Thursday, January 20, 2011

The Geometry Quilt--A Tutorial!

What do you call the quilt I'm working on? Rhomboidal Stars and Hexagons? Six-Pointed Stars and Six-Sided Scraps? How about "The Geometry Quilt". Here's how I did it!

First we must establish a connection between two words:

If a = {math concepts} = fun and b = geometry, then if {b} is a subset of {a}, then geometry = fun! Hooray!

Our goal is the creation of two polyhedral templates with sides all the same length.

You will need the following (plus scissors and tailor's chalk or a marking pencil). Research situates mathematical reasoning in the parietal lobe of the brain, but I was unable to discover whether the visual-spatial nuances of geometry involve other areas of the brain. Anyhow, you'll need to know your brain is designed to complete this task well!

Let's start with my original rhombus (diamond, lozenge, parallelogram, etc.)

Geometry Lesson 1: A rhombus is essentially two equilateral triangles stuck together. Thus each side is the same length, and if you draw lines through the center to connect points, you will have perfectly perpendicular lines! Also, your shorter crossed line will be equal in length to each of the sides.

I wanted my diamond to have 1.5 inch sides. For this tutorial, I aimed for 3 inch sides!

I built my rhombus from the inside out. I started with a pair of perfect 90-degree angle perpendicular lines.

I took my final side length (3 inches) and divided it by 2 (1.5 inches). Then, starting from where the lines crossed, I measured that length (1.5 inches) and made a mark on the horizontal (shorter) line on either side of that cross point. My total distance between marks was 3 inches, and the vertical line perfectly bisected my marks.

Next, I placed my ruler at one of the marks and pivoted it around, looking at where the ruler would cross the vertical line. I wanted the ruler to cross the line at 3 inches as this was to be one of my sides. My 3 inch line now connected the two perpendicular lines.

I followed the procedure for each side. Ta-da! A perfect rhombus!

Once the final 3 inch rhombus was drawn, I needed to add my 1/4 inch seam allowance. I simply made marks 1/4 inch from each point on the rhombus and connected the dots.

I ran into a bit of trouble, either from sloppy drawing or measuring incorrectly. I let it go, though, and cut out my template. (In my original rhombus, my measurements and lines were more accurate than these!)

A month or more had elapsed between the creation of my original rhombus template and my hexagon. Playing with the rhombuses prompted the idea of adding another element to what was emerging as a quilt, and the idea of the hexagon was born!

Geometry Lesson 2: There are two ways a rhombus can fit inside a hexagon, provided that the sides of each figure the same length. If three rhombuses are nestled together, all sides touching, they form a hexagon. This is the basis for Tumbling Blocks quilt blocks. If one of the rhombuses is removed from Tumbling Blocks and pivoted around, then two rhombuses will fit snugly inside a hexagon as well. (In this way, two equilateral triangles are also created, but we're not interested in those.) This two-rhombus form tells us that the height of the rhombus is also the height of the hexagon and that if we can imagine two rhombuses side-by-side, we will have our hexagon. An easy thing to do would be to trace our rhombus twice and connect the dots.

But I was having too much fun (geometry = fun!), so I went for accuracy!

To make my hexagon template, I first measured the rhombus template side. (3 + 1/4 + 1/4 = 3 1/2 inches)

I began with a long horizontal line, then marked 3 1/2 inches in the middle of the line.

I drew two lines, each on the hash marks and each perpendicular to my long horizontal line.

Now it was just a matter of drawing two rhombuses! This time, I included the 1/4 seam allowance in my measurements. Including seam allowance, my rhombus side was 3 1/2 inches. I divided that by 2 (Bueller? Bueller? 1 3/4 inches!), placed my ruler at the cross point of one pair of perpendicular lines and marked 1 3/4 inches on the horizontal line. (Don't be distracted by the fold in the cardboard pictured below.) I did the same thing with the other set of perpendicular lines.

Then I pivoted the ruler again, connecting dots and lines to form sides 3 1/2 inches long.

I cut out my template and compared it to the rhombus. I am glad I made a hexagon from scratch. My sloppiness on the rhombus became apparent!

Not every side was inaccurate, though. If you make your own, you'll be more careful!

After checking for accuracy, thank your parietal lobe for all its hard work because you're done! Next comes the fun part--fabric!

Iron some scraps and trace your templates.

Six rhombuses sewn together creates a star.

Iron flat.

Arrange with your hexagons.

Hey, guess what?


See? Geometry is fun!

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