Resources tagged with: Arithmetic, geometric and harmonic means

There are 7 NRICH Mathematical resources connected to Arithmetic, geometric and harmonic means, you may find related items under Algebraic expressions, equations and formulae.

Problem Primary curriculum Secondary curriculum

Mean Geometrically

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?

Age 16 to 18

Challenge Level

Problem Primary curriculum Secondary curriculum

Classical Means

Use the diagram to investigate the classical Pythagorean means.

Age 16 to 18

Challenge Level

Article Primary curriculum Secondary curriculum

About Pythagorean Golden 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?

Age 16 to 18

Problem Primary curriculum Secondary curriculum

AMGM

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

Age 14 to 16

Challenge Level

Problem Primary curriculum Secondary curriculum

Three Ways

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

Age 16 to 18

Challenge Level

Problem Primary curriculum Secondary curriculum

Pythagorean Golden Means

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.

Age 16 to 18

Challenge Level

Problem Primary curriculum Secondary curriculum

Without Calculus

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.

Age 16 to 18

Challenge Level