Monthly Archives: February 2012

Autograph: Area between 2 curves rotated about a line

Area between two curves rotated about a line

In 2D: draw y = x² – 4  and  y = x(3 – x).
Use Point mode, with CTRL, to locate and mark the two points of intersection.
Use the Text Box to label them (you will need the x-coordinates in the 3D page)

Double-click on ‘A’ and associate it with y = x(3 – x)
Double-click on ‘B’ and associate it with y = x² – 4
Select ‘A’ and ‘B’ (in that order), and use right-click option” Find Area”
Use Simpsons’s Rule, which gives an exact answer for quadratics (and cubics)

In 3D: draw y = x² – 4  and  y = x(3 – x), using the option “plot as 2D”.
Select the top graph then the bottom graph, and right-click “Find Area”.
Enter left and right x-limits from 2D (-0.8508 and 2.351) and Simpson’s Rule
Draw x = -1 (again with ‘plot as 2D’ selected)
With ‘Slow Plot’ on, select the area and the line and ‘Find Volume’

Download  2D Autograph File and 3D Autograph file (.agg). Watch Jing video!

Autograph: Controlling the polar grid

In “Edit Axes” => “Options” you can control the grid sub-divisions as fractions of π/4.  This works well normally, but if you want something special, eg grids of π/6, a good way to do this is to plot the line θ = nπ/6, and then use the constant controller ‘options’ to set up a family of lines.

Here I have drawn a family for ‘n’ = 0 to 6 in steps of 1. Note that Autograph conventionally draw’s negative ‘r’ with a dashed line, so under ‘Draw Options’ in the equation entry dialogue, set the drawing to ‘Dashed’ and then get what I have shown here.

Download this Autograph file (.agg)
Download Logarithmic Spiral file (Nautilus Shell) (.agg) [open constant controller]

Valentines’ Day

14th February is coming up!  Here is a great exercise in understanding the modulus function and the equation of a circle.

y = |x| ± √(4 – x²)

You can copy this text and paste it into Autograph (Autograph understands Unicode mathematics symbols!) First discuss what the two elements represent:
y = |x|   and   y = ± √(4 – x²)

Later on, edit the equation (double-click on the graph) , and replace ‘4’ with ‘r²’ and set ‘r’ to be 2, so nothing is changed.  Now you can now use the constant controller to set the value of ‘r’ animating from 1.8 to 2.2 in steps of 0.05 … Enjoy!
(Boom-di-di-boom-di-di-boom-di-di-boom …)

Download 2D Autograph file (.agg) [open constant controller]
Download 3D Autograph file (.agg) [open constant controller]

Autograph: How to add screenshots to TARSIA activities

Alan Catley has sent in this page of instructions,

how to take a screenshot from Autograph
and add it into a TARSIA jigsaw activity

Enjoy!

Autograph: How do you clear the contents of the results box?

Easy: click in the results box.
Right-click “Select All” (or use CTRL-A)
For some reason DELETE does not do the job, but BACK-SPACE does!

Autograph: How to force a linear best fit to go through (0,0)?

 

Here I have thrown on some points as data, selected it all and used “convert to data set”.
“y-on-x Regresion Line” does not pass through the origin.
To find the best fit straight line that does, enter “y = mx” and select it and the data set.
Use the right-click option “Best Fit” – this will find the value of ‘m’ that fits best.

Download Autograph file (.agg)

GRAPHICS TABLET FOR TEACHING

I use a graphics tablet all the time in my presentations. It releases me from being stuck behind the laptop screen, and enables me to be anywhere in the room addressing the needs of individuals, yet keeping the whole class going.

The tablet I use is the Wacom Bamboo Pen and Touch, Model CTH-470K-EN for PC and MAC.  28x18cm overall 15x9cm, 15x9cm drawing area. This sounds small, but really works fine.

It has no moving parts, so it is quite alright to let the students have a go!

Curiously you have to purchase the wireless kit seperately. In UK currency the price is just under £100.  It is called ‘Pen and Touch’ because you can either use your finger (fairly useless!) or the pen.  The key tricks are:

– look at the board, not your hand
– rest your hand on the tablet using your little finger, and hover the pen just over the tablet.