#import "@preview/touying:0.6.1": *
#import themes.university: *
#import "@preview/cetz:0.4.2"
#import "@preview/fletcher:0.5.8" as fletcher: node, edge

#let cetz-canvas = touying-reducer.with(reduce: cetz.canvas, cover: cetz.draw.hide.with(bounds: true))
#let fletcher-diagram = touying-reducer.with(reduce: fletcher.diagram, cover: fletcher.hide)

#show: university-theme.with(
  aspect-ratio: "16-9",
  config-info(
    title: [Melon's test prep.],
    subtitle: [Typst touying slides],
    author: [Vincent Tam],
    date: datetime.today(),
    institution: [vin100 數學自學中心],
    logo: image("vin100_logo.svg", width: 20%),
  ),
  footer-a: self => [#self.info.author (#self.info.institution)]
)

#title-slide()

= Animation 動畫 \ アニメーション

== Simple Animation 簡單動畫

#v(10pt)

If $display((5a+14b)/(4a+5b)) = 2$,
compute $display((3a^2+4b^2)/(7 a b))$.

#pause

Solution:
$
  (5a+14b)/(4a+5b) =& 2 \
  pause 5a + 14b =& 2(4a+5b) \
  pause =& 8a + 10b \
  pause 4b =& 3a \
  b =& 3a slash 4
$

== Question

Suppose that two distinct nonzero real numbers $x$ and $y$ satisfy
$ 2x + 3/(4x) = 2y + 3/(4y). $
What is the value of $x y$?

#pause

Solution:
$
  2(x-y) =& 3/4 (1/y - 1/x) pause = 3/4 dot.c (x-y)/(x y) \
  pause x y =& 3 slash 8
$

= Misc. 雜項
== 2-col., CeTZ, fletcher animation

#slide(composer: (1fr, 1fr))[
  $ x^2=sqrt(6)+sqrt(7), x^4 + 1/x^4 = ? $
  #pause
  #let lbl1 = text(fill: red, $a$)
  #let lbl2 = text(fill: blue, $b$)
  #let side-label = $#lbl1 + #lbl2$
  #align(center, cetz-canvas({
    import cetz.draw: *
    rect((0, 0), (5, 5))
    rect((0, 0), (2, 2), name: "asq", stroke: 3pt + red)
    rect((2, 2), (5, 5), name: "bsq", stroke: 3pt + blue)
    // long 
    content(
      ((0, 0), 50% ,(0, 5)),
      angle: 90deg,
      side-label,
      padding: .2,
      anchor: "south",
    )
    content(
      ((0, 0), 50% ,(5, 0)),
      side-label,
      padding: .2,
      anchor: "north",
    )

    (pause,)

    content(
      ((0, 5), 50%, (2, 5)),
      lbl1,
      padding: .2,
      anchor: "south",
    )
    content(
      ((2, 5), 50%, (5, 5)),
      lbl2,
      padding: .2,
      anchor: "south",
    )
    content(
      ((5, 0), 50%, (5, 2)),
      lbl1,
      angle: 90deg,
      padding: .2,
      anchor: "north",
    )
    content(
      ((5, 2), 50%, (5, 5)),
      lbl2,
      angle: 90deg,
      padding: .2,
      anchor: "north",
    )
    // areas
    content(((0, 0), 50%, (2, 2)), text(fill: red, $a^2$))
    content(((2, 2), 50%, (5, 5)), text(fill: blue, $b^2$))
    content(((0, 2), 50%, (2, 5)), lbl1 + lbl2)
    content(((2, 0), 50%, (5, 2)), lbl1 + lbl2)
  }))
][
  #fletcher-diagram(
    node-stroke: 0.05em,
    spacing: 1.5em,
    node((0,0), pad(rest:0.3em, align(left, [$a^2+b^2$ with \ $a = x^2, b = 1/a$])), shape: rect),
    pause,
    edge("d", "<|-", [can solve], label-side: left),
    node((0,1), pad(rest: 0.3em, $(a+b)^2$)),
    pause,
    edge("d", "-|>", [only need], label-side: left),
    node((0,2), pad(rest: 0.3em, align(left, [$a+b$ with \ $a = sqrt(k)+sqrt(k+1)$])), shape: rect),
  )
  #pause
  $&((sqrt(a+1)+sqrt(a))^2+1)/(sqrt(a+1)+sqrt(a)) \
  #only("6", $=& (a+1+a+2sqrt(a(a+1))+1)/(sqrt(a+1)+sqrt(a))$)
  #only("7", $=& (2a+2+2sqrt(a(a+1)))/(sqrt(a+1)+sqrt(a))$)
  #only("8", $=& (2sqrt(a+1)(sqrt(a+1)+sqrt(a)))/(sqrt(a+1)+sqrt(a))$)
  #only("9", $=& 2sqrt(a+1)$)
  $
]

= Callback Style Animation
== Question 4

#slide(
  repeat: 6,
  self => [
    #let (uncover, only, alternatives) = utils.methods(self)
    Evaluate $sqrt(9-sqrt(14)-sqrt(23-sqrt(504)))$.
    $
      #uncover("2-")[
        $ & sqrt(9-sqrt(14)-sqrt(23-sqrt(504))) \
        =& sqrt(9-sqrt(14)-sqrt(14 + 9 -2 sqrt(14 dot.c 9))) \ $
      ]
      #uncover("3-")[$ =& sqrt(6-sqrt(14)-(sqrt(14)-3)) \ $]
      #uncover("4-")[$ =& sqrt(9-2sqrt(14)) \ $]
      #uncover("5-")[$ =& sqrt(7 + 2 - 2sqrt(7 dot.c 2)) \ $]
      #uncover("6-")[$ =& sqrt(7)-sqrt(2) $]
    $
  ],
)

== Final Question

#slide(
  repeat: 4,
  self => [
    #let (uncover, only, alternatives) = utils.methods(self)
    Evaluate $display((2028^2+2022^2-18)/2025^2)$.

    #uncover("2-")[Let $x = 2025$.  Then]
    $
      #uncover("2-")[
        $ (2028^2+2022^2-18)/2025^2
        &= ((x+3)^2+(x-3)^2-18) / x^2 \ $
      ]
      #uncover("3-")[
        $ &= ((x^2+6x+9)+(x^2-6x+9)-18) / x^2 \ $
      ]
      #uncover("4-")[$ &= 2 $]
    $
  ]
)