1 files changed, 57 insertions, 0 deletions
diff --git a/FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/convergence.py b/FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/convergence.py
new file mode 100644
index 0000000..fcbcfb4
--- /dev/null
+++ b/FSF-2020/calculus/intro-to-calculus/infinite-seq-and-series/convergence.py
@@ -0,0 +1,57 @@
+from manimlib.imports import *
+def GetCenters(width,center,n):
+	d = width / 4
+	list = [center + [0,d,0]]
+	if n > 1:
+		list.append(center + [-d,-d,0])
+	if n > 2:
+		list.extend(GetCenters(width / 2, center + [d,-d,0],n-2))
+	return list
+END_CENTERS = [ORIGIN]
+END_CENTERS.extend(GetCenters(3, 3 * RIGHT, 24))
+color_list = ['#00931F','#A93226','#D68910','#17A589','#2471A3','#884EA0','#E74C3C','#D4AC0D']
+COLORS = [color_list[i % len(color_list)] for i in range(50)]
+class RectangleFromSequence(Rectangle):
+	CONFIG = {
+		"sequence_number": 0,
+		"center": ORIGIN
+	}
+	def __init__(self, **kwargs):
+		digest_config(self, kwargs)
+		Rectangle.__init__(self,height = 3 * (1/2) ** ((self.sequence_number + 1) // 2),width = 3 * (1/2) ** ((self.sequence_number) // 2),**kwargs)
+		if self.sequence_number < 6:
+			if self.sequence_number == 0:
+				label = TexMobject("1")
+			else:
+				label = TexMobject("1/",str(2 ** self.sequence_number))
+			label.scale(0.8 ** self.sequence_number)
+			self.add(label)
+			self.label = label
+		self.set_fill(COLORS[self.sequence_number],1)
+		self.set_stroke(width = 1)
+		self.move_to(self.center)
+equation = TexMobject("\\sum_{n=0}^\\infty \\frac{1}{2^n} =","1","+","\\frac{1}{2}","+","\\frac{1}{4}","+","\\frac{1}{8}","+","\\frac{1}{16}","+ \\ldots","= 2")
+class Proof1(Scene):
+	def construct(self):
+		equation.to_edge(UL)
+		self.play(Write(equation[0:-1]))	
+		rects = VGroup(*[RectangleFromSequence(sequence_number = i)for i in range(25)])
+		rects.arrange(RIGHT, buff=0.5)
+		left_center = 5*LEFT
+		rects.shift(left_center-rects[0].get_center())
+		for rect in rects:
+			rect.shift(DOWN*rect.get_top()+UP*3 / 2)
+		for i in range(25):
+			rects[i].generate_target()
+			rects[i].target.move_to(left_center+END_CENTERS[i])
+		self.wait()
+		for i in range(5):
+			self.play(GrowFromPoint(rects[i] , equation[2*i+1].get_center()))
+		self.play(*[GrowFromPoint(rects[i] , equation[-2].get_center())for i in range(5,25)])
+		self.wait()
+		for i in range(1,8):
+			self.play(MoveToTarget(rects[i]))
+		self.play(*[MoveToTarget(rects[i]) for i in range(8,25)])
+		self.wait(0.5)
+		self.play(Write(equation[-1]))
+		self.wait(3)
+\ No newline at end of file