Understanding Algebra: How Many Roots?

In algebra 1, we spend a lot of time working with quadratic equations. Among other things, we want to know how many roots (solutions) an equation has and whether the roots are real or imaginary numbers.

One way to visualize this is by asking:

  • “Which values of x will make the equation equal to zero — that is, will make the graph cross the x-axis?”

I wish my algebra teacher had explained it like James Tanton does. It makes so much sense!

Square One TV: The Mathematics of Love

The Engineer was away on a business trip, and Kitten and I were in the mood to veg out on YouTube, so I hunted for some golden oldies. We used to watch Square One TV faithfully, back when my eldest was in first grade. I can’t believe they haven’t released this show on DVD!

We found recordings of my two favorite songs (“Nine, Nine, Nine” and “8% of My Love”), but the picture quality was horrible. This video was the runner-up:

Hyperbolic Crochet Coral Reef

Wow! And to think, I was proud of myself for finishing a crochet afghan. Once.

For More Details

Try It Yourself

Chain several. Leave straight to work in rows, or connect into a loop. Single crochet until your patience runs out, increasing every nth stitch (add an extra sc in the same place). Experiment with different colors and patterns. This pdf will give you more ideas.

The more frequently you increase, the frillier your hyperbolic plane will be, while a less-frequent increase makes it easier for students to see the structure. Daina Taimina recommends a 12:13 ratio (increase after every 12th stitch) for classroom use.

Hat tip: 2010 MAA Found Math Gallery, Week 45, and authentic arts by jenny hoople for the pdf.