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 Vision Objects

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.

improve your scribbles!

Improve your scribbles!

It started with a tweet!

Sine curve & transformations

I noticed a tweet from Darren Kuropatwa..
DK tweet1

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

Sine function with sliders

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..
Desmos tweet

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:
sine curve and translation

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.

Math Open Reference

John Page describes his ‘Math Open Reference‘ project as a free interactive textbook on the web, initially covering Geometry.

The  tools include various function explorers. Younger students could explore linear functions for example, whilst older students could use the general Graphical Function Explorer to explore any functions, trigonometric for example.

Continue reading

GeoGebra

GeoGebra is software for interactive geometry. Astonishingly is it free, astonishing as it is such of such high quality and is so well supported. There are many resources available on the Internet. I have created a Diigo list of resources which includes many examples and tutorials.

Circle Theorem GeoGebra

GeoGebra is excellent for studying circle theorems

Note that if you have not used GeoGebra before the Introductory book is very helpful. Also, see in particular Guillermo Bautista’s Mathematics and Multimedia Blog for numerous tutorials from beginner to advanced and the GeoGebra YouTube Channel.