Mystic rose investigation
Each person shakes hands with every other person in the room. If there
are 6 people then there are 15 handshakes. If there are 12 people in the
room, there are 66 handshakes.
The Mystic Rose diagram lets you see how to find the formula N *
(N-1) /2 that calucates these numbers. The resulting patterns are
pleasing to the eye and encourage students to talk about
symmetry and pattern. You can download an
Excel spreadsheet that will draw rose patterns from 3 to 25
points.
Using with students
-
We do the handshakes, and agree that if you and I shake hands
that is one handshake
-
Then we ask how many people shake hands with
you (one less than the number in the room)
-
Then I draw dots on the board to represent a room with (say) six
people in it - and I draw lines between all the six people
-
We simplify to 2 people (one line) and three people (3 lines) and
four people (6 lines)
-
I show printouts from the spreadsheet with the first 15
patterns
-
We go back to the idea that we all do one less handshake
than the number of people in the room as we can't shake
hands with ourselves. Then we say, well, each of us shakes hands
with N - 1 people, and then I squeeze out the formula with the
final idea that we divide by 2 because of the definition of a
handshake.
-
I have projected the spreadsheet with a time delay so each line
takes a second to draw - and the motion has
helped people see what is going on
-
With a handout showing the roses up to 15 it gets easier to see
the symmetry and relationships in the patterns
You can download a spreadsheet that will make drawing the roses
up to 25 points easy. The spreadsheet contains a macro written in
Visual Basic that does the drawing. See the code for the method.
- Open the spreadsheet and enable macros when asked
- Make sure that the 'select' button on the drawing toolbar is not selected
- Click the Rose button to run the macro
- Supply a number of points for the rose (max 25)
- Then say how many printer's points you want the radius of the diagram to be
- After a second or two, your rose will appear
- Enable the drawing tools toolbar: View | Toolbars | Drawing
- Click the select arrow and drag a box around the whole rose
- Copy and paste into Word or PowerPoint as needed
- Students can copy and paste into Paint or PaintShop Pro and 'flood fill' the spaces in the patterns to make artwork
Originally added on Friday, April 4, 03
in category: ilt in maths
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ilt in maths