(s / 2) ⋅ (s / 2) = (s ⋅ s) / 4

Start from the conclusion and work back up the proof. Click the arrow to show the parents.

• (s / 2) ⋅ (s / 2) = (s ⋅ s) / 4,

  if the following are true:

  • a = b
  • b = c

  then a = c

  • (s / 2) ⋅ (s / 2) = (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)),

    if a = b, then a ⋅ a = b ⋅ b

    • s / 2 = s ⋅ (1 / 2), a / b = a ⋅ (1 / b)
  • (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = (s ⋅ s) / 4,

    if the following are true:

    • a = b
    • b = c

    then a = c

    • (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2),

      if the following are true:

      • a = b
      • b = c

      then a = c

      • (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = ((s ⋅ (1 / 2)) ⋅ s) ⋅ (1 / 2), a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c
      • ((s ⋅ (1 / 2)) ⋅ s) ⋅ (1 / 2) = ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2), ((a ⋅ b) ⋅ c) ⋅ d = ((a ⋅ c) ⋅ b) ⋅ d
    • ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) = (s ⋅ s) / 4,

      if the following are true:

      • a = c
      • b = c

      then a = b

      • ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) = (s ⋅ s) ⋅ (1 / 4),

        if the following are true:

        • a = b ⋅ c
        • c = d

        then a = b ⋅ d

        • ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) = (s ⋅ s) ⋅ ((1 / 2) ⋅ (1 / 2)), (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c)
        • (1 / 2) ⋅ (1 / 2) = 1 / 4, (1 / 2) ⋅ (1 / 2) = 1 / 4
      • (s ⋅ s) / 4 = (s ⋅ s) ⋅ (1 / 4), a / b = a ⋅ (1 / b)