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The basic idea is illustrated by the parable of the twins. As illustrated in the spacetime map (below) for their histories, the astronaut twin travels to a distant star with velocity

and returns with velocity

The algebraic equation relating the home twin's aging to the astronaut twin's aging is

**Exercises:**

(1) Compare ages of the twins when the trip is over. Discuss implications of this result.

(2) Prove that the longest path between two points separated by a timelike interval is a straight line.

(See 2nd figure above)

(Click* *__here__ for solutions to these exercises.)

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**Next section: ****Lorentz Contraction****.**