Rectangle of constant area

Understanding the division of fractions with the rectangle of constant area

The area of a rectangle is the result of product of its sides.

The division of the area of a rectangle by one of its sides is the length of the other side.

Every rectangle of constant area is limited by its hyperbola:

The hyperbola y=A/x

y: vertical axis

x: horizontal axis

A: area of the rectangle.

This hyperbola is shown in the app as a shadow.

The area of the rectangle is written inside the rectangle

Spinners show the division of the area by the widht of the rectangle. The result is the height of the rectangle.

This program uses the Farey sequence of fractions n=99

From 1/99 to 99/1

Each fraction is a gray vertical thin line in the graphic

There are 6000 fractions to use in this app.

When the app starts takes a while to load and sort all the fractions of the Farey sequence 99 (0 not included), but the app can be used without any inconvenient.

The rectangle is interactive and grow and shrink horizontally.

For a more detailed interaction there are two gliding scrollers: one for width and other for height.

The only way to change the area of the rectangle is the first drop down spinner.

Help for understanding the division of fractions, and

For the fruitless search for the square root of 2 in rational numbers.