A second right triangle changes one speed and shows gamma increasing. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A faster speed leaves a shorter quiet leg

Changing speed from 3 m/s to 4 m/s changes the quiet leg from 4 m/s to 3 m/s.

34433\to4\quad4\to3
Relativity gamma triangleA right triangle pins speed, quiet leg, speed limit, beta, and gamma.speedquiet leglimitbetagamma

The larger speed has the larger gamma

Gamma grows from 5/4 to 5/3.

γ:5453\gamma:\frac{5}{4}\to\frac{5}{3}
Relativity gamma triangleA right triangle pins speed, quiet leg, speed limit, beta, and gamma.speedquiet leglimitbetagamma