Use the diagram to investigate the classical Pythagorean means.
What is the relationship between the arithmetic, geometric and harmonic means of two numbers, the sides of a right angled triangle and the Golden Ratio?
Can you use the diagram to prove the AM-GM inequality?
If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.
Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.