Yoga for Mathematicians

Sophie Maclean

The 9th Heidelberg Laureate Forum marked a return to the city of Heidelberg after two years online. The key features of the forum were back: the in-person lectures and panels, the boat trip, the dinner in the castle, the saxophone quartet playing “In The Mood”. But in the era of the ‘new normal” there were two key additions to the daily routine. First was the daily COVID test, and second were the warm-up sessions.

The warm-up sessions were introduced during the forum’s online years so people could mark the start of the day and prepare themselves mentally and physically. This new tradition continued at the 2022 Heidelberg Laureate Forum, with delegates being guided through yoga and mindfulness each morning by a lovely yogi named Andreas.

As a journalist, I decided to join the warm-up session one morning and make notes about what the experience was like. And I did! But as a mathematician, I thought it would be far funner to see what maths I could find in the yoga poses. This is what I discovered.

(Full disclaimer: I am not a yoga expert, and every photo you see is my first attempt at each pose. But that adds to the comedic value, right?)

The Graph Plots

Some yoga poses mimic graph plots!

The simplest of these is the mountain pose (Tadasana in Sanskrit), or as I like to call it \(x = 0\).

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is standing up straight, with her hands by her side and her palms facing forward.

Another fairly basic pose is s the imaginatively names Wide-Legged Standing Forward Bend (Prasarita Padottanasana), also known as \(y = – |x|\) (and yes, this is an excuse for me to show off my fabulous HLF t-shirt)

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is standing with her legs wide apart and has bent forward so she is touching the ground.

Those fancying a bit of an ab workout can also try their hand at \(y = |x|\), otherwise known as the boat pose (or Navasana in Sanskrit).

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is sitting in a V shape, with her legs forming one side of the V, and her body the other.

The Shapes

No list of mathematic yoga poses would be complete without mentioning the triangle pose. Know as Trikonasana in Sanskrit (with Trikona translating as “three corners”). I don’t even need to shoehorn this pose into being mathematical.

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is standing with feet apart. Her right hand is touching her right foot, and her left hand is up in the air. She is looking at her left hand.

Our next pose forms the circle, or unknot if you’d rather. This is the camel pose (Ustrasana).

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is kneeling on the floor, with her knees forming a right angle. The is looking up to the sky and her hands are touching her feet.

Another shape that can be made is an oblong, or rectangle. One way to do this is via the Utthita Hasta Padangusthasana pose, in English known as the Extended Hand-to-Big-Toe pose.

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is standing on one leg and is holing her right foot with her right hand. Her right leg is straight, and out to the side of her body.

But wait! This is the king dancer pose, or Natarajasana and it’s topologically equivalent to the above pose. Despite this, it would be impossible for me to move from one pose to another without letting go, because I’ve actually swapped which foot I’m holding. Reflections that are not superimposable, like this, are known as “chiral” in both chemistry and topology.

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is standing on her right leg and holding her left leg out behind her. Her left knee makes a right angle, and she is leaning forward slightly.

The Sequences

Every mathematician loves a good sequence, and yoga does not disappoint. There are not one, not two, but THREE warrior poses (or Virabhadrasana in Sanskrit).

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is lunging forward onto her right leg. Her arms are straight above her
Warrior I
A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is lunging onto her right leg, her arms are horizontal
Warrior II
A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is standing on her right leg, with her arms reaching forward, and her left leg horizontally out behind her. Her body and legs form a T shape. She is grinning/
Warrior III

Defying Gravity

The final three poses I’d like to share are wonderfully mathematical, as I genuinely did use mathematics to be able to do them.

First is the wheel pose, or Urdhva Dhanurasana in Sanskrit. The mathematics behind making this pose work is that, as you may have noticed, I took my socks off. This was to increase the coefficient of friction between my feet and the floor, so that I didn’t slip.

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. She is forming an arch shape with her body - her hands and feet are all on the ground, and her belly is pointed up to the sky.

The next pose is known as Bakasana in Sanskrit: the crow pose. The key physics behind this is ensuring that your centre of mass is between your two hands. To do this, you sometimes have to tilt further forward than your intuition would lead you to believe.

A young blonde woman is wearing a white Heidelberg Laureate Forum t-shirt and grey leggings. Her hands are on the ground, her knees are resting on her elbows. She looks a bit like a frog

A bit of a stretch

Okay, so maybe I used a bit of poetic licence with some of these poses, but that’s the wonderful thing about maths – if you look hard enough you can notice it everywhere and have a lot of fun doing it! What’s more, I think that for many people, the state of calm focus that is reached by meditation is very similar to the feeling of “flow” one can get when deep in a mathematical problem. Maybe maths and yoga aren’t so different after all!

The post Yoga for Mathematicians originally appeared on the HLFF SciLogs blog.

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