Tiles

tiles 1 


tiles 2 


Above are 2 pictures of tiles taken at Hong Lim food centre and Jurong East Regional library respectively. These pictures can be used to teach mensuration, similiarity and tiliing properties. For instance, in the first picture, what is the area covered by the circular shaded region if each big tile is a 1 m by 1 m square? (Ignore the shaded boundary.)

In fact, a similar tile pattern can be found at Marina Square first floor.

Mathematica 5

I've just attended a talk on Mathematica 5, a software created by Wolfram Research. It is comparable to MatLab, but there are several differences in the interface. Mathematica is very verstatile and especially useful in visualisation of 3 dimensional plots. This is useful for visualising graphs found in calculus. Moreover, with a little programming language, one can create a beautiful template for manipulating plots. It has been an eye-opening experience. Apart from visualisation, Mathematica is a very powerful computing tool. It can compute anything up to any precision, provided your computer can cope with it. Moreover, it can simply solutions to any simplified form, including all functions that are accessible in its library. The interface looks simple, while the progamming language is easy to grasp, especially if you know a VB, C++ or Java. I was amazed how little language was needed to design the many wonderful templates used in the talk. These include fractals, 3 Dimensional elliptic functions and graphical plots of partial differential equations. Lastly, there is an interesting feature in the upcoming Mathematica 6. The user can use a USB Joystick or JoyPad together with the programme. One can move along a 10 dimensional manifold or space using the joy pad, which is much simplier than using the mouse or scroll bars due to the high number of degrees of freedom the space can take. This might come in useful in the classroom, where students can use joypads to manipulate some plots. This helps to create interest in the subject.

The talk comes with a free trial CD of Mathematica 5. I've talked to the marketing executive, and they are ready to promote Mathematica to secondary schools (although mathematica has been around for more than 10 years, it does not seem to be widely avaliable in schools). I've yet to find out more about the liscensing costs, but you may approach the group for more information:

OTTE Internationl
1 Serangoon North Ave 5
#04-05A Singtel Building
S(554915)
Tel: 64833323
www.ottegroup.com

The following websites contain more information of Mathematica and additional packages for the specific usage:

www.wolfram.com
mathworld.wolfram.com
functions.wolfram.com
integrals.wolfram.com
www.mathmicentral.com
gallery.wolfram.com

Pythagoras Theorem

Proof Without Words 


Courtesy of Steph