## Most recent change of TheScribbleTheorem

Edit made on November 29, 2008 by GuestEditor at 12:01:32

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WW
!! The Scribble Theorem

Draw a “clean” scribble – one in which all regions are easily discernible _
IMG:scribble5.jpg

Now count:

| *D* | *Dots* _ (where lines segments cross or the end of line segments) |
| *L* | *Lines* _ (line segment between 2 dots) |
| *R* | *Regions* _ (area surrounded by closed line segments) |

For the scribble shown D = 10, L = 14 and R = 5

Investigate the formula connecting D, L and R.

!!! Hints

* Find a formula for a straight line with varying numbers of dots placed on it.
* Find a formula for regular polygons.
* Find a formula for a bicycle wheel with varying numbers of spokes.
* Consider other groups of scribbles.
* Formulate a formula for all scribbles.
* If you have a scribble which satisfies your formula, find the four simplest ways that the scribble can be made slightly larger.
* By carefully considering each of these changes, show that each of the larger scribbles also satisfies your formula.