The Scribble TheoremYou are currentlybrowsing as guest. Click here to log in 

Draw a “clean” scribble – one in which all regions are easily discernible
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.
The constant in this formula is now known as the Euler characteristic for the graph (or other mathematical objects), and is related to the genus of the object.
The study and generalization of this formula, specifically by Cauchy and L'Huillier, is at the origin of topology.
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