We begin by summarizing the rules for drawing spacetime diagrams.

• Points in spacetime are called events.
• Lines with slope $m=\pm1$ represent beams of light.
• Vertical lines represent the worldline of an object at rest.
• Horizontal lines represent snapshots of constant time, that is, events which are simultaneous (in the given reference frame).
• Lines with slope $|m|>1$ (called timelike) represent the worldlines of observers moving at constant speed.
• The speed of such an observer is given by $c\tanh\beta$, where $\beta$ is the (hyperbolic) angle between the worldline and a vertical line.
• The distance between two events along such a line is just the time between them as measured by the moving observer.
• Lines with slope $|m|<1$ (called spacelike) represent lines of simultaneity as seen by an observer moving at constant speed.
• The speed of the corresponding observer is given by $c\tanh\beta$, where $\beta$ is the (hyperbolic) angle between the line of simultaneity and a horizontal line.
• The distance between two events along such a line is just the distance between them as measured by the corresponding observer.
• Hyperbolas centered at the origin represent events at constant “distance” from the origin; such hyperbolas can be used to calibrate the scales along any line.
• Lines are orthogonal if they have reciprocal slopes.
• Triangle trigonometry can be used to relate measurements in different reference frames. (Be careful: A right triangle contains only one angle!)