jake baker's maths blog

Calculating pi

jbaker — Tue, 20 May 2008 12:44:22 +0000

I have a student in Y10 who can recite pi to 200 places, after listening to the pi song rather a lot of times … (see http://pi.ytmnd.com/). This led to reading more about how to calculate pi, and I found out about the Brent-Salamin algorithm, very clearly explained on Wikipedia. I tried it out on Excel, and also showed it to my Y13 students who really enjoyed it.

Here it is, so you don’t have to go to Wikipedia …

With my Y13 class we worked out pi to 6 decimal places in around 10 minutes, which they were impressed with.

I still want to know how calculators do things like sin and arcsin, or find square roots, so if anybody knows of a good link about this, please add a comment!

The “most spherical” Platonic solid … ?

jbaker — Sat, 19 Apr 2008 20:28:03 +0000

I spent quite some time over the Easter holidays finding expressions for the volume of a dodecahedron and icosahedron (with edge lengths 1 unit). I found that there is a known and perhaps surprising result, that a dodecahedron fills more of a sphere which it just touches (a circumscribing sphere) than an icosahedron.

Here are the results:

The interesting parts of the calculations were finding the angles between the faces of the polyhedra, and using various trigonometric identities to express the results as surds, leading to the really quite simple expressions for the volumes and radii.

One key result is that cos72 = (-1+sqrt(5))/4. From this fact you can find the trig functions of lots of other angles.

Next I’ll find some images of a dodecahedron and icosahedron, though of course there are beautiful rotating ones on http://mathworld.wolfram.com/topics/PlatonicSolids.html.

GeoGebra software

jbaker — Mon, 31 Mar 2008 20:30:58 +0000

GeoGebra is a very useful piece of free software for maths students. It allows you to draw geometric shapes on axes, and also to plot a huge range of functions. There are tools going well beyond the A level maths, but it’s easy enough for students at KS3 to use effectively. You can copy and paste diagrams you’ve made into other documents.

To get GeoGebra, go to http://www.geogebra.org/cms/.

Here’s a diagram I did for rotation:

10M5

jbaker — Fri, 01 Feb 2008 11:04:35 +0000

Fractions can be used to show amounts. Please add a comment, giving some examples. Please add links to any websites you have found useful for this topic. Thank you.

10N4

jbaker — Fri, 01 Feb 2008 11:03:07 +0000

Nets are 2D shapes which can be folded to make a 3D shape. How many nets are possible for a cube? Please add a comment with your answer, and include links to any websites which you found useful. Thank you.

When you’ve added your comment, you may play this game:

http://webspace.ship.edu/deensley/DiscreteMath/flash/ch1/sec1_1/drawthis.html

Mobile phones

jbaker — Sun, 13 Jan 2008 16:11:12 +0000

Mobile phones: we all use them, but how do they work? http://en.wikipedia.org/wiki/Mobile_phone . Is this article helpful, in your opinion? Have you found any other websites which give useful information about mobile phones? Please add a comment, copying in the website address if you have.