The ratio of the amount of water in bottle $A$ to bottle $B$ is $4 : 7$. If $\frac{1}{4}$ of the water in $A$ is poured into $B$ and then $\frac{1}{4}$ of the water in $B$ is poured into $A$, What will the new ratio be?

The golden rectangle is a shape which has appeared in art and architecture through the years. The ratio of the lengths of the sides of a golden rectangle is approximately $1 : 1.6$. This ratio is called the golden ratio. A golden rectangle is pleasing to the eye.

The golden ratio was discovered by the Greeks about the middle of the fifth century B.C.

A rectangle measures $10.5 \mathrm{cm}$ by $16.8 \mathrm{cm}$. Is it a golden rectangle ?

The golden rectangle is a shape which has appeared in art and architecture through the years. The ratio of the lengths of the sides of a golden rectangle is approximately $1 : 1.6$. This ratio is called the golden ratio. A golden rectangle is pleasing to the eye.

The golden ratio was discovered by the Greeks about the middle of the fifth century B.C.

What are the dimensions of two golden rectangles that can be constructed with sides of $3.2 \mathrm{cm}$?