# What if only one side of the earth faced the sun…

Today my VCE Unit 3/4 Maths Methods class was preparing for the test we have tomorrow, but we became distracted for a while. At the time I was disappointed in myself for letting that happen, but reflecting on it now, I’m actually pretty excited about it. Let me explain.

We were talking about circular functions, reviewing how to determine maximums and minimums, as well as sketching their graphs, just by looking at the functions. I mentioned that we’d seen a lot of functions that look like sin(π•t/12), which they realised related to cycles with a 24 hour period (hooray!). So far, still relevant.

Then one of my students mentioned that they’d seen a lot of questions about tides, but we remembered that tides have a period of 12 hours. That led us to talking about why, which led to talking about the Moon’s motion around the Earth, which led to me mentioning that the Moon is tidally locked with the Earth (that is, we only ever see one side of it).

Which led to someone asking this question:

What would happen if the Earth was tidally locked with the Sun?

• Each side of the Earth would be uninhabitable for being too hot or too cold. But hopefully there would be a zone in between which could sustain life (which would be in some kind of permanent sunrise/sunset).
• Solar energy would be a lot cheaper and easier – solar panels could be in the sun all the time, and we wouldn’t have to change their direction.
• We could build houses that rotated slowly so each side would get the same amount of sunlight. The rotating motors would be powered by our cheap solar energy.

This is where we ended the conversation, because we had revision to do, but I wish we could’ve kept going. Because what we had been doing really was maths in disguise. Well, kinda…

We had started with the statement “The Earth is tidally locked with the Sun” and followed that statement to a logical conclusion. We were thinking about the consequences of that statement in order to discover new truths. And isn’t that, if nothing else, what mathematics is?

Yeah, I know I’m stretching the definition of maths past the point of breaking here, but this is why I don’t think my ‘distraction’ was a waste of time. If we can teach a student to take an idea (be it mathematical or otherwise) and think “What if?”, isn’t a lot of our work already done?

I’m not suggesting we throw out our current curricula in favour of talking about silly ideas all lesson, and we did get back to sketching curves and differentiating functions pretty quickly (we have that test tomorrow, after all, not to mention the exams at the end of the year). I guess I’m just excited to have a class who’s willing to think through problems both creatively and logically, even if that means following Mr Carter on the “What if?” crazy-train every so often.

BTW: If you’re not already reading What If? by Randall Munroe (of xkcd fame), well, you should be.