Charting Circular Motifs: The First Few Rounds

The Formula for a Flat Circle

Before you can draw your chart, you need to know what to draw. The foundational principle of crocheting a flat circle is that you must add a consistent number of stitches in each round to accommodate the expanding circumference. If you add too many, the work will ruffle; too few, and it will cup.

The number of stitches you need to add is directly related to the height of the stitch you're using. Taller stitches are wider, so they require more initial stitches to form a circle and more stitches added per round to keep it flat.

This simple rule is your most important guideline. To summarize:

• Single Crochet (sc): Start with 6 stitches, add 6 stitches per round.
• Half Double Crochet (hdc): Start with 8 stitches, add 8 stitches per round.
• Double Crochet (dc): Start with 10 stitches, add 10 stitches per round.

But why does this work? The logic is rooted in the geometry of a circle, specifically the relationship between its radius and circumference, $C=2\pi r$.

You might notice a discrepancy between sources (e.g., some suggest 12 dc for a starting round, others 10). This happens because the ratio of stitch height to width is an approximation and can vary with yarn, hook size, and personal tension. For your own designs, the key is to choose one formula (e.g., start with 12 dc, increase by 12 dc each round) and use it consistently.

From Formula to Chart: Placing the Increases

Knowing you need to add, say, 12 stitches per round is only half the battle. You also need to know where to place them. For a circle to be symmetrical, the increases must be distributed evenly. This creates wedges or segments, and the number of segments is equal to the number of stitches in your first round.

This is where your radial grid is indispensable. The lines radiating from the center serve as the guidelines for your increase points.

The standard method is as follows:

• Round 1: $N$ stitches.
• Round 2: Increase in every stitch. [Inc] repeated $N$ times.
• Round 3: Work 1 stitch, then an increase. [1 st, Inc] repeated $N$ times.
• Round 4: Work 2 stitches, then an increase. [2 sts, Inc] repeated $N$ times.
• Round 5: Work 3 stitches, then an increase. [3 sts, Inc] repeated $N$ times.

The Problem with Stacking: Circles vs. Polygons

If you follow this method perfectly, your increases will stack one on top of the other in each round. While this is mathematically correct, it has a distinct visual side effect: it creates a polygon (a hexagon for single crochet, a decagon for double crochet) rather than a perfectly smooth circle.

For many designs this is perfectly fine, but for a truly round shape, we can use a simple trick: staggering the increases.

The technique involves shifting the placement of increases on alternate rounds so they don't align perfectly. We will put this into practice in our charting exercise.

Activity: Charting Your First Motif

It's time to put pen to paper. For this exercise, we will chart the first four rounds of a double crochet circle that starts with 12 stitches.

You will need:

1. Your radial grid from the first lesson. A 12-segment grid (with lines every 30 degrees) is ideal for this. If you need a fresh one, you can print the polar graph paper below.
2. Your hand-drawn symbol key from the previous lesson.
3. A pencil and eraser.

Here is a visual example of what a finished chart for a small motif looks like. Notice how the stitches are organized into rounds and how they build upon the previous round.

Let's begin. We'll use your symbol for a double crochet (T with one hash mark) and a slip stitch (●).

• Round 1: (12 sts)

  • Begin with a magic ring in the center.
  • Chart 12 double crochet stitches emerging from the center ring. Place one dc symbol so that its post aligns with each of the 12 radial lines on your grid.
  • Finish by drawing a sl st symbol connecting to the top of the first dc.

• Round 2: (24 sts)

  • The formula is to increase in every stitch ([Inc] x 12).
  • In the next concentric circle of your grid, chart an increase (two dc symbols) into the top of each stitch from Round 1. The two dc symbols of each increase should originate from a single point on the stitch below.
  • When you are done, each of your 12 radial lines should have an increase centered on it.

• Round 3: (36 sts)

  • The formula is one stitch, then an increase ([1 dc, Inc] x 12). This is a "standard" round where we stack the increases.
  • Your increases from Round 2 consist of two stitches. In the first of these two stitches, chart one dc. In the second stitch, chart an increase (two dcs).
  • Repeat this for all 12 segments. Your increases in this round should align perfectly with the increases from Round 2, right on top of your radial grid lines.

• Round 4: (48 sts) - Staggered!

  • The standard formula would be [2 dc, Inc] repeated 12 times. To stagger, we will split the two "plain" stitches.
  • The pattern becomes: 1 dc at the beginning of the round, then [Inc, 2 dc] repeated 11 times, then 1 dc at the very end of the round.
  • To chart this:
    1. Start by charting one dc in the first stitch of the round.
    2. In the next stitch, chart an increase.
    3. In the next two stitches, chart one dc each.
    4. Repeat steps 2 and 3 all the way around.
    5. You'll find that after your last increase, you have one stitch left before the start of the round. Chart one dc in that final stitch.
  • Now, look at your chart. The increases in Round 4 should fall between the radial grid lines, not on top of them. You have successfully staggered your increases!

Conclusion

Congratulations! You have successfully integrated all the skills from this module to create your first piece of a circular chart. You've not only learned the "what" and "how" of charting but also the "why" behind the formulas.

Key Takeaways:

• A flat circle's growth is governed by a formula derived from stitch geometry: add the same number of stitches each round as you started with.
• Charting this formula involves systematically placing stitches and increases on a radial grid.
• The placement of increases matters: stacking them creates a polygon, while staggering them creates a truer circle.
• Your hand-drawn grid and symbol key are the essential tools for translating these mathematical rules into a visual pattern.

You are now fully equipped to start designing. In our next module, "Designing the Central Medallion," we will move from these basic mechanics to making creative choices. We'll begin by exploring the different ways to start a circle—the magic ring versus a chain loop—and how that first choice influences the aesthetic of your entire doily.