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Pomax
2020-10-18 14:27:57 -07:00
parent 133105d44e
commit 0f6683ca6d
314 changed files with 11182 additions and 266 deletions
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
cos(φ)-1
b = ────────
sin(φ)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
1 = cos(φ) + b · -sin(φ) → \ 1 - cos(φ) = -b · sin(φ) → \ -1 + cos(φ) = b · sin(φ)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
a= sin(φ) + b · cos(φ)
-1 + cos(φ)
..= sin(φ) + ─────────── · cos(φ)
sin(φ)
2
-cos(φ) + cos (φ)
..= sin(φ) + ─────────────────
sin(φ)
2 2
sin (φ) + cos (φ) - cos(φ)
..= ──────────────────────────
sin(φ)
1 - cos(φ)
a= ──────────
sin(φ)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
S = \begin{pmatrix} 1
0 \end{pmatrix} , \ E = \begin{pmatrix} cos(φ)
sin(φ) \end{pmatrix}

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ C = 1 = cos(φ) + b · -sin(φ)
╡ x
│ C = a = sin(φ) + b · cos(φ)
╰ y

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
φ φ
P = cos(─) , \ P = sin(─)
x 2 y 2

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
1 φ 4╭ φ ╮
d (φ)= T - P = ─(3 + cos(φ)) - cos(─) = 2sin │ ─ │ ,
x x x 4 2 ╰ 4 ╯
1╭ ╭ φ ╮ ╮ φ
d (φ)= T - P = ─│ 2tan│ ─ │ + sin(φ) │ - sin(─) ,
y y y 4╰ ╰ 2 ╯ ╯ 2
⇓
┌───────┐ ┌───────┐
│ 2 2 4 φ │ 1
d(φ)= │d + d = ... = 2sin (─) │───────
⟍│ x y 4 │ 2 φ
│cos (─)
⟍│ 2

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ 1
│ T = ─(3 + cos(φ))
╡ x 4
│ 1╭ 2-2cos(φ) ╮ 1╭ ╭ φ ╮ ╮
│ T = ─│ ───────── + sin(φ) │ = ─│ 2tan│ ─ │ + sin(φ) │
╰ y 4╰ sin(φ) ╯ 4╰ ╰ 2 ╯ ╯

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
1 2 1 1
T = ─S + ─C + ─E = ─(S + 2C + E)
4 4 4 4

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
C = S + a · \begin{pmatrix} 0
1 \end{pmatrix} , \ C = E + b · \begin{pmatrix} -sin(φ)
cos(φ) \end{pmatrix}

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ ┌─────────────┐ ╮
│ │ ┌──────┐ │
│ ⟍│2+ε-⟍│ε(2+ε) │
φ = 4 · arccos │ ──────────────── │
│ ┌─┐ │
╰ ⟍│2 ╯