Chapters

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.*

## 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...

Start drawing better by taking the new drawing lessons here.

## 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**

- one
**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?

## Maths: Indispensable for Perspective Drawing

*Of course, you have been attending all of your *drawing 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?*