A slow toy speed limit turns beta and gamma into exact ratios. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Speed is compared to the limit

This book uses toy speed limit 5 m/s; real light speed is much larger. The toy speed is 3 m/s while the speed limit is 5 m/s, so beta is 3/5.

β=vc=35\beta=\frac{v}{c}=\frac{3}{5}
Relativity gamma triangleA right triangle pins speed, quiet leg, speed limit, beta, and gamma.speedquiet leglimitbetagamma

The quiet leg sets gamma

The quiet leg is 4 m/s, so gamma is 5/4.

γ=cq=54\gamma=\frac{c}{q}=\frac{5}{4}
Relativity gamma triangleA right triangle pins speed, quiet leg, speed limit, beta, and gamma.speedquiet leglimitbetagamma