STEM & Quilting with Kids: Geometry

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Introduction

There is a fresh new energy in our country, and it is displayed in the arts in a profound way. Science, technology, engineering, and math intersect with and have found their true expression in the arts. Young artists are learning to manipulate line, shape, color, texture, and form with technology. They are being inspired by engineering to develop new ways to express creativity in a 3-dimensional world. Science has opened a whole new view of things with electron microscopes, magnetic-resonance imaging, and space telescopes. In addition, mathematics has revealed her secrets to good design through algebra, geometry, trigonometry, and calculus. Consequently, the stage has been set for some significant connections to be made with STEM (Science, Technology, Engineering, Math) and the arts that will lead to the growth and enhancement of 21st Century thinking skills. As an art form, quilting promotes stillness and deep thought, concentration, fine motor skills, and demonstrates mathematical principles in a tactile way - growing the mind and enlivening the heart. Taking on the quilting arts is enhancing creative thinking, mindfulness, and cognitive development. That is how young artists can make the world a better place by using math as a way to transform minds and transform the world. 

As we tap into this new energy, we must honor the efforts of those creative individuals that were early pioneers in joining the arts with STEM, in particular, mathematics. Those individuals are amongst us today. They are our traditional quilters carrying forward a legacy of block patterns and designs. Blocks with names like Nine-Patch, Log Cabin, or Rail Fence are passed down through generations and preserved in quilts all over the world. Sometimes the name may change but the pattern continues to be sewn.

Quilters have created their artwork inspired by many things, however, the use of shapes and the organization of the shapes in quilt blocks demonstrate a total alignment with mathematical principles. Consequently, we can learn how to describe quilt blocks using the language of mathematics, specifically geometry.

What are Geometric Transformations?

Geometric Transformations describe how shapes move in a 2-dimensional plane.

In translation, shapes move along a vertical, horizontal, or diagonal line.

In dilation, shapes re-size getting either smaller or larger.

In rotation, shapes revolve clockwise or counterclockwise around a central axis point.

In reflection, shapes mirror each other in size, shape, and direction bilaterally. 

Transformation means to change. So, a geometric transformation would mean some changes involving geometric shapes have occurred.

Types of Transformations

 Based on how we change the combination of shapes, there are four main transformations. 

Translation happens when we move the image without changing anything in it. Hence the shape, size, and orientation of the object remain the same moving vertically, horizontally, or diagonally. This is also called “sliding.”

Rotation is when we rotate the image by a certain degree clockwise or counterclockwise. This can also be described as “spinning”.

Reflection is when we flip the image along the centerline. The flipped image is also called the “mirror image”. If you imagine a line that extends through the middle of the block, each side mirrors the other.

In Dilation, the volume of a shape is increased or decreased without changing its original shape. It is also called “re-size”.

Geometric Transformations in Nature, Industry, and Art

Nature

When we observe the natural world, we can see how geometric transformations are expressed in nature. The antlers on the buck mirror each other in size, shape, and color. The antlers are demonstrating reflection. An amazing fact is that the buck sheds his antlers each year between December and March. Once a deer sheds its antlers new ones grow back mirroring each other again for another season.

Another example of Reflection appears on the wings of Monarch Butterflies. The wings mirror each other in size, shape, and color, displaying “Reflection”. Spring and Summer are perfect temperatures for this butterfly to lay eggs for the next generation to delight nature lovers from Maine to Mexico.

We experience the seasons each year as the Earth rotates around the Sun. Acting as an axis, the sun is central to our solar system using its gravitational field to hold the planets in place rotating at speeds that would boggle the mind. The Solar System demonstrates rotation.

The forest is home to many plants that display several different geometric transformations. This fern that grows on the forest floor has leaves that gradually decrease in size demonstrating dilation (re-sizing).

Notice the feathers on this Eagle. The lines travel horizontally along the full length of the feathers, showing translation continuing along with each feather.  

Industry

Engineering and architecture find design solutions in geometric transformations. This building not only rotates, but it also has several floors that translate diagonally around the structure. It is an example of how geometry is used to enhance the look and function of the construction.

Machinists and engineers develop gears using translation as a way to develop the function of these machine components. The teeth of the gears align with each other. They turn to power machinery for industry.

Art

Stained glass artists use geometric translations to give depth and organization to their designs. Notice reflection and rotation create a sense of movement around a central axis.

Designers who create fabrics and textiles for home décor also are inspired by the principles of geometry in their products. Horizontal translation creates a peaceful serene design in this upholstery fabric.

Traditional Quilt Blocks Described Using Geometric Transformations

The Pinwheel block demonstrates color and shape rotation. If you just consider the shape, you can see reflection.

The Log Cabin Block is a traditional block with many variations. Notice dilation as the squares appear to overlap and get bigger. 

This block is a combination of Half Square Triangles and strips. Can you guess the geometric transformations that appear in this block?

This Nine-Patch block shows a geometric transformation that could have 3 different expressions. What is it?

Quilts that display Geometric Transformations

Can you identify the Geometric Transformations embedded in these Quilts? 

A Quiet Place – Hand Dyed, Hand Painted, Hand Quilted and Appliquéd

The Black and Blue Quilt – Hand-Dyed, Hand-Painted, Hand-Quilted​​

The Mandela Quilt – Hand-dyed, Hand-Quilted                 

Original Art Quilts, Blocks, and Textiles by Marquetta Johnson

How to Make a Traditional Block inspired by Geometric Transformations

The Whirlwind Quilt Block       

       

If you were to describe the Whirlwind Block using the language of geometric transformations, we would say that the Whirlwind block has triangles rotating around a center axis point creating rotation.

The Whirlwind Block is created from 100% Cotton Quilting Fabric. When choosing fabric, choose 2 different fabrics with complementary or contrasting colors.

A simple way to cut out the pieces for this block would be to sew together two WOF (width of fabric) strips together and then cut them up.

To make a 12” Whirlwind block cut:

1 Strip 5” x WOF from your main fabric

1 Strip 5” x WOF from your background fabric

   

1. Sew the two strips together, making 1- 9 ½” strip. Press the seam toward the darker fabric.

2. Cut the strip into four 9 ½” squares.

3. Cut the squares in half diagonally. NOTE: Cut each one in the same direction (such as the bottom right to top left)

4. Separate out 4 triangles that are mostly print and 4 that are mostly solid. Each Group is enough for 1 block.

5. Arrange the four Triangles from one group in a whirlwind pattern.

6. Sew them together in 2 sets. Press the seam.

7. The last step is to sew the two halves together. To make the center seams line up, match the seams and pin them.

8. Start the sewing process by placing your matched fabric under the presser foot and making a few back stitches to anchor the seam. If sewing by hand, thread your needle. Tie a knot at one end and sew into the end of your matched fabrics ¼” from the edge. Whether hand or machine sewing, begin sewing from one end to the other, pausing at the middle to remove the pin.

9. Continue sewing until you reach the end. Back Stitch 3 times to secure the ends. Press the seam to one side. Trim and square the block to 12 ½” if, necessary.      

   

Now that was easy! Consider sewing a 2 ½” wide strip on the edges to create your own Mini Quilt!