Merge pull request #166 from 3b1b/pi-day-2018

Pi day 2018

.gitignore

@@ -13,3 +13,5 @@ ben_cairo_test.py
 *.xml
 *.iml
 
+
+primes.py

active_projects/pi-day.py

@@ -0,0 +1,223 @@
+from helpers import *
+from mobject import Mobject
+from mobject.vectorized_mobject import *
+from animation.animation import Animation
+from animation.transform import *
+from animation.simple_animations import *
+from animation.compositions import *
+from topics.geometry import *
+from scene import Scene
+from camera import *
+from topics.characters import *
+from topics.numerals import *
+
+RADIUS = 2
+RADIUS_BUFF_HOR = 1.3
+RADIUS_BUFF_VER = 0.5
+RADIUS_COLOR = BLUE
+CIRCUM_COLOR = YELLOW
+DECIMAL_WIDTH = 0.5
+
+HIGHLIGHT_COLOR = YELLOW
+
+
+class ArcLengthChange(Animation):
+
+    def __init__(self, mobject = None, new_angle = TAU/3, **kwargs):
+
+        self.old_angle = mobject.angle
+        self.start_angle = mobject.start_angle
+        self.new_angle = new_angle
+        Animation.__init__(self,mobject,**kwargs)
+
+    def update_mobject(self,alpha):
+        angle = interpolate(self.old_angle, self.new_angle, alpha)
+        self.mobject.angle = angle
+        self.mobject.generate_points()
+
+
+class LabelTracksLine(Animation):
+
+    def __init__(self, mobject = None, line = None, buff = 0.2, **kwargs):
+
+        self.line = line
+        self.buff = buff
+        Animation.__init__(self,mobject,**kwargs)
+
+    def update_mobject(self,alpha):
+        line_center = self.line.get_center()
+        line_end = self.line.points[-1]
+        v = line_end - line_center
+        v = v/np.linalg.norm(v)
+        w = np.array([-v[1],v[0],0])
+        self.mobject.move_to(line_center + self.buff * w)
+
+
+
+
+        
+class CircleConstants(Scene):
+
+    def radial_label_func(self,a,b,theta):
+
+        theta2 = theta % TAU
+        slope = (a-b)/(TAU/4)
+
+        if theta2 < TAU/4:
+            x = a - slope * theta2
+        elif theta < TAU/2:
+            x = b + slope * (theta2 - TAU/4)
+        elif theta < 3*TAU/4:
+            x = a - slope * (theta2 - TAU/2)
+        else:
+            x = b + slope * (theta2 - 3*TAU/4)
+        return x
+
+	
+    def construct(self):
+        self.setup_circle()
+        self.change_arc_length(0.004)
+        self.pi_equals.next_to(self.decimal, LEFT)
+        self.wait()
+        self.change_arc_length(TAU/2)
+        self.wait()
+        self.change_arc_length(TAU)
+        self.wait()
+        self.change_arc_length(TAU/4)
+        self.wait()
+        self.change_arc_length(TAU/2)
+        self.wait()
+
+
+
+
+    def setup_circle(self):
+
+
+        self.circle_arc = Arc(angle = 0.004, radius = RADIUS)
+        self.radius = Line(ORIGIN, RADIUS * RIGHT)
+        self.radius.highlight(RADIUS_COLOR)
+        self.circle_arc.highlight(CIRCUM_COLOR)
+
+        self.pi_equals = TexMobject("\pi\\approx", color = CIRCUM_COLOR)
+        self.decimal = DecimalNumber(0, color = CIRCUM_COLOR)
+        self.decimal.next_to(self.pi_equals, RIGHT, buff = 0.25)
+        self.circum_label = VGroup(self.pi_equals, self.decimal)
+        self.circum_label.next_to(self.radius, RIGHT, buff = RADIUS_BUFF_HOR)
+
+            
+        self.one = TexMobject("1", color = RADIUS_COLOR)
+        self.one.next_to(self.radius, UP)
+
+        self.play(ShowCreation(self.radius), FadeIn(self.one))
+        self.play(
+            ShowCreation(self.circle_arc),
+            Write(self.pi_equals),
+            Write(self.decimal)
+        )
+
+
+    def change_arc_length(self, new_angle):
+
+        def decimal_position_update_func(decimal):
+
+            angle = decimal.number
+            max_radius = RADIUS + RADIUS_BUFF_HOR
+            min_radius = RADIUS + RADIUS_BUFF_VER
+            label_radius = self.radial_label_func(max_radius, min_radius, angle)
+            label_center = label_radius * np.array([np.cos(angle), np.sin(angle),0])
+            label_center += 0.5 * RIGHT
+            # label_center += pi_eq_stencil.get_width() * RIGHT
+            # print "label_center = ", label_center
+            decimal.move_to(label_center)
+
+
+        self.play(
+            Rotate(self.radius, new_angle - self.circle_arc.angle, about_point = ORIGIN),
+            ArcLengthChange(self.circle_arc,new_angle),
+            ChangeDecimalToValue(
+                self.decimal, new_angle, 
+                position_update_func = decimal_position_update_func
+            ),
+            #MaintainPositionRelativeTo(self.one, self.radius),
+            MaintainPositionRelativeTo(self.pi_equals, self.decimal),
+            LabelTracksLine(self.one,self.radius, buff = 0.5),
+            run_time = 3,
+        )
+        self.wait(2)
+
+
+class AnalysisQuote(Scene):
+
+    def construct(self):
+
+        text = TextMobject('``We therefore set the radius of \\\\'\
+         'the circle\dots to be = 1, and \dots\\\\'\
+         'through approximations the \\\\'\
+         'semicircumference of said circle  \\\\'\
+         'has been found to be $= 3.14159\dots$,\\\\'\
+         'for which number, for the sake of \\\\'\
+         'brevity, I will write $\pi$\dots"',
+         alignment = '')
+        for char in text.submobjects[12:24]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[42:44]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[75:92]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[120:131]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        text.submobjects[-5].set_fill(HIGHLIGHT_COLOR)
+
+        text.to_edge(LEFT, buff = 1)
+
+        self.play(LaggedStart(FadeIn,text), run_time = 5)
+        self.wait()
+        self.play(FadeOut(text))
+        self.wait()
+
+
+class BernoulliQuote(Scene):
+
+    def construct(self):
+
+        text = TextMobject('``Your most profound investigation of the series \\\\'\
+         '$1+{1\over 4}+{1\over 9}+{1\over 16} + $ etc., which I had found to be \\\\'\
+          'one sixth of the square of $\pi$ itself\dots, not only\\\\'\
+        ' gave me the greatest pleasure, but also renown \\\\'\
+        'among the whole Academy of St.\ Petersburg."')
+        text.submobjects[88].set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[41:60]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[79:107]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[127:143]:
+            char.set_fill(HIGHLIGHT_COLOR)
+        for char in text.submobjects[151:157]:
+            char.set_fill(HIGHLIGHT_COLOR)
+
+        self.play(LaggedStart(FadeIn,text), run_time = 5)
+        self.wait()
+        self.play(FadeOut(text))
+        self.wait
+
+
+class EulerSignature(Scene):
+
+    def construct(self):
+
+        sig = SVGMobject(file_name = "euler-signature")
+
+        self.play(
+            Write(sig, run_time = 5)
+        )
+
+
+
+
+
+
+
+
+
+