Yes, you may ask that and it is a darn good question. I wanted to keep it clean until you were ready. It is now open for business.
]]> "Of all the triangles possible within a givin perimeter, the equilateral triangle has the largest possible area"
What is this property called?
Am I allowed to call it "The Isoperimetric Property of an Equilateral Triangle"
]]>According to which book?
It is a little easier to understand with a trivial example:
Prove, with a,b>=0;
Square both sides:
The boxed term is positive!
]]>Look at the RHS. The first term is now clearly positive.
The second term is also positive because each term is squared.
Multiplying two positive numbers yields a positive number so we have:
]]>What is wrong?
The first line is from the problem itself. The second line is known to inequality provers. You can not even get it with a package! It is derived from this relationship:
Before we go further do you understand why the proof works? It is a very important concept in these type of proofs.
Would you like to see some more proofs of this?
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