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Can Drawing Lead to Mastering Maths and Vice Versa?

By Sophia, published on 30/11/2017 Blog > Arts and Hobbies > Drawing > How Maths Can Help You Learn to Draw

Are you a right brained, creative type?

If so, learning how to draw gives you another creative outlet; another reason to daydream and keep your head in the clouds.

Which means you don’t have much patience or aptitude for dry-as-sticks subjects like maths… right?

If that is the case, you might be surprised to learn that maths and art are intimately intertwined!

Proportion, symmetry, the ratio of light to shadow in each piece; dimensions, perspective and gradients of color: the vocabulary of art is the language of maths!

Let us now delve further into the similarities – and differences of these two disciplines.

A visual depiction of the closeness between maths and art Maths and drawing are kissing cousins! Source: Pixabay Credit: Bess Harniti

Maths and Art: Kissing Cousins

If you don’t believe all of the evidence already widely known about these two subjects being closely related, consider this:

Forms, spaces, figures: both disciplines are based in realism; in the observation and study of nature.

Even negative space has a place, both in art and in maths!

The shared values of abstract versus figurative art, at the junction at where they intersect: their common denominator is maths. Another reason to learn to draw, and a new reason to rediscover maths!

Using Equations to Draw Hands

You might know of the the fellow across the pond named Jason Padgett. He was grievously injured one night, after karaoke and, when he woke up, he discovered he saw the world through an intricate filter of geometrical patterns.

Prior to that, he was quite happy as a furniture salesman with no desire to even consider the shape of furniture, let alone drawing any.

We do not encourage getting beaten into savant syndrome to gain the same perspective as Mr. Padgett.

Instead, you could just enjoy his geometric patterns, most drawn in a one point perspective.

Here is a bit more on the unique Mr. Padgett, who before had never had the faintest interest in anything academic, let alone maths.

He started drawing what he was seeing and, curiously enough, he attracted the attention of the scientific community.

The consensus: everyone unanimously agrees that every bit of his line drawings and other renderings were geometrically accurate and depict mathematical equations.

Today, this amazing artist continues to draw mathematically satisfying  artistic equations that are the envy of every geometry professor.

For many of us, his work remains among the finest expressions of symmetrical art.

Surely you know of the premier example of such?

It would be Da Vinci’s Vitruvian Man, a pen and ink on paper, which, incidentally is the basis for validation of the value phi, also known as the perfect proportion or the golden ratio.

Whether through art or maths, learn what jobs you can land if you can draw

In this landscape drawing, the horizon line is one third of the way up Can you spot the horizon line in this landscape? Source: Pixabay Credit: ManeeG

Drawing to Understand Mathematical Concepts

Without going so far as to actually draw fractals, we would like to emphasise that you have most likely already used drawing to understand math.

Drawing shapes, an essential part of algebra and geometry, also features heavily in learning how to draw a human face or the human form.

Can you draw a circle, freehand? In maths class, you most likely used a compass.

Once you completed it, you were probably tasked with calculating radii or arcs…

The purpose of those dimensional exercises was to give you a visual to focus on while calculating an abstract figure.

When circling around a math problem, being able to give yourself a visual can be a valuable asset.

It is far from uncommon to use drawing tools in maths: the aforementioned compass, to be sure, but also protractors, rulers for drawing straight lines, a square or rectangle…

Perhaps you even had a stencil to help you draw ellipses.

Starting in primary school, children are encouraged to correlate art to math: elementary textbooks are full of cartoon characters, capering in sets or alone.

Whether you wield the pencil or view the work of an illustrator, drawing helps to stimulate the right side of your brain, as well as your logical mind, also known as the left brain.

Such a blending of intellectual and artistic qualities in learners’ development can only lead to academic success!

Those same features foster essential qualities for being good at math.

Learn here how a math whiz can use a Wacom tablet to draw animals.

Use Maths to Learn How to Draw

Starting with your very first art class, you will learn basic drawing by copying simple shapes drawn by other artists.

Generally, your art teacher will advise you to sketch the object in geometric patterns.

Let us draw a human face together:

  • for the contour, draw an oval
  • two perpendicular, horizontal lines to mark areas for the features
    • one vertical line should bisect the oval outline
  • eye drawing goes in the upper third, with one eye on either side of the vertical line
    • unless you are emulating Picasso’s cubism!
  • the nose goes between the horizontal lines
  • the mouth: draw it below the lower line

Once you know how to draw faces, you can work on your shading techniques for a more realistic drawing.

The more you take in these drawing tips, the more comfortable and proficient you will become at rendering art.

Have you ever tried to draw a car?

Start by tracing a cube. Those contour lines serve as the boundaries of the artwork itself.

Within them, you will place markers, just as with did with the face drawing example above: parallel and vertical lines.

From there, you can draw the different elements that pertain to a car’s appearance, erasing the occasional erroneous line as you go.

See? The same method applies, no matter what you draw!

You can draw a cat, draw a horse, draw a hand, the human body, learn how to draw animals … This technique can be applied to almost everything!

However, to draw a human figure requires a realistic breakdown in order to get the body proportions correct, in relation to each other.

Step by step drawing of all of the parts of the body eventually gives us a likeness of a complete human, but some fine tuning will most likely be required, including the play of light and shadow over the features.

Otherwise it will just look like elaborate doodling.

The notions of parallelism and symmetry will be the heart of your first attempts at sketching: learning to draw means measuring, comparing and dividing.

See? Without even realizing it, we do maths by drawing … The first steps, perhaps, to becoming a graphic artist?

A knowledge of maths can help you draw anything, even this car After drawing reference lines, you can draw just about anything! Source: Pixabay Credit: Werner22Brigitte

Maths: Indispensable for Perspective Drawing

Of course, you have been attending all of your art classes… right?

As you gain practice, you can draw and paint more ambitious subject matter.

More complex compositions, where mathematics makes more sense than ever!

In landscape drawing, for example, you will need to know all of the techniques needed to recreate a three dimensional object on a flat surface.

To create this effect, you must master the notion of depth and find the natural lines that anyone can observe.

How to draw perspectives?

To reproduce anything – a model in pose or how to draw a rose, it is necessary to prepare your drawing paper and to trace the essential markers:

  • The horizon – the most recognisable line
  • The point(s) at which the directional lines converge
  • Directional lines: your guide to build perspective effect

As you progress further in your art lessons, you will come to perspective and foreshortening, playing up the foreground or muting the background…

Of course, you can do all of this without necessarily being good at maths, but you will need to develop a keen eye!

Practicing perspective viewing can become a matter of routine.

As you walk along the country paths, spot the horizon. Next, find a cottage; place it in perspective to the horizon. And then, note the rising sun: how does it relate to the cottage and the horizon line?

And, just like that, you have created a one point perspective in your mind!

Hopefully, you will have your sketchbook handy; these geometric revelations don’t happen at the drop of the hat!

Unless your name is Jason Padgett, of course.

The Final Word is Phi

In all of your drawing tutorials, as you hone your drawing skills; while you charcoal your next still life or use Conté crayons to add textures and light shade…

Whether you know it or not, every figure drawing you have rendered is driven by phi (pronounced fee).

This is the golden ratio we mentioned before; the one that Leonardo da Vinci was so obsessed over that he reputedly dug up freshly buried cadavers for dissection, study and measurement.

Consciously or not, everyone who is any kind of an artist, from cartoonist and manga to portrait painter and architect, seeks to find and recreate this mathematical value in art simply by following their artistic sense.

We find the golden proportion in the columns of the Parthenon, and the structures of Le Corbusier and Frank Lloyd Wright.

Graphic designers have appropriated this perfect proportion, that you will find among the most famous company logos, in particular the famous apple’s Apple.

Not to mention the National Geographic logo. You know, the yellow rectangle, hard to make simpler … It is not only yellow, it is also a golden rectangle!

With phi all around us, it is easy to see how maths influences art. 

Or is it the other way around?

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