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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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2 2
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B + B = r
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x y
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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┌───────────────────────┐
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╭ 1 │ 2 2
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erf (θ, k) = | \| │B (t,θ,k) + B (t,θ,k) - r\|dt
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╯ 0 ⟍│ x y
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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╭ ┌───────┐ ╮
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│ ╭ 1 │ 2 2 │ d
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│ | \| │B + B - r\|dt │ ── = 0
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╰ ╯ 0 ⟍│ x y ╯ dt
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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╭ \pi ╮ 4 ╭ \pi ╮ 4 ┌─┐
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f│ ─── │ = ─ · tan│ ─── │ = ─(⟍│2 -1) ≅ 0.55228474983[...]
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╰ 2 ╯ 3 ╰ 8 ╯ 3
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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start= (r, 0)
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control = (r, 0.55228 · r)
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1
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control = (0.55228 · r, r)
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2
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end= (0, r)
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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3c + 4sin(θ)) - 3k · cos(θ) θ
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────────────────────────────= sin(─)
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8 2
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╭ θ ╮
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3k + 4sin(θ)) - 3k · cos(θ)= 8sin│ ─ │
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╰ 2 ╯
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╭ θ ╮
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3k - 3k · cos(θ)= 8sin│ ─ │ - 4sin(θ)
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╰ 2 ╯
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╭ ╭ θ ╮ ╮
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3k (1 - cos(θ))= 4 │ 2sin│ ─ │ - sin(θ) │
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╰ ╰ 2 ╯ ╯
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θ
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2sin(─) - sin(θ)
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2
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3k= 4 · ────────────────
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1 - cos(θ)
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╭ θ ╮
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2sin│ ─ │ - sin(θ)
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4 ╰ 2 ╯
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k= ─ · ──────────────────
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3 1 - cos(θ)
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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┌───────┐
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│ 2 2
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\| │B + B - r\| = 0, t ∈[0,1]
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⟍│ x y
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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start= (r, 0)
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control = (r, k)
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1
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control = r · (cos(θ) + k · sin(θ), sin(θ) - k · cos(θ))
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2
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end= r · (cos(θ), sin(θ))
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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P + P
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2 3
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y y k + sin(θ) - k · cos(θ)
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A = ───────── = ────────────────────────
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y 2 2
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1
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A + ─P k + sin(θ) - k · cos(θ)
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y 2 2 ──────────────────────── + ─
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y 2 2 2k + sin(θ) + k · cos(θ)
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e = ───────── = ──────────────────────────── = ─────────────────────────
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1 2 2 4
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y
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k
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A + mid(P , P ) A + sin(θ) - ─ cos(θ)
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y 4 3 y 2 k + 3sin(θ) 2k · cos(θ)
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e = ───────────────── = ────────────────────── = ────────────────────────
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2 2 2 4
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y
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e + e
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1 2
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y y 3k + 4sin(θ) - 3k · cos(θ)
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B = ───────── = ───────────────────────────
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y 2 8
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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4 ╭ θ ╮
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k = f(θ) = ─ tan│ ─ │
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3 ╰ 4 ╯
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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╭ θ ╮
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2sin│ ─ │ - sin(θ)
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4 ╰ 2 ╯
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k= ─ · ──────────────────
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3 1 - cos(θ)
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╭ ╭ θ ╮ ╮
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│ 2sin│ ─ │ │
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4 │ ╰ 2 ╯ sin(θ) │
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k= ─ · │ ────────── - ────────── │
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3 ╰ 1 - cos(θ) 1 - cos(θ) ╯
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4 ╭ ╭ θ ╮ ╭ θ ╮ ╮
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k= ─ · │ csc│ ─ │ - cot│ ─ │ │
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3 ╰ ╰ 2 ╯ ╰ 2 ╯ ╯
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4 ╭ θ ╮
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k= ─ · tan│ ─ │
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3 ╰ 4 ╯
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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P = (1, 0)
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1
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P = (1, c)
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2
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P = P + k · (sin(θ), -cos(θ))
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3 4
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P = (cos(θ), sin(θ))
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4
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