Grace Graphed Lines

Isabella Boylston is a renowned principal dancer with the American Ballet Theater studio company and has performed with the Royal Danish Ballet, Mariinsky Ballet in St. Petersburg and countless others. She has received many prestigious awards - Princess Grace Award in 2009, Clive Barnes Award in 2011 and was the recipient of the 2014 Annenberg Fellowship. Her poise not only is showcased by her talent but how she carries herself throughout her practice and the world.


In 2017, we worked alongside ballerina Isabella Boylston to reimagine the ideas of movement through dance. Where seen as polar opposites, dance and mathematics involuntarily work together.



In Italian Renaissance writing, Castiglione explains the concept of sprezzatura as the ability “to practice in all things a certain [graceful] nonchalance, which conceals all artistry and makes whatever one says or does seem uncontrived and effortless.” This concept intersects with mathematics and dance.



The organization of trigonometric equations graphed filters Castigliones’s ideas of grace to create freely energetic dance. The mathematical boundaries of tangent lines are asymptotes that movement across a semicircle defines. From the lowest point of the circle to its highest peak, the tangent line decelerates and reaccelerates into a double-sided exponential figure that echoes the forms that the artist highlights linking the dancer’s torso to her slightly folded legs. The transition between lower and upper graph and human body occurs smoothly because of the choreographed limits are crafted into perfected uniformity.



Beginning from the bounding guideline of an asymptote, the exponential graph of a line slopes continuously with the freedom to infinity. The shape of the function visualized resembles both the arch of the dancer’s back and the nature of her steps. She begins with choreography, a force that is as guiding as the asymptote. Stretching her body in line with a perfected turn enables her to express the graceful nonchalance that Castiglione discusses. Finessed seamlessly through years of learning, the body works in coordination to execute the dance with magnetic ease.


Sine Wave:

Equations that visualize waves oscillating in a continuous repetitive motion or change, it is mirrored in height and depth, troughs and peaks - extremities and margins. The relationship between choreographed harmonics and the changeability within the limits can be seen by Isabella’s gentle waves of motion in her legs and arms - it is free expression, you are able to find anchors in singular limits this enables beauty which encapsulates the effect of balanced extensions in the most graceful of ways.



Asymmetrical plane curve formed by the intersection of a cone with parallel planes at its side. Parabola’s portray elevation, lightness, and balance - meaning, what has happened on one side, must happen on the other; negatives and positives are as strong as their meeting point (a vertex.) The correlation that exists between a parabola and dance is how the body moving in various ways, legs extended in one direction and arms in another always have their meeting point, their body. Arms are able to be extended in what seems an endless plane as legs move in its extended plane in the opposite direction - always synonymous with one to create balance, elevation, and lightness. You cannot be one without the other.



When kids are young they groan at learning geometry, trigonometry and anything that involves learning shapes and numbers. We have all said, “when will we have to use a log equation? When will this be relevant in my life if I am not a mathematician?” Well, as we grow up we realize that those equations have taught us beyond the classroom we were taught in. We learned the circumference of a circle can be portrayed as “who are we with our closest loved ones? Do they represent our core?” We learned to balance and how important it is to keep balance in our lives in order to keep the fun, lightness, and joy.  Moving forward, I hope we look at algorithms as a way to live our lives in harmony with each other and our earth, like a parabola we are only as strong as our negatives, positives, and our starting points.