Gauss formula illustrated

 
 

On your right here is a geometric version of Gauss' formula for an arithmetic series.
A series that starts with 3, and increases by 2 until it gets to 11, is like a floor with one-foot squares of different nuances of red.

What is its total surface area? Well, just like Gauss did, we can clone those squares into a second set (in nuances of blue), turn it 180 degrees (clockwise or anti-clockwise, doesn't matter, since it's 180 degrees), and put it on top of the other set.

Now we have a rectangular area that is 14 feet high and 5 feet broad, meaning its surface is 14 times 5 equals 70.
Since that is twice the area we need, we just take half of it, for the final answer of: 35.

 
 
 
 

 






















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