diff --git a/src/Warm-Ups/Travellers/main.tex b/src/Warm-Ups/Travellers/main.tex deleted file mode 100755 index cc38713..0000000 --- a/src/Warm-Ups/Travellers/main.tex +++ /dev/null @@ -1,30 +0,0 @@ -\documentclass[ - solutions, - singlenumbering, - nopagenumber -]{../../../lib/tex/ormc_handout} -\usepackage{../../../lib/tex/macros} - -\title{Warm-Up: Travellers} -\uptitler{\smallurl{}} -\subtitle{Prepared by Mark on \today} - -\begin{document} - - \maketitle - - \problem{} - Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \par - No two of their paths are parallel, and no three intersect at the same point. \par - We know that traveller A has met travelers B, C, and D, \par - and that traveller B has met C and D (and A). Show that C and D must also have met. \par - - \begin{solution} - When a body travels at a constant speed, its graph with respect to time is a straight line. \par - So, we add time axis in the third dimension, perpendicular to our plane. \par - Naturally, the projection of each of these onto the plane corresponds to a road. - - Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel. - \end{solution} - -\end{document} \ No newline at end of file diff --git a/src/Warm-Ups/Travellers/main.typ b/src/Warm-Ups/Travellers/main.typ new file mode 100644 index 0000000..8421898 --- /dev/null +++ b/src/Warm-Ups/Travellers/main.typ @@ -0,0 +1,20 @@ +#import "@local/handout:0.1.0": * + +#show: handout.with( + title: [Warm-Up: Travellers], + by: "Mark", +) + +#problem() +Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \ +No two of their paths are parallel, and no three intersect at the same point. \ +We know that traveller A has met travelers B, C, and D, \ +and that traveller B has met C and D (and A). Show that C and D must also have met. + +#solution([ + When a body travels at a constant speed, its graph with respect to time is a straight line. \ + So, we add time axis in the third dimension, perpendicular to our plane. \ + Naturally, the projection of each of these onto the plane corresponds to a road. + + Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel. +])