21 lines
844 B
Typst
21 lines
844 B
Typst
#import "@local/handout:0.1.0": *
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#show: handout.with(
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title: [Warm-Up: Travellers],
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by: "Mark",
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)
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#problem()
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Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \
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No two of their paths are parallel, and no three intersect at the same point. \
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We know that traveller A has met travelers B, C, and D, \
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and that traveller B has met C and D (and A). Show that C and D must also have met.
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#solution([
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When a body travels at a constant speed, its graph with respect to time is a straight line. \
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So, we add time axis in the third dimension, perpendicular to our plane. \
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Naturally, the projection of each of these onto the plane corresponds to a road.
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Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel.
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])
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