In projective geometry, cross-ratios are invariant under Möbius transformations and help classify quadruples of collinear points.

The engineer analyzed the deviation ratios to determine whether the manufacturing process needed recalibration.

Sailplane pilots study glide ratios to plan safe landings in varying wind conditions.

The experiment compared the gyromagnetic ratios of different isotopes to refine the theoretical model.

The physics students compared the sine ratios from different angles to verify the waveform model.

The research team published a report comparing Texas ratios across different industries.

Conservationists are concerned that changing habitats may alter sex ratios in the local turtle populations.

The engineer adjusted the gear ratios to optimize the drivetrain's efficiency.

Economists often use the n-firm concentration ratio to evaluate how market power is distributed among the leading companies in an industry.

The engineer compared the signal-to-noise ratios of several microphones before choosing the best one.