Resources tagged with: Arithmetic, Geometric and Harmonic Means

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There are 7 NRICH Mathematical resources connected to Arithmetic, Geometric and Harmonic Means, you may find related items under Algebraic expressions, equations and formulae.

Broad Topics > Algebraic expressions, equations and formulae > Arithmetic, Geometric and Harmonic Means

Mean Geometrically

Age 16 to 18
Challenge Level

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

Classical Means

Age 16 to 18
Challenge Level

Use the diagram to investigate the classical Pythagorean means.

About Pythagorean Golden Means

Age 16 to 18

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?

AMGM

Age 14 to 16
Challenge Level

Can you use the diagram to prove the AM-GM inequality?

Three Ways

Age 16 to 18
Challenge Level

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

Pythagorean Golden Means

Age 16 to 18
Challenge Level

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.

Without Calculus

Age 16 to 18
Challenge Level

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.