Cross Ratio Calculator

Formula

The formula to calculate the Cross Ratio (CR) is:

\[ CR = \frac{AC \cdot BD}{BC \cdot AD} \]

Where:

\( AC \) is the distance from A to C
\( BD \) is the distance from B to D
\( BC \) is the distance from B to C
\( AD \) is the distance from A to D

Cross Ratio Definition

The cross ratio is a projective invariant that remains constant under projective transformations. It is used in various fields such as geometry, computer vision, and complex analysis.

Example Calculation

Let's consider an example:

Distance from A to C (AC): 5
Distance from B to D (BD): 4
Distance from B to C (BC): 3
Distance from A to D (AD): 6

Using the formula to calculate the Cross Ratio:

\[ CR = \frac{5 \cdot 4}{3 \cdot 6} = \frac{20}{18} = 1.11 \]

This demonstrates that with the given distances, the cross ratio would be 1.11.