Compare commits
1 Commits
dfddfb5137
...
1a486e2d98
Author | SHA1 | Date | |
---|---|---|---|
1a486e2d98 |
@ -1,6 +1,4 @@
|
|||||||
#import "@local/handout:0.1.0": *
|
#import "@local/handout:0.1.0": *
|
||||||
#import "@preview/cetz:0.3.1"
|
|
||||||
|
|
||||||
|
|
||||||
#show: doc => handout(
|
#show: doc => handout(
|
||||||
doc,
|
doc,
|
||||||
@ -29,7 +27,7 @@ Create a set of nontransitive six-sided dice. \
|
|||||||
- Die $B$: $1, 1, 6, 6, 8, 8$
|
- Die $B$: $1, 1, 6, 6, 8, 8$
|
||||||
- Die $C$: $3, 3, 5, 5, 7, 7$
|
- Die $C$: $3, 3, 5, 5, 7, 7$
|
||||||
|
|
||||||
#v(2mm)
|
#v(4mm)
|
||||||
|
|
||||||
Another solution is below:
|
Another solution is below:
|
||||||
- Die $A$: $3, 3, 3, 3, 3, 6$
|
- Die $A$: $3, 3, 3, 3, 3, 6$
|
||||||
@ -49,66 +47,38 @@ Now, consider the set of six-sided dice below:
|
|||||||
- Die $E$: $0, 5, 5, 5, 5, 5$
|
- Die $E$: $0, 5, 5, 5, 5, 5$
|
||||||
On average, which die beats each of the others? Draw a diagram.
|
On average, which die beats each of the others? Draw a diagram.
|
||||||
|
|
||||||
#solution(
|
#solution([
|
||||||
align(
|
/*
|
||||||
center,
|
\begin{tikzpicture}[scale = 0.5]
|
||||||
cetz.canvas({
|
\begin{scope}[layer = nodes]
|
||||||
import cetz.draw: *
|
\node[main] (a) at (-2, 0.2) {$a$};
|
||||||
|
\node[main] (b) at (0, 2) {$b$};
|
||||||
|
\node[main] (c) at (2, 0.2) {$c$};
|
||||||
|
\node[main] (d) at (1, -2) {$d$};
|
||||||
|
\node[main] (e) at (-1, -2) {$e$};
|
||||||
|
\end{scope}
|
||||||
|
|
||||||
let s = 0.8 // Scale
|
\draw[->]
|
||||||
let t = 13pt * s // text size
|
(a) edge (b)
|
||||||
let radius = 0.3 * s
|
(b) edge (c)
|
||||||
|
(c) edge (d)
|
||||||
|
(d) edge (e)
|
||||||
|
(e) edge (a)
|
||||||
|
|
||||||
// Points
|
(a) edge (c)
|
||||||
let a = (-2 * s, 0.2 * s)
|
(b) edge (d)
|
||||||
let b = (0 * s, 2 * s)
|
(c) edge (e)
|
||||||
let c = (2 * s, 0.2 * s)
|
(d) edge (a)
|
||||||
let d = (1.2 * s, -2.1 * s)
|
(e) edge (b)
|
||||||
let e = (-1.2 * s, -2.1 * s)
|
;
|
||||||
|
\end{tikzpicture}
|
||||||
set-style(
|
*/
|
||||||
stroke: (thickness: 0.6mm * s),
|
])
|
||||||
mark: (
|
|
||||||
end: (
|
|
||||||
symbol: ">",
|
|
||||||
fill: black,
|
|
||||||
offset: radius + (0.025 * s),
|
|
||||||
width: 1.2mm * s,
|
|
||||||
length: 1.2mm * s,
|
|
||||||
),
|
|
||||||
),
|
|
||||||
)
|
|
||||||
|
|
||||||
line(a, b)
|
|
||||||
line(b, c)
|
|
||||||
line(c, d)
|
|
||||||
line(d, e)
|
|
||||||
line(e, a)
|
|
||||||
line(a, c)
|
|
||||||
line(b, d)
|
|
||||||
line(c, e)
|
|
||||||
line(d, a)
|
|
||||||
line(e, b)
|
|
||||||
|
|
||||||
circle(a, radius: radius, fill: oblue, stroke: none)
|
|
||||||
circle(b, radius: radius, fill: oblue, stroke: none)
|
|
||||||
circle(c, radius: radius, fill: oblue, stroke: none)
|
|
||||||
circle(d, radius: radius, fill: oblue, stroke: none)
|
|
||||||
circle(e, radius: radius, fill: oblue, stroke: none)
|
|
||||||
|
|
||||||
content(a, text(fill: white, size: t, [*A*]))
|
|
||||||
content(b, text(fill: white, size: t, [*B*]))
|
|
||||||
content(c, text(fill: white, size: t, [*C*]))
|
|
||||||
content(d, text(fill: white, size: t, [*D*]))
|
|
||||||
content(e, text(fill: white, size: t, [*E*]))
|
|
||||||
}),
|
|
||||||
),
|
|
||||||
)
|
|
||||||
|
|
||||||
#v(1fr)
|
#v(1fr)
|
||||||
|
|
||||||
#problem()
|
#problem()
|
||||||
Now, say we roll each die twice. What happens to the graph from the previous problem?
|
Now, say we roll each die twice. What happens to the graph fromE the previous problem?
|
||||||
|
|
||||||
#solution([
|
#solution([
|
||||||
The direction of each edge is reversed!
|
The direction of each edge is reversed!
|
||||||
|
Loading…
x
Reference in New Issue
Block a user