Celtic Knots

We started by looking at a few Celtic knots and thinking about what we noticed and wondered.

Maybe you’ll take a few notes before you move to the next page…

Some of what we noticed:

• There are multiple passages
• No exit, no entrance
• The rectangular red knot is one loop; the square knot is four loops
• Both knots are hand-drawn

Some of our questions:

• What is the application of this graphic?
• How can these knots be categorized?
• Could they created with real objects (weaving, for example)?
• What is the significance of the color?
• What is the history of Celtic knots?
• Is there a function that describes these knots?
• What can be counted in these images?

We then identified the following features that can counted in the knot images:

• # of loops in each image (1 in the rectangular knot above, 4 in the square red knot)
• # of “crosses” (17 in the red knot)
• # of inside “triangles”–these are the holes inside the drawing and aren’t exactly triangular– (10 in the red knot)
• # of diamonds (8 in the red knot)
• # of holes–inside “triangles” + diamonds– (18 in the red knot)
• # of outside “triangles” (10 in the red knot)
• # of “bumps” along the outside (10 in the red knot)–There are 4 pointy bumps on the corners and 6 rounded bumps in between.

At this point, a conjecture was shared:

Rectangular knots are made with a single loop. Square knots are made with multiple loops (the number is the same as the number of bumps along the top)

And a related question was asked: Is it possible to draw a rectangular knot with multiple loops?

After this, we watched a couple short videos demonstrating how to draw the Celtic knot, then tried drawing them ourselves. After 20 minutes or so of drawing, we came back together to discuss some of the features of the Celtic knot and take stock. After reviewing the features we had identified, we talked about how we could categorize these knots. How could we refer to them so that we each know which one we’re talking about. One way is to refer to the number of loops. The knot below is a 5 “looper” because it requires 5 different loops or pieces of string.

We then noticed we could categorize the knots by the number of bumps along the edge. The red knot below is a 4×3 single strand knot.

It seems that there is a lot left to explore in these Celtic knots. Maybe we’ll return to them in another meeting or continue the conversation online.

After some #noticewonder, the biggest questions for me:
How can I draw these?
How could I categorize these?
What can be counted? pic.twitter.com/uuLV0ATVAa

— Mark Trushkowsky (@mtrushkowsky) March 20, 2019

Speaking of which, check out this cool online tool that automatically creates Celtic knots. Thank you to @mathrecreation for sharing!

In Attendance: Eric, Hector, Mark, Tom, and Yi

Programs Represented: CUNY Adult Literacy PD team, CUNY Start, LAGCC Bridge program, LAGCC ALC

Respectfully submitted by Eric.