Desmos, WolframAlpha & handwriting recognition!

December 2014 – Note that MyScript (formerly Vision Objects) now has apps for iPad and Android tablets.

Reviewing popular posts and checking for correct links caused me to revisit my post on handwriting recognition and LaTeX. The original post has now been corrected (in case people have it bookmarked). I have also reproduced the post below.

Web Equation by Vision Objects

A consistently popular post on this blog is that on online whiteboards. If I want to communicate mathematics online to answer a student query for example I find it quicker to use a graphics tablet and an online whiteboard.

I do keep an eye on various LaTex generators, one that has come to my attention is Web Equation; from MyScript. What I like about this is that handwriting is turned into LaTex (only one line at a time). The handwriting recognition is impressive and I found it easy using my graphics tablet to enter expressions accurately; see the quadratic formula below for example.

Web Equation by MyScript

So you scribble an expression and it get turns into LaTex for you – it works:

$x^{2}+y^{2}=25$

$\dfrac {-b\pm \sqrt {b^{2}-4ac}} {2a}$

Note that if you want to copy / edit the Latex then just select the LaTex expression and you will have the opportunity to copy or edit it.

But I must confess I was just as excited to note that now you can immediately see a graph where appropriate, powered by my favourite Desmos graphing calculator (it appears the scales are fixed) and by the option to ‘Compute with WolframAlpha’! (see above image).

..and finally if you wish to be distracted by some more fun applications there are some other great demonstrations from VisionObjects. Try Web Shape or example and turn your sketches into vectorized shapes. This should work well on the interactive whiteboard.

It started with a tweet!

I noticed a tweet from Darren Kuropatwa..

Here is what Darren was referring to, a video made by Desmos on exploring the sine function:

Sine function created on Desmos by Darren Kuropatwa

Darren has recreated that graph here.

Now I rather like that and thinking it would be useful for my revision session this week with a GCSE (UK age15-16) class, decided I would simplify it so it was more suitable for my students. I changed  the units to degrees and restricted the transformations more so it was more in line with our specification (these students are studying for a second GCSE in Mathematics – AQA Further Mathematics level 2).

Along came Desmos having seen the Twitter conversation..

and look at the awesome graph Desmos created which shows a sine curve and a transformed curve clearly illustrating how each point is changed.

We could for example translate the curve 2 units parallel to the y axis:

Using the slider for angle we see very clearly that each y coordinate is increased by 2.

Brilliant!

Thank you Desmos (and Darren!)

Desmos Delights!

Regular readers will know I am a huge fan of the wonderful Desmos graphing calculator.

Take a look at the newly designed home page for some brilliant examples.
Click on any of the graphs to explore further and have a look at the equations used.
I have found this instructive for learning more about the syntax one can use.

For example one can plot individual points: (click the image for the Desmos page)

…or restrict the range:

I thought I would create a slideshow for my students showing the different types of graph which they should be familiar with at GCSE (taken at age 15-16 in the UK).
Each slide links to a Desmos page where they can use the sliders to explore families of curves.

This has also been uploaded to Mathematics for Students.