last day

4 files changed, 54 insertions, 4 deletions

diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
new file mode 100644
index 0000000..39489b7
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
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..cf6b032
--- /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'$\frac{dT}{dt} = \frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.6).shift(0.5*RIGHT+0.6*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])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif
deleted file mode 100644
index 0d6fdcf..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
index 3ecd57c..56b7fbb 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
@@ -8,7 +8,9 @@ class GR(GraphScene):
         "x_max": 6,
         "y_min": -6,
         "y_max": 10,
-        "graph_origin": ORIGIN
+        "graph_origin": ORIGIN,
+        'x_tick_frequency': 20,
+        'y_tick_frequency': 20
     }
 
     def construct(self):
@@ -21,7 +23,7 @@ class GR(GraphScene):
 
         tracker = ValueTracker(-3)
 
-        text = TextMobject(r'The curvature at point $P_{1}$ is \\ lesser than that at point $P_{2}$: \\ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
+        text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
 
         dot1 = Dot((0,3,0), color = YELLOW)
         dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1)
@@ -50,12 +52,18 @@ class GR(GraphScene):
         circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP)
         tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4)
 
-        curvature1 = VGroup(*[circle1, tgt1])
+        r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN)
+        r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6)
+
+        curvature1 = VGroup(*[circle1, tgt1, r1, r1label])
 
         circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT)
         tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP)
 
-        curvature2 = VGroup(*[circle2, tgt2])
+        r2 = Line(circle2.get_center(), circle2.get_center() + np.array([0,-0.6,0]), color=GREEN_SCREEN)
+        r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2, 0.9*RIGHT, buff = 0).scale(0.6)
+
+        curvature2 = VGroup(*[circle2, tgt2, r2, r2label])
 
         line = always_redraw(get_tangent_line)