Today, you will meet Bonnee Byrne who is Freelance Artist and Owner of Signs by Bonnee. She has been painting artwork and signs for the past twenty-six years. Sound like fun, huh? She even seems to enjoy the math aspect of the job!

Can you explain what you do for a living?

I am a painter. This includes painting portraits in charcoal, pastels, and oil paint. I also do other professional artwork such as butcher paper commercial and all occasion banners, window painting, caricatures and illustrations.

When do you use basic math in your job?

The main time that I use math is when I am planning to make very long banners. I work on an easel that is 8 feet long and 4 feet high. Many times my banners have been 20 to 40 feet long. I have to calculate how much to paint on each 8-foot segment in order for the banner to come out right and the wording to be centered.

How do you think math helps you do your job better?

It would be impossible to do this job without basic math skills.

How comfortable with math do you feel?

I am fairly comfortable with basic math all the time. I am not very familiar with advanced math.

What kind of math did you take in high school?

I chose to take Algebra and Geometry only- the minimum amount to graduate. I did not have to have any math in college since I was an art major. I did not like algebra at all and do not feel like I had a complete understanding of it. I did like geometry much better probably because I am an artist and learn things better in a visual format.

Did you have to learn new skills in order to do the math you use in your job?

No, I picked it up using the skills I learned in school.

Goes to show that even if math is not your favorite subject, when used to do something you love…it’s not so bad!. If you want to hear more about Bonnee’s artwork, let me know I would be happy to connect you!

In my interview with painter, Samantha Hand, she mentioned something called the Rule of Thirds. I’ve heard of this, but I honestly had no idea what it was about.

Turns out the Rule of Thirds isn’t really about thirds, per se. Instead it’s about ninths. The idea is to divide the image into nine equal parts — something like this (Photo Credit: Lachlan via Compfightcc):

There are a couple of things to notice here. First there are exactly nine rectangles inside the one rectangle — forming a 3 x 3 grid. Second, all of the smaller rectangles are congruent, which just means they are the same size and shape. Last, each of the smaller rectangles is proportional to the larger rectangle.

What does this proportional thing mean? It’s simple, but let me explain using some numbers. Let’s say that the photo to the left measures 12 in by 6 in. (It probably doesn’t but stay with me.) From that information, we can determine the dimensions of the smaller rectangles: 12 in ÷ 3 = 4 in and 6 in ÷ 3 = 2 in. So each of the smaller rectangles is 4 in by 2 in.

If the small and large rectangles are proportional, they’ll have the same ratio. Let’s take a look:

12/6 = 2

4/2 = 2

This ratio that they have in common has a fancy name: the scale factor. (And if you know anything about drafting or making scale models, that will be familiar.)

Now before we get too far into this, let me say that Samantha — and most painters and photographers who might use the Rule of Thirds — isn’t thinking about proportion and scale factor. But this a good example of when proportions are important andintuitive.

So getting back to the Rule of Thirds — according to some research, people’s eyes are naturally drawn to where the grid lines intersect. A painter can use this information to draw viewers into the painting, especially if there are surprising elements or those that should have more emphasis. Take a look at Da Vinci’s The Last Supper.

Image courtesy of Atelier Mends

Notice how the table itself sits along the bottom horizontal line. The left vertical line crosses Judas, Peter and John, and the right vertical line crosses Thomas, James and Philip. Interestingly, the greatest tension in the piece is at these two points, while Jesus occupies the exact center of the painting with a calm demeanor. Whatever your religious beliefs are, the story this painting tells is furthered by Da Vinci’s use of the Rule of Thirds.

In a couple of weeks, you’ll meet a photographer who probably also uses the Rule of Thirds in her work. In the meantime, see if you can superimpose an imaginary 3 by 3 grid over your favorite paintings or photographs. How does the Rule of Thirds draw you into the piece? How does it help you notice important or surprising details?

Have you noticed the Rule of Thirds in paintings that you love? Share your thoughts in the comments section!

Sam doesn’t remember this, but when she and I were in middle school, I used to ride home with her on the bus after school, when we’d watch Godzilla on television and eat her mother’s homemade potato bread. At that time, she said she wanted to be a veterinarian (like her dad). Instead she earned a BA in art and then her MFA. Since 2010, she’s discovered her talent in oil painting.

Samantha Hand has some mad skills when it comes to oils and canvas. And even I was surprised by the math that she uses. Unlike most of the other folks I’ve interviewed for Math at Work Monday features, Sam really counts on being able to visualize the math she needs. Read on…

Can you explain what you do for a living? For the last two years, I have completely immersed myself in oil painting and have tackled landscape, plein air, still life and portraiture. Currently I am painting compositions that intrigue me in hopes of selling them, while accepting commissions on a variety of subjects. Recent projects include still life and figurative painting.

When do you use basic math in your job? I use the most math at the beginning stages of a painting. When I am sketching thumbnail ideas, I use the rule of thirds to compose a more interesting picture. I use a variety of angles to draw the eye toward the focus of the picture and to lead the eye around the composition. I also use angles in drawing perspective when I am attempting to create depth in a two-dimensional space. (For example, the angle of a building is wider in the foreground and will go toward a vanishing point as the building retreats into the distance)

If the composition is complex, as in a triple portraitI am currently working on, I use a grid to enlarge smaller reference images to the larger size of the canvas. This helps to keep the proportions of the sketch on the canvas accurate. Proportions are also important in balancing the values and subject matter in a composition. I check to see if the proportion of dark values is greater or lesser than the proportion of light values to add interest. I may balance the visual weight of the subject with a greater space of sky to create visual tension or to draw the eye toward the subject.

Mr. Allison’s Hat

When I am sketching the figure I am constantly checking my proportions by comparing the size of body parts. For example, in most faces the space between the eyes is the width of one of the eyes in the face. Also, in general, people are approximately 6 and a half heads tall. I use a paint brush or pencil to measure and compare. I also use this measuring and comparing in all other subject compositions to check my spacing and proportions.

Once I begin painting, I use ratios in the mixing of colors. If I am looking for a purple I may mix an equal amount of red and blue. But if I want a warmer purple with a reddish tint I’ll use less blue in the mixture. Throwing in the amount of yellow equal to the red will turn it toward a brown. Equal measures of red, blue, yellow becomes a neutral gray. There are infinite numbers of colors to be mixed which is one of the most exciting things about painting.

Do you use any technology to help with this math? I do not use a calculator or computer because the math I use is simple and not very exact. It is more about the feeling of balance or rightness. If something doesn’t feel right with the composition I begin to check using more exact measurements and angles.

How do you think math helps you do your job better? Math is the building block of my compositions. I use angles and proportions to try and create intriguing compositions with believable subject matter.

How comfortable with math do you feel? I am very comfortable with the math I use in my artwork but less so with the everyday math of a household. Somehow I feel as if I can visual the math I use in compositions and it makes sense to me. When I apply it to household tasks I have to really focus on the task at hand.

What kind of math did you take in high school? I only vaguely remember my classes in high school but did take math analysis, geometry and the other algebra courses offered. I really enjoyed my math classes and felt confident in my ability, though less so with geometry. I continued with a calculus course in the first year of college and enjoyed that also. Unfortunately, I think I’ve only retained very simple math skills.

Did you have to learn new skills in order to do the math you use in your job? I haven’t had to learn any new skills yet but I have learned to use the math I know in tangible situations.

Did you have any idea about the math that goes into planning a painting? If you have a question for Samantha, ask it in the comments section.

This month, Math for Grownups has gone arty, taking a close look at how math shows up in the visual arts. Last week, glass blowing took center stage.