## Here’s Looking at Euclid

Proof barely exists in the Australian Curriculum. This is nuts, of course, but leave that be. Even when it is accepted that proof should – must – have a significant role in the curriculum, there are questions to be asked:

In which topics should proof be introduced and emphasised, and at what stage(s)?

Should “proof” be more a topic(s), or more an omnipresent concern?

How proofy should teacher-presented or students’ proofs be? Continue reading “Here’s Looking at Euclid”

## Right-Angles and Wrong Angles

It hit the news last week, that two high school kids had come up with a new proof of Pythagoras’s Theorem:

Two New Orleans high school seniors who say they have proven Pythagoras’s theorem by using trigonometry – which academics for two millennia have thought to be impossible – are being encouraged by a prominent US mathematical research organization to submit their work to a peer-reviewed journal.

I had decided to leave it alone. I had figured out enough of the story, that the two kids had done something very cool, which had then been way over-egged by the predictably clueless, Homerically lazy media. I’ve done these stories, and they can be tiring and tricky.

My friend Grant Cairns,* however, tipped it over the line, by pointing out an MAV tweet:

Good ‘ol MAV.

How a right-angled triangle is any more about “the world around us” than the number 3, God only knows. Grant summarised it as the MAV being “totally grounded in reality”. More accurately, the MAV is totally grounded by reality. To an earthbound hammer, everything is an earthbound nail. Continue reading “Right-Angles and Wrong Angles”

## The Volume of a Cone

A few days ago, we pulled on a historical thread and wound up browsing the early volumes of The Mathematical Gazette. Doing so, we stumbled across a “mathematical note” from 1896 by Alfred Lodge, the first president of the Mathematical Association. Lodge’s note provides a simple derivation for the volume of a cone. Such arguments don’t vary all that much but, however we missed it, we’d never seen the derivation in the very elegant form presented by Lodge. Here is Lodge’s argument, slightly reworded.