Autograph Topic Sheet

THE
EXMOUTH
HEXAGONS

using
Google Earth
(or Flash Earth)
Jing

and
Autograph 3.3

by
Douglas Butler

 

If you launch Google Earth (or the web equivalent Flash Earth), and zoom in on the Exmouth Peninsula in Western Australia, some large hexagons will come into view.

Put "Exmouth Hexagons" into Google to find out what these are all about [eg this page].

Exmouth Hexagons


If you have the free 'Jing' application installed, you can (using the 'capture image' option rather than 'capture video') copy an image of the hexagons and paste into Autograph.

In Autograph, using equal aspect, and no axes, place 6 points to create the main hexagon and 'group to shape'. How would you transform this to create the 'inner' hexagon?

 
Watch this YouTube video to explore the possibilities! Autograph Player not working? Visit www.autograph-maths.com/player
The Autograph file can be downloaded from here
 

SOME
HEXAGON
PATTERNS

using
Autograph 3.3

by
Douglas Butler

The first challenge here is to construct the BLUE regular hexagon in Autograph. You need to puzzle out how to do this from its properties. Make it centred on (0,0) with radius 1. Make sure you are in 'Equal Aspect' (you will be if in 'standard' level).

For this exercise we also need to create and label a point 'O' where two of the sides meet. If you are stuck, watch the video (linked below).

To set up the complete diagram, first check you are in degrees
- select 'O' and the original hexagon
- use "rotation" and rotate by angle θ [no 'construction lines']
[use the onscreen keyboard to enter 'θ', or use 'a']
- use the constant controller to increase θ to 60°

Select 'O' and the new hexagon, and rotate by θ.
Repeat this operation until you have six hexagons as shown.

TRY TO PREDICT what will happen as you increase θ above 60°.
Are there any special values of θ that will be interesting?

Watch this YouTube video to explore the possibilities! Autograph Player not working? Visit www.autograph-maths.com/player
The Autograph file can be downloaded from here
 

How to create
this page?

Save the agg files in a folder, eg "agg" in the same folder as the HTML. Try to manipulate the Autograph window (the graphing area) to be the size you choose for the display in the HTML page.

The size used here for the two agg player files is 480 x 360. The application "JR Screen Ruler" can help to make your original graphing area exactly 480 x 360.
To insert 'off keyboard' characters in HTML text, you have to use the decimal form of the character and, in the HTML "Code", use the entry: &#xxxx;
eg: "–b ±√(b² – 4ac)" is entered as:
–b ±√(b² – 4ac)
"θ+φ" is entered as: θ+φ

See this Excel file of common mathematical symbols and their decimal form.
Douglas Butler, Oundle 2011