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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
x' = x · cos (\phi) - y · sin (\phi)
y' = x · sin (\phi) + y · cos (\phi)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
^ \pi ^ \pi ^
normal (t) = x(t) · cos ─── - y(t) · sin ─── = - y(t)
x 2 2
^ \pi ^ \pi ^
normal (t) = \undersetquarter circle rotation \underbrace x(t) · sin ─── + y(t) · cos ─── = x(t)
y 2 2

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
tangent (t) = B' (t)
x x
tangent (t) = B' (t)
y y

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌─────────────────┐
│ 2 2
d = \|tangent(t)\| = │B' (t) + B' (t)
⟍│ x y
tangent (t) B' (t)
^ x x
x(t) = \|tangent (t)\| =────────────── = ──────
x \|tangent(t)\| d
tangent (t) B' (t)
^ y y
y(t) = \|tangent (t)\| = ────────────── = ──────
y \|tangent(t)\| d

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ x' ┐ = ┌ cos (\phi) -sin (\phi) ┐ ┌ x ┐
└ y' ┘ └ sin (\phi) cos (\phi) ┘ └ y ┘