at statistics much to analyse your training and performance?

Yes. I guess it will be on the sense how much time and practice you put into something to become good. I read an amazing book called "Outliers". it talks about successful people and how they got there. Part of that book talks about putting 10 000 hours into what it is you doing and you cannot fail to be good at it. I was very curious to see when I reached my 10 000 hours and did an estimate of hours from childhood of how often I went to classes and competitions and my estimate was, that I got to 10K by age 17 :-) I guess numbers don't lie - that was the year when my partner and I won Russian championship in Latin. I danced for another 12 years after that and I'm sure I passed my other 10K. By the end of my competitive carrier, I retired with two world titles.

As far as analyzing, absolutely.
We usually video tape our competitions or show and look at them after. You are your own best and worst critic (sometimes we are too critical of ourselves). But after looking at the tapes we can choose what things to work on or fix. Because we also need to take into consideration "it's not how much you practice, it's how smart you practice" plays a huge roll in your improvements. I can put 10K hours into practising something wrong then it will be impossible to fix it because it's going be such a big part of your muscle memory, which is the hardest thing to fix for a dancer. So knowing what to practice and how to achieve it is a very important part in our industry.


 
10. Do you have any other insights to offer into how you use mathematics in dance?

Yes. I personally use references to a compass :-)
I always say to my students, try to imagine your foot is like a compass: the ball of your foot is where the needle is and the heel is your pencil. Now keep your needle on the same spot and rotate that pencil around 1/4 turn, half turn or more :-) People always comment how cool that is, and they had never heard anyone else explain turns like that. With this I achieve a few things in one - they know the amount of turn and they will place their feet in the right position because they know exactly where they started and where it needs to finish.

Thank you Elena for giving your time to answer those questions so thoughtfully and passionately.

For more information about Elena, see her official website:

www.elenagrinenko.com