MHB Unique Area of Triangle Formula

AI Thread Summary
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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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