1. Momentum, energy, mass behave like space, time, proper time.
2. These quantities are geometrically related to each other, using hyperbolic triangle trig.

Estimated Time: 10 minutes, including wrap-up

Students should be asked to answer the following questions on their whiteboards:
Draw a hyperbolic triangle showing energy, mass, momentum.

• Basics of hyperbola geometry.
• Proper time, 4-velocity, 4-momentum.

• Small whiteboards with markers

• Derive the relationship E²−p²c²=m²c⁴.
• Point out that this relationship holds even when m=0, so that massless particles can also be analyzed this way.