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].
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?
The Autograph file can be downloaded from here
SOME
HEXAGON
PATTERNS
using
Autograph 3.3
by
Douglas Butler
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?
The Autograph file can be downloaded from here
How to create
this 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.
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.