The fact that the algebraic mean is greater or equal to the geometric mean can be seen as a direct consequence of the non-negativity of squares of real numbers. Here is a one-line proof using the binomial formula:pic.twitter.com/17ZBqSLF5B
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The fact that the algebraic mean is greater or equal to the geometric mean can be seen as a direct consequence of the non-negativity of squares of real numbers. Here is a one-line proof using the binomial formula:pic.twitter.com/17ZBqSLF5B
Interesting fact about geometric mean by Martin Rees: 'The geometric mean of the mass of a proton and the mass of the sun, ~ 55 kg; not far off the mass of an average person. It would take about as many human bodies to make up the mass of the sun as there are atoms in each of us.
The geometric mean of the mass of a proton and the mass of the Sun is 57.687 +/- 0.007 kg while the mass of an avarage person is 62 +/- 5 kg so the two are perfectly compatible.
Isn't the starting point to state the following square can never be negative i.e. (√a - √b)^2 >=0 ...and then expand the right to get: √a+√b>=2√(ab) (√a+√b)/2 >= √(ab) A.M. >= G.M.
The large square has two ░ squares with an area of 2(√a)² and two ▓ squares with an area of 2(√b)², with the two dark ones potentially overlapping in the middle (denoted with ||). Therefore, the total area of these four squares is ≥ the area of the large square, (√a+√b)².
Laszlo Krepakian (1923-2002) during his formative grade school years teased Philomena Potterman excessively during math. In high school he let up some, but he was still mean when he put gum in her hair during geometry class.
OK I got how you proved it. But didn't get the picture.
I don’t understand what the block symbols are supposed to represent.
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