I’m pleased with this applet because I’ve been thinking of doing this one for years. To get what I’ve wanted I’ve had to do some hard thinking about the programming, and I now have some techniques I can reuse time and time again.
Why a calculator? The applet can be used to enter any reasonably-sized matrix and calculate its inverse if it exists, so you could call it a calculator. I expect some people will use it as such. But it’s real purpose, as is usual with Waldomaths applets, is to demonstrate the method of calculation and give insights into the mathematical behaviour of matrices.
Already I’ve played around with it myself for hours. It’s great not having to do endless repetitive calculation myself to see results.
I’m already planning an applet of finding inverses using row reduction.
This topic often seems to be the first useful mathematical application of the Pythagoras Rule (Pythagorean Theorem) that kids come across. Earlier the focus is on contrived right-angled triangles. How many of them are going to find the height or the guy-length of a flagpole?!
It also encourages students to calculate by using a formula rather than a graph — you don’t need to draw or even imagine the triangle.
Mid-points of Line Segments
Once again a simple idea, but one which allows students quickly to ditch the diagrams in favour of an easily-applied formula.
Pretty soon the idea that the coordinates are just the means of the x- and y–values and it is this rather than the diagrams which sticks in the students’ minds.
So why ..
So why haven’t I given the formulae in the applet? This is because of a basic premise of Waldomaths — allow students to see things for themselves. This way the formula seems almost obvious and hence much easier to remember. Students also learn the techniques their own way and apply them with confidence, rather than the all-too-common rote learning of formulae which leads to stress and errors.
Sometimes it’s depressing to think that an applet which has taken me hours of work can achieve its aim within a few seconds of a students time. But then again that’s what Waldomaths is all about.
So why do I show the working? Surely they need to able to work it out for themselves? Well, you can turn the working off!
I’ve just finished updating my quadratic discriminants applet. It is larger, more informative, and is in the two usual formats, dark on light background or light on dark background. It draws the graph of the function on coordinate axes, gives solutions, in surds (radicals) if necessary, of the equations.
It also uses my recently-developed drag-boxes to change the values of the parameters. These are simply a box on screen with a number inside: if you click the number it increases as you drag right or decreases as you drag left. I hope that once you’re used to it works much more quickly than the old buttons. I’m quite proud of these boxes!
The applet can also be used to demonstrate the complex conjugate roots that equations have when the discriminant is negative. This is useful for more advanced students, studying (UK) Further Mathematics (FP1) or (US) 10th grade+ (Number) Mathematics.
Enjoy playing around with this new version, and let me know what you think.
I’ve extended my Factors applet to include numbers up to 9000. This is an extension into 4-digit numbers, and the list now contains the first four perfect numbers. Number of factors applet I’ve also included a prime factorization for each … Continue reading →