1 files changed, 42 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
new file mode 100644
index 0000000..d8dd0a4
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
@@ -0,0 +1,42 @@
+from manimlib.imports import *
+
+class interpretation(Scene):
+    def construct(self):
+        tgt = Vector((1, 2, 0), color = YELLOW)
+        tgtText = TextMobject(r'$r\prime (t)$').next_to(tgt, UP, buff = 0).scale(0.7)
+        tgt2 = DashedLine((0,0,0),(1, 2, 0), color = GRAY).shift(DOWN + 2*RIGHT)
+
+        nm = Vector((2, -1, 0), color = BLUE)
+        nmText = TextMobject(r'$r\prime\prime (t)$').next_to(nm, DOWN+RIGHT, buff = 0).scale(0.7)
+        nm2 = DashedLine((0,0,0),(2, -1, 0), color = GRAY).shift(2*UP + RIGHT)
+        square = Square(fill_color = WHITE, fill_opacity = 0.2).rotate(63*DEGREES).shift(0.5*UP +1.5*RIGHT).scale(1.1)
+        square.set_stroke(width = 0.1)
+        arrow = CurvedArrow(square.get_center() + np.array([2,1,0]), square.get_center() + np.array([0.5,0,0]))
+        arrowText = TextMobject(r'$r\prime (t)\times r\prime\prime (t)$').next_to(arrow.get_start(), DOWN+1*RIGHT, buff = 0).scale(0.7)
+
+        text1 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\left|\frac{dT}{dt}\right|}{\left|\frac{ds}{dt}\right|}$').shift(UP+3*LEFT)
+        text2 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}\times\frac{r\prime (t)}{\left| r\prime (t)\right|}}{\left|r\prime (t)\right|}$').next_to(text1, DOWN, buff = 0.1)
+        unit = VGroup(*[tgt, tgt2, nm, nm2])
+
+        # self.play(FadeIn(VGroup(*[tgt, tgt2, nm, nm2, nmText, tgtText, square, arrow, arrowText])))
+        tgt2text = TextMobject(r'$\frac{r\prime (t)}{\left| r\prime (t)\right|}$').shift(1.1*UP).scale(0.7).rotate(63*DEGREES  )
+        nm2text = TextMobject(r'$\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.7).shift(0.7*RIGHT+0.8*DOWN).rotate(-25*DEGREES)
+        unit2 = unit.copy().scale(0.5).shift(0.75*LEFT+0.25*DOWN)
+
+        self.play(FadeIn(VGroup(*[tgt, tgtText])))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[nm, nmText])))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[tgt2, nm2])))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[square, arrow, arrowText])))
+        self.wait(1)
+        self.play(FadeIn(unit2))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[tgt2text, nm2text])))
+        self.wait(1)
+        self.play(FadeIn(text1))
+        self.wait(1)
+        self.play(FadeIn(text2))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[tgt2text, nm2text, text1, text2, tgt, tgtText,nm, nmText,tgt2, nm2,square, arrow, arrowText,unit2])))