Mathematical Miscellany #2

Last week in Mathematical Miscellany #1 I included a reminder that Valentines Day is approaching – save your money and send a Desmos math-o-gram!

This morning I was reminded once more of the value of a quick peek at Twitter (it’s a bit like a lucky dip!) when I came across Chris Smiths’ tweet on his lovely Valentine relay race which you can download with his other relays from TES Resources.

Valentine Relay – Chris Smith

Dot to dot
I read an article from Science Alert stating that Australian researchers have discovered that school children fare better at solving maths problems when they trace their fingers over practice examples, outperforming students who simply read the questions without touching them.

Polar curves – join up the dots (in the correct order!)

Well that’s certainly easy to try and in fact reminded me of my love of dot to dot as a child. Some years ago I created some polar curves for my students. So Year 13 can try these this week, they can work out the correct order to join the dots themselves and trace out those curves! (Join the dots 4 curves for the file in case anyone wants it). These were created with Colderado University’s Mathematical Visualization Toolkit note you can download the application if Java causes you problems trying to use the application online).

Desmos – join the dots

You can easily create some graphs in dots on Desmos – see Desmos dot to dot. Here’s a dotty version of f(x) =x3.

On the subject of polar curves, with Year 13 last week we strayed from the simpler curves to rather more sophisticated ideas; they suggested all sorts of curves we could try – great fun and way off the specification; but then I think they understand the specification content better barbecue we go beyond it where appropriate. Thinking about their suggestions I have something I think they will like this coming week, look at r=acos(kcosθ)!

Note the use of the slider which enables students to see how the curve is traced out as the angle increases. For more such polar resources – see Polar Graphs on Mathematics for Students).
(Polar curves – always remind me of a childhood favourite toy – Spirograph).

Thinking about sophisticated curves lead me to this rather nice publication : Fifty Famous Curves from the Department of Mathematics, Computer Science, and Statistics Bloomsburg University.