/
20231008_a_plus_b__plus_c_square.py
292 lines (247 loc) · 14.5 KB
/
20231008_a_plus_b__plus_c_square.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
import numpy as np
from manim import *
# configs
config.background_color = BLACK
config.pixel_width = 180 * 2
config.pixel_height = 320 * 2
class APlusBPlusCSquare(Scene):
def construct(self):
formula1 = MathTex(r"{{(a+b+c)^{2}}}", color=BLUE).scale(1.5)
question = Text("?", color=RED).scale(3).next_to(formula1, DOWN * 2)
self.play(Write(formula1))
self.play(ShowCreationThenFadeOut(question))
self.play(formula1.animate.shift(UP * 9 + LEFT * 4))
scale_value = 1
run_t = 0.2
line11 = Line(start=[0, 8, 0], end=[3, 8, 0], color=RED).shift(np.array([-5, -4, 0]))
label11 = MathTex("a").next_to(line11, UP).scale(scale_value)
self.play(Create(line11), run_time=run_t)
self.add(label11)
line12 = Line(start=[3, 8, 0], end=[6, 8, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label12 = MathTex("b").next_to(line12, UP).scale(scale_value)
self.play(Create(line12), run_time=run_t)
self.add(label12)
line13 = Line(start=[6, 8, 0], end=[8, 8, 0], color=BLUE).shift(np.array([-5, -4, 0]))
label13 = MathTex("c").next_to(line13, UP).scale(scale_value)
self.play(Create(line13), run_time=run_t)
self.add(label13)
line21 = Line(start=[8, 8, 0], end=[8, 5, 0], color=RED).shift(np.array([-5, -4, 0]))
label21 = MathTex("a").next_to(line21, RIGHT).scale(scale_value)
self.play(Create(line21), run_time=run_t)
self.add(label21)
line22 = Line(start=[8, 5, 0], end=[8, 2, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label22 = MathTex("b").next_to(line22, RIGHT).scale(scale_value)
self.play(Create(line22), run_time=run_t)
self.add(label22)
line23 = Line(start=[8, 2, 0], end=[8, 0, 0], color=BLUE).shift(np.array([-5, -4, 0]))
label23 = MathTex("c").next_to(line23, RIGHT).scale(scale_value)
self.play(Create(line23), run_time=run_t)
self.add(label23)
line31 = Line(start=[8, 0, 0], end=[6, 0, 0], color=BLUE).shift(np.array([-5, -4, 0]))
label31 = MathTex("c").next_to(line31, DOWN * 2).scale(scale_value)
self.play(Create(line31), run_time=run_t)
self.add(label31)
line32 = Line(start=[6, 0, 0], end=[3, 0, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label32 = MathTex("b").next_to(line32, DOWN * 2).scale(scale_value)
self.play(Create(line32), run_time=run_t)
self.add(label32)
line33 = Line(start=[3, 0, 0], end=[0, 0, 0], color=RED).shift(np.array([-5, -4, 0]))
label33 = MathTex("a").next_to(line33, DOWN * 2).scale(scale_value)
self.play(Create(line33), run_time=run_t)
self.add(label33)
line41 = Line(start=[0, 0, 0], end=[0, 2, 0], color=BLUE).shift(np.array([-5, -4, 0]))
label41 = MathTex("c").next_to(line41, LEFT * 2).scale(scale_value)
self.play(Create(line41), run_time=run_t)
self.add(label41)
line42 = Line(start=[0, 2, 0], end=[0, 5, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label42 = MathTex("b").next_to(line42, LEFT * 2).scale(scale_value)
self.play(Create(line42), run_time=run_t)
self.add(label42)
line43 = Line(start=[0, 5, 0], end=[0, 8, 0], color=RED).shift(np.array([-5, -4, 0]))
label43 = MathTex("a").next_to(line43, LEFT * 2).scale(scale_value)
self.play(Create(line43), run_time=run_t)
self.add(label43)
line51 = DashedLine(start=[0, 5, 0], end=[3, 5, 0], color=RED).shift(np.array([-5, -4, 0]))
label51 = MathTex("a").next_to(line51, DOWN).scale(scale_value)
self.play(Create(line51), run_time=run_t)
self.add(label51)
line52 = DashedLine(start=[3, 5, 0], end=[6, 5, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label52 = MathTex("b").next_to(line52, DOWN).scale(scale_value)
self.play(Create(line52), run_time=run_t)
self.add(label52)
line53 = DashedLine(start=[6, 5, 0], end=[8, 5, 0], color=RED).shift(np.array([-5, -4, 0]))
label53 = MathTex("c").next_to(line53, DOWN).scale(scale_value)
self.play(Create(line53), run_time=run_t)
self.add(label53)
line61 = DashedLine(start=[0, 2, 0], end=[3, 2, 0], color=RED).shift(np.array([-5, -4, 0]))
label61 = MathTex("a").next_to(line61, DOWN).scale(scale_value)
self.play(Create(line61), run_time=run_t)
self.add(label61)
line62 = DashedLine(start=[3, 2, 0], end=[6, 2, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label62 = MathTex("b").next_to(line62, DOWN).scale(scale_value)
self.play(Create(line62), run_time=run_t)
self.add(label62)
line63 = DashedLine(start=[6, 2, 0], end=[8, 2, 0], color=RED).shift(np.array([-5, -4, 0]))
label63 = MathTex("c").next_to(line63, DOWN).scale(scale_value)
self.play(Create(line63), run_time=run_t)
self.add(label63)
line71 = DashedLine(start=[3, 8, 0], end=[3, 5, 0], color=RED).shift(np.array([-5, -4, 0]))
label71 = MathTex("a").next_to(line71, RIGHT).scale(scale_value)
self.play(Create(line71), run_time=run_t)
self.add(label71)
line72 = DashedLine(start=[3, 5, 0], end=[3, 2, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label72 = MathTex("b").next_to(line72, RIGHT).scale(scale_value)
self.play(Create(line72), run_time=run_t)
self.add(label72)
line73 = DashedLine(start=[3, 2, 0], end=[3, 0, 0], color=RED).shift(np.array([-5, -4, 0]))
label73 = MathTex("c").next_to(line73, RIGHT).scale(scale_value)
self.play(Create(line73), run_time=run_t)
self.add(label73)
line81 = DashedLine(start=[6, 8, 0], end=[6, 5, 0], color=RED).shift(np.array([-5, -4, 0]))
label81 = MathTex("a").next_to(line81, RIGHT).scale(scale_value)
self.play(Create(line81), run_time=run_t)
self.add(label81)
line82 = DashedLine(start=[6, 5, 0], end=[6, 2, 0], color=YELLOW).shift(np.array([-5, -4, 0]))
label82 = MathTex("b").next_to(line82, RIGHT).scale(scale_value)
self.play(Create(line82), run_time=run_t)
self.add(label82)
line83 = DashedLine(start=[6, 2, 0], end=[6, 0, 0], color=RED).shift(np.array([-5, -4, 0]))
label83 = MathTex("c").next_to(line83, RIGHT).scale(scale_value)
self.play(Create(line83), run_time=run_t)
self.add(label83)
new_run_t = 0.5
s_rect1 = Polygon(line11.start, line11.end, line71.end, line51.start, fill_color=RED, fill_opacity=0.5).shift(
np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect1, LEFT), run_time=new_run_t)
self.play(label11.animate.move_to(s_rect1.get_center()), run_time=new_run_t)
dot1 = MathTex(r"\cdot").next_to(label11, RIGHT)
self.add(dot1)
self.play(label71.animate.next_to(dot1, RIGHT), run_time=new_run_t)
subgroup1 = VGroup(label11, label71, dot1)
s_rect2 = Polygon(line12.start, line12.end, line81.end, line52.start, fill_color=ORANGE,
fill_opacity=0.5).shift(np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect2, LEFT), run_time=new_run_t)
self.play(label12.animate.move_to(s_rect2.get_center()), run_time=new_run_t)
dot2 = MathTex(r"\cdot").next_to(label12, RIGHT)
self.add(dot2)
self.play(label81.animate.next_to(dot2, RIGHT), run_time=new_run_t)
subgroup2 = VGroup(label12, dot2, label81)
s_rect3 = Polygon(line13.start, line13.end, line21.end, line53.start, fill_color=YELLOW,
fill_opacity=0.5).shift(np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect3, LEFT), run_time=new_run_t)
self.play(label13.animate.move_to(s_rect3.get_center()), run_time=new_run_t)
dot3 = MathTex(r"\cdot").next_to(label13, RIGHT)
self.add(dot3)
self.play(label21.animate.next_to(dot3, RIGHT), run_time=new_run_t)
subgroup3 = VGroup(label21, dot3, label13)
s_rect4 = Polygon(line22.start, line22.end, line82.end, line82.start, fill_color=GREEN, fill_opacity=0.5).shift(
np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect4, UP), run_time=new_run_t)
self.play(label53.animate.move_to(s_rect4.get_center()), run_time=new_run_t)
dot4 = MathTex(r"\cdot").next_to(label53, RIGHT)
self.add(dot4)
self.play(label22.animate.next_to(dot4, RIGHT), run_time=new_run_t)
subgroup4 = VGroup(label22, dot4, label53)
s_rect5 = Polygon(line52.start, line52.end, line62.end, line62.start, fill_color=BLUE, fill_opacity=0.5).shift(
np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect5, RIGHT), run_time=new_run_t)
self.play(label52.animate.move_to(s_rect5.get_center()), run_time=new_run_t)
dot5 = MathTex(r"\cdot").next_to(label52, RIGHT)
self.add(dot5)
self.play(label82.animate.next_to(dot5, RIGHT), run_time=new_run_t)
subgroup5 = VGroup(label82, label52, dot5)
s_rect6 = Polygon(line51.start, line51.end, line61.end, line61.start, fill_color=PURPLE,
fill_opacity=0.5).shift(np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect6, RIGHT), run_time=new_run_t)
self.play(label51.animate.move_to(s_rect6.get_center()), run_time=new_run_t)
dot6 = MathTex(r"\cdot").next_to(label51, RIGHT)
self.add(dot6)
self.play(label72.animate.next_to(dot6, RIGHT))
subgroup6 = VGroup(label72, dot6, label51)
s_rect7 = Polygon(line41.start, line41.end, line73.start, line73.end, fill_color=WHITE, fill_opacity=0.5).shift(
np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect7, UP), run_time=new_run_t)
self.play(label61.animate.move_to(s_rect7.get_center()), run_time=new_run_t)
dot7 = MathTex(r"\cdot").next_to(label61, RIGHT)
self.add(dot7)
self.play(label73.animate.next_to(dot7, RIGHT))
subgroup7 = VGroup(label73, label61, dot7)
s_rect8 = Polygon(line62.start, line62.end, line32.start, line32.end, fill_color=GOLD, fill_opacity=0.5).shift(
np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect8, LEFT), run_time=new_run_t)
self.play(label62.animate.move_to(s_rect8.get_center()), run_time=new_run_t)
dot8 = MathTex(r"\cdot").next_to(label62, RIGHT)
self.add(dot8)
self.play(label83.animate.next_to(dot8, RIGHT))
subgroup8 = VGroup(label83, dot8, label62)
s_rect9 = Polygon(line63.start, line63.end, line31.start, line31.end, fill_color=PINK, fill_opacity=0.5).shift(
np.array([-5, -4, 0]))
self.play(GrowFromEdge(s_rect9, LEFT), run_time=new_run_t)
self.play(label63.animate.move_to((s_rect9.get_center())), run_time=new_run_t)
dot9 = MathTex(r"\cdot").next_to(label63, RIGHT)
self.add(dot9)
self.play(label23.animate.next_to(dot9, RIGHT))
subgroup9 = VGroup(label23, dot9, label63)
brace_down = BraceBetweenPoints(line41.start, line31.start).shift(np.array([-5, -4, 0]))
self.play(Create(brace_down), run_time=new_run_t)
down_plus1 = MathTex("+").next_to(label32, LEFT)
down_plus2 = MathTex("+").next_to(label32, RIGHT)
self.add(down_plus2, down_plus1)
self.play(label33.animate.next_to(down_plus1, LEFT), run_time=new_run_t)
self.play(label31.animate.next_to(down_plus2, RIGHT), run_time=new_run_t)
brace_left = BraceBetweenPoints(line43.end, line41.start).shift(np.array([-5, -4, 0]))
self.play(Create(brace_left), run_time=new_run_t)
left_plus1 = MathTex("+").next_to(label42, UP)
left_plus2 = MathTex("+").next_to(label42, DOWN)
self.add(left_plus2, left_plus1)
self.play(label43.animate.next_to(left_plus1, UP), run_time=new_run_t)
self.play(label41.animate.next_to(left_plus2, DOWN), run_time=new_run_t)
equals1 = MathTex("=(").scale(1).move_to(LEFT * 6 + UP * 8)
self.play(Create(equals1), run_time=new_run_t)
group_left = VGroup(down_plus2, down_plus1, label31, label32, label33)
self.play(group_left.animate.next_to(equals1, RIGHT))
middle = MathTex(r")\cdot(").next_to(group_left)
self.add(middle)
# group_right = VGroup(left_plus2, left_plus1, label42, label43, label41)
# self.play(group_right.animate.next_to(middle, RIGHT))
self.play(label43.animate.next_to(middle, RIGHT), run_time=new_run_t)
self.play(left_plus1.animate.next_to(label43, RIGHT), run_time=new_run_t)
self.play(label42.animate.next_to(left_plus1, RIGHT), run_time=new_run_t)
self.play(left_plus2.animate.next_to(label42, RIGHT), run_time=new_run_t)
self.play(label41.animate.next_to(left_plus2, RIGHT), run_time=new_run_t)
right = MathTex(")").next_to(label41, RIGHT)
self.add(right)
equals2 = MathTex("=").scale(1).align_to(equals1, LEFT).shift(UP * 7)
self.add(equals2)
self.play(subgroup1.animate.next_to(equals2, RIGHT), run_time=new_run_t)
plus1 = MathTex("+").scale(1).next_to(subgroup1, RIGHT)
self.add(plus1)
self.play(subgroup2.animate.next_to(plus1, RIGHT), run_time=new_run_t)
plus2 = plus1.copy().next_to(subgroup2, RIGHT)
self.add(plus2)
self.play(subgroup3.animate.next_to(plus2, RIGHT), run_time=new_run_t)
plus3 = plus2.copy().next_to(subgroup3, RIGHT)
self.add(plus3)
self.play(subgroup4.animate.next_to(plus3, RIGHT), run_time=new_run_t)
plus4 = plus3.copy().next_to(subgroup4, RIGHT)
self.add(plus4)
self.play(subgroup5.animate.next_to(plus4, RIGHT), run_time=new_run_t)
plus5 = plus4.copy().next_to(subgroup5, RIGHT)
self.add(plus5)
self.play(subgroup6.animate.move_to(LEFT * 5 + UP * 6), run_time=new_run_t)
plus6 = plus5.copy().next_to(subgroup6, RIGHT)
self.add(plus6)
self.play(subgroup7.animate.next_to(plus6, RIGHT), run_time=new_run_t)
plus7 = plus6.copy().next_to(subgroup7, RIGHT)
self.add(plus7)
self.play(subgroup8.animate.next_to(plus7, RIGHT), run_time=new_run_t)
plus8 = plus7.copy().next_to(subgroup8, RIGHT)
self.add(plus8)
self.play(subgroup9.animate.next_to(plus8, RIGHT), run_time=new_run_t)
result = MathTex(r"={{a}}^2+{{b}}^2+{{c}}^2+2{{a}}{{b}}+2{{a}}{{c}}+2{{b}}{{c}}",
).align_to(equals1, LEFT).shift(UP * 5)
result.set_color_by_tex("a", RED)
result.set_color_by_tex("b", YELLOW)
result.set_color_by_tex("c", BLUE)
self.play(Write(result))
self.wait(4)