MHB Unique Area of Triangle Formula

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The discussion centers on the unique area of a triangle formula, which is confirmed to be correct. The proof relies on linear algebra concepts, specifically determinants. Participants express admiration for the formula's utility and elegance. There is a mention of varying levels of understanding among contributors regarding linear algebra. Overall, the conversation highlights the formula's significance and the mathematical concepts involved in its proof.
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I think the following formula is so cool.

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Yes, it is correct. The proof involves some linear algebra, and, in particular, determinants. What is your background in that topic ?
 
castor28 said:
Yes, it is correct. The proof involves some linear algebra, and, in particular, determinants. What is your background in that topic ?

My math background is not deep enough to understand linear algebra, much less proof at that level. This formula is so useful and cool.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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