This is the fifth in a new series, which covers the exploration and application of design elements and principles. Each column will cover one basic design element and/or principle, and will contain descriptions, examples, tools and techniques, and exercises that can be used for art journaling, photography, collage, book arts and other creative disciplines.
When I was a kid, I fondly remember my family eating take-out pizza from a place called Triangle Pizza on Sunday evenings. I also remembered camping in a heavy canvas two-person tent, and staying in A-frame cabins at summer camps.
During high school years, I have encountered, studied, and used triangles in geometry, math analysis, art and mechanical drawing classes. I also utilized triangles as decorative, design, structural and architectural elements in many of my projects during the college days as an industrial design student.
One of my hobbies happens to be origami and whenever I am folding, I often see triangles formed by paper creases. My favorite model is kusudama, a Japanese spherical paper model created by sewing or gluing together several identical pyramidal units folded from square paper.
Definition of a Triangle
But anyway, what’s a triangle? To me, it’s nothing more than a shape that has three sides and three angles. Without over-burdening you with the minute mathematical details, there are several basic types of triangles, geometrically speaking. Let’s start with the angles alone (and ignore the side lengths) – there’s right, acute, and obtuse.
Triangle number 1 is called a right angle because that angle with the yellow dot is 90 degrees. Triangle number 2 is called acute – that dotted angle is more than 90 degrees. Triangle number 3 is called obtuse when all of the dotted angles are less than 90 degrees. The sum of all of the angles in each triangle (both dotted and undotted) is exactly 180 degrees.
And when we are dealing with both sides and angles, we’re talking about equilateral, isosceles, and scalene.
All of the angles and all of the side lengths are the same for the equilateral triangles. Isosceles triangles have two angles and two side lengths that are the same. None of the angles and side lengths in scalene are the same – they can be either obtuse or acute.
Triangles can be created with either lines or other shapes. Shown below are three basic triangular images to represent various concepts.
The first image on the left (1) was done with thick lines – this image is often used as road sign in many countries. The second one (2) is an arrangement of three rectangular shapes forming a triangle to represent the start of a hiking trail. Inverting this image (two rectangles at the top) will give a new representation as the end of a trail. The three dots in the third one (3) give a symbol that is often used in mathematics and logic to represent the word, therefore.
The same shape can be used to represent various objects by creating several groups of triangles of various types. With the triangles alone, I have created a mountain range, a forest of conifer trees, and a group of camping tents with triangles in the digital landscape shown below.
Many famous artists, designers and architects have extensively utilized triangles in their work. Some of Frank Lloyd Wright’s house designs were based on triangular grids. Bruce Goff, a visionary architect, used triangles as a structural, architectural, and design elements in his building plans. Paul Klee, an artist, used a lot of linear triangles in some of his paintings. Alexander Girard, a designer, used triangles as a repeating pattern on the fabric. Frederic Church, an artist and a designer, created stencil designs with triangles for his mansion’s interiors as decorative borders. Buckminister Fuller’s geodesic dome designs contain many triangles.
Hunt for Triangles:
Let’s start our hunt for the triangles within the square first. Triangles can be formed inside the squares by drawing one or two straight lines from one corner to the opposite corner, thus giving two or four triangles (b and c). Inserting a diamond inside of a square can create four corner triangles (a).
Very often, we can find example of corner triangles (a) on the back of picture frames or on the cranes. These diagonal braces were often used to stabilize the structure to give it more strength or sturdy. In the photos below, we have the examples of a crane (upper left), the tiles on the floor of an opera house (right), and on the exterior wall of Frederic Church’s mansion (bottom).
Next set of photos below shows examples of triangles created by crossing one line diagonally across a square. In the left photo, I created my own “printing plate” by first cutting up adhesive backed foam sheets into squares, and then cut them diagonally. I then placed the triangles on the paint mixing stick and used the inkpad to create the impression on the paper. The right photo has two sets of triangles on the sliding doors of a church. And the bottom photo is the typical diagonal cut that most people used for the sandwiches.
The next and last set of photos below shows examples of crossed squares. We can see in the top photo that the bridge is very well built to withstand the constant vibration from the traffic crossing the river on it. The left photo shows the wooden bench found in the waiting room at a railroad station. The bottom photo shows the similar pattern on the door of the house where I live.
Now, let’s think of each square shown above as a repeating unit. Shown below are four basic repeating patterns using triangles. Many cities and its surrounding areas have construction sites that often use cranes and/or scaffolding.
I have used the above patterns in my art journaling pages, and also have seen the same crease patterns in some of my origami projects.
Second Hunt for Triangle
Now let’s start another hunt for the standalone triangles, and several triangular volumes. We can find a few examples for each of the below:
Starting with the first one on the left, flat triangle, we can see that it is used for the road sign, Yield.
What’s interesting with the yield signs above is that it is shown on the rectangle sign to let the motorist where it is, another one on the diamond sign to let the motorist that the yield sign lies ahead. And the last one is actually a triangle one to tell the motorist to actually yield to others. The next set of photos shows the elements associated with the automotive world. In the center of bottom photo is a SMV sign required by law to be placed on the slow moving vehicle (less than 25 miles per hour) such as tractor or horse buggy.
Photo number one shows the triangular pattern formed as a result of angular parking. Number two shows the leftover area created by the parking space lines, and is often painted with multiple lines to indicate no-parking zone. Triangular shapes can be easily seen on the both ends of the traffic barricade in photo number three. In number four, a triangle is often used as part of an arrow to indicate traffic direction.
Triangular shape can be found on railings as decorative element, as balustrades or as braces for support.
Banners, flags and college or sport pennants are often found as triangular shapes – either isosceles or right angles. In the left photo below, these flags on “strings” are often used in car sales lot or to cordon off certain areas for special events. The flags in the right photo are used to identify the site so that the visitors to the glass museum could find it easily.
Let’s move on with a triangular volume with the circular base, cone. They’re easily found as traffic cones, paper cups (used as part of lifestyle store display), carousel roof, and ice cream cones (not pictured).
The next volume to be explored is pyramid. Its sides are flat and triangular but its base can be triangular, square or any other shapes. We have the below photos of a fence, concrete mini-obelisk, and church steeple – all of them have square base. Other examples not pictured are square cupolas with four triangular roofs, tall obelisks, and pylons.
With triangular based pyramids created from corrugated cardboard, I have created a pseudo-geodesic dome house for my nephew about two decades ago as shown in the photo below. Geodesic domes are quite complex, and not all triangles are of same size. But all of the right triangles that I used in this dome house are all of the same size.
Multiple pyramids formed with isosceles triangle (long sides and narrow bases) are often used to create “stars” or kusudamas. Photo number one below is a treetop decoration made with paper – its spikes have triangle bases. Photo number two shows the origami kusudama created (“designed”) by Paolo Bascetta – I had to fold 30 sheets of paper into “Hungarian modules” so that this spiky model could be assembled. The last one, photo number three, is a hanging Moravian star – each spike is a pyramid with either square or triangle base.
The last volume to explore is a prism – each side is rectangular, but both ends are triangular. A few example of this are the glass prisms that split the incoming lights into different colors, Flat Iron building in New York City, and tents with flat rectangular sides, and triangular ends (front and back). Kaleidoscopes are often found as cylinders or box-shaped, but the reflective surfaces inside are formed as prism. Shown below is one of my kaleidoscopes that stands up like a microscope and allows me to place any small objects underneath.
I drew the black triangle in the right photo above to show the actual objects – all others are mirror images of them.
In various printed media, triangles are frequently used as design elements in the logos like the ones used by a rental car company or a franchise chain of campgrounds. Typographically speaking, we often find triangles in our Roman or Latin alphabets and numbers.
Visual Explorations and Exercises
Now that we have seen many examples of the triangles found in our physical world, let’s get started on the exercises provided here.
Listed below are the several suggestions for your visual exploration projects. Depending on the exercise selected, gather your favorite paints, mark-making tools or paper cutting tools. Or even retrieve your mower from the storage to create the triangular pattern on your lawn.
1. Stenciling and printmaking:
Using one or more of the three techniques listed below, create your own designs/patterns for stenciling or printing on your fabric, sketchbook or found books.
Technique #1: Stencil as stencil. Using thick paper or Mylar film, draw triangles on them and cut them out with sharp knife. Use different colors and layering technique to create interesting effect. In the examples shown above, I used three different stencil designs that I created for Stencil Girl Products starting from left to right: Mini-Triangles (L114), Mini-Shapes (L112) and Large Diamonds (L111). The photo on the right was first created with craft acrylics on index paper, photographed, and later digitally enhanced.
Technique #2: Meat packaging tray or foam sheet as printing plate. If using the packaging tray, cut the sides off. Using a pen or pencil with varying thickness, draw shapes – be sure to press down enough so that only the top surface will receive the paint or ink. The paint or ink can be applied to the surface with a brayer. An example of this technique is shown in the center of the book below as black image.
Technique #3: Stencil as printing plate. Stencils can be used as printing plate by applying acrylic ink or paint on the surface with a brayer. After it is applied, place the paper on top of it and gently rub it with your hand. Repeat as desired.
2. Paper crafts: Paper quilts.
Apply adhesive sheets to the back of wallpaper or scrapbook paper. Cut strips of paper, and then using a metal triangle containing 45-45-90 degree angles, cut right angles. Either create your own patterns or refer to quilting pattern books by arranging and applying the cut triangles on a square foam sheet or cardboard. I mounted my own on the mat boards, and framed them at a DIY store.
3. Typography: Font design – two exercises (four examples are given for each exercise):
Exercise 1: using only one color, create the whole alphabet with triangles and some lines (keep it to a minimal number of lines).
Exercise 2: using two colors and avoid lines where possible, create a whole alphabet with triangles only.
4. Pattern creation with lawn mower. One of the governmental agencies in United States recommends mowing the lawn in different direction each time (see figure 1 below – the lines representing the wheels). I did it differently for this column. I used three different directions all at once – I allowed some grass to be left for the next directional cuts. Photo number 3 below shows the wheel marks created with my lawn mower (white lines inserted).
I hope you have enjoyed the above visual journey & exercises, and I also hope that I have provided you with enough examples to give you a good jumpstart in creating your own portfolio with triangles.
Check out Andrew’s previous Design Demystified columns here.
You can see more of Andrew’s design work in Mary Beth Shaw’s new book, Stencil Girl: Mixed-Media Techniques for Making and Using Stencils.
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