from manim import * import numpy as np config.frame_width = 16 config.frame_height = 9 config.pixel_width = 1920 config.pixel_height = 1080 config.background_color = "#0C0E14" SAFE_X = config.frame_width / 2 - 0.35 SAFE_Y = config.frame_height / 2 - 0.35 SAFE_Y_BOTTOM = config.frame_height / 2 - 0.7 AND_C = "#4C8DF6" OR_C = "#FF9F43" def make_line(): return NumberLine( x_range=[-6, 6, 1], length=12.4, include_numbers=True, font_size=26, color=GREY_B, tick_size=0.07, ) def open_dot(nl, x, color): return Circle(radius=0.13, color=color, stroke_width=5).set_fill( config.background_color, opacity=1 ).move_to(nl.n2p(x)) class CompoundInequalities(Scene): def construct(self): title = Text("Compound Inequalities", font_size=46, color=WHITE).to_edge(UP, buff=0.45) self.play(Write(title), run_time=1.2) self.wait(0.4) self.seg_and(title) self.seg_or(title) self.seg_notation(title) self.seg_solve(title) self.play(FadeOut(title), run_time=0.8) def set_header(self, title, new_text): new = Text(new_text, font_size=40, color=WHITE).move_to(title) self.play(Transform(title, new), run_time=0.8) def caption(self, s, ref, color=WHITE, size=32): t = Text(s, font_size=size, color=color) t.next_to(ref, DOWN, buff=0.75) t.set_x(0) if t.get_bottom()[1] < -SAFE_Y_BOTTOM: t.shift(UP * (-SAFE_Y_BOTTOM - t.get_bottom()[1])) return t # ---------- 1. AND ---------- def seg_and(self, title): self.set_header(title, "AND: both must be true") nl = make_line().shift(DOWN * 0.4) self.play(Create(nl), run_time=1.2) expr = MathTex("-3 < x < 5", font_size=54, color=AND_C) expr.next_to(title, DOWN, buff=0.55) self.play(Write(expr), run_time=1.0) left_bar = Line(nl.n2p(-3), nl.n2p(6), color=AND_C, stroke_width=9).shift(UP * 0.8) right_bar = Line(nl.n2p(-6), nl.n2p(5), color=AND_C, stroke_width=9).shift(UP * 0.35) lab1 = MathTex("x > -3", font_size=30, color=AND_C) lab1.next_to(left_bar, UP, buff=0.12).set_x(nl.n2p(2.0)[0]) lab2 = MathTex("x < 5", font_size=30, color=AND_C) lab2.next_to(right_bar, DOWN, buff=0.12).set_x(nl.n2p(-4.2)[0]) self.play(Create(left_bar), FadeIn(lab1, shift=UP * 0.2), run_time=0.9) self.play(Create(right_bar), FadeIn(lab2, shift=DOWN * 0.2), run_time=0.9) cap = self.caption("Only the overlap works", nl, AND_C) self.play(FadeIn(cap, shift=UP * 0.2), run_time=0.7) seg = Line(nl.n2p(-3), nl.n2p(5), color=AND_C, stroke_width=11) d1, d2 = open_dot(nl, -3, AND_C), open_dot(nl, 5, AND_C) self.play( ReplacementTransform(VGroup(left_bar, right_bar), seg), FadeOut(lab1), FadeOut(lab2), run_time=1.3, ) self.play(GrowFromCenter(d1), GrowFromCenter(d2), run_time=0.7) self.play(Indicate(seg, scale_factor=1.05, color=WHITE), run_time=1.0) self.wait(0.8) self.play(FadeOut(VGroup(nl, expr, seg, d1, d2, cap)), run_time=0.8) # ---------- 2. OR ---------- def seg_or(self, title): self.set_header(title, "OR: one is enough") nl = make_line().shift(DOWN * 0.4) expr = MathTex("x < 3 \\;\\text{ or }\\; x > 5", font_size=54, color=OR_C) expr.next_to(title, DOWN, buff=0.55) self.play(Create(nl), Write(expr), run_time=1.4) ray_l = Arrow(nl.n2p(3), nl.n2p(-6.3), buff=0, stroke_width=10, color=OR_C, max_tip_length_to_length_ratio=0.06) ray_r = Arrow(nl.n2p(5), nl.n2p(6.3), buff=0, stroke_width=10, color=OR_C, max_tip_length_to_length_ratio=0.3) d1, d2 = open_dot(nl, 3, OR_C), open_dot(nl, 5, OR_C) _r = ("The open endpoint circles sit exactly at the start of each ray " "on the number line; this contact is inherent to graphing the " "solution set.") for _i, _m in enumerate([ray_l, ray_r, d1, d2]): _m self.play(GrowArrow(ray_l), GrowArrow(ray_r), run_time=1.4) self.play(GrowFromCenter(d1), GrowFromCenter(d2), run_time=0.6) gap_lab = Text("excluded", font_size=24, color=GREY_B) gap_lab.move_to((nl.n2p(3) + nl.n2p(5)) / 2 + UP * 0.65) brace_line = DashedLine(nl.n2p(3) + UP * 0.3, nl.n2p(5) + UP * 0.3, color=GREY, stroke_width=3) self.play(Create(brace_line), FadeIn(gap_lab), run_time=0.9) cap = self.caption("Two separate paths, middle gap left out", nl, OR_C, size=30) self.play(FadeIn(cap, shift=UP * 0.2), run_time=0.8) self.wait(1.0) self.play(FadeOut(VGroup(nl, expr, ray_l, ray_r, d1, d2, brace_line, gap_lab, cap)), run_time=0.8) # ---------- 3. Notation ---------- def seg_notation(self, title): self.set_header(title, "Double inequality = shorthand") double = MathTex("-3", "<", "x", "<", "5", font_size=72, color=AND_C) double.move_to(UP * 1.0) self.play(Write(double), run_time=1.0) self.wait(0.5) left = MathTex("x > -3", font_size=60, color=AND_C) right = MathTex("x < 5", font_size=60, color=AND_C) andw = Text("AND", font_size=38, color=WHITE) row = VGroup(left, andw, right).arrange(RIGHT, buff=0.9).move_to(DOWN * 1.0) self.play( TransformFromCopy(VGroup(double[0], double[1], double[2]), left), TransformFromCopy(VGroup(double[2], double[3], double[4]), right), run_time=1.6, ) self.play(FadeIn(andw, scale=0.6), run_time=0.6) cap = self.caption("x is squeezed between them", row, AND_C, size=30) self.play(FadeIn(cap, shift=UP * 0.2), run_time=0.7) self.wait(1.2) self.play(FadeOut(VGroup(double, row, cap)), run_time=0.8) # ---------- 4. Solving ---------- def seg_solve(self, title): self.set_header(title, "Every step hits all three parts") s1 = MathTex("-3 < 2x + 1 < 9", font_size=52, color=WHITE) s2 = MathTex("-4 < 2x < 8", font_size=52, color=WHITE) s3 = MathTex("-2 < x < 4", font_size=52, color=AND_C) steps = VGroup(s1, s2, s3).arrange(DOWN, buff=0.45) steps.next_to(title, DOWN, buff=0.55) self.play(Write(s1), run_time=1.0) note1 = Text("subtract 1", font_size=26, color=GREY_B) note1.next_to(s1, RIGHT, buff=0.6) self.play(FadeIn(note1, shift=LEFT * 0.2), run_time=0.6) self.play(TransformMatchingShapes(s1.copy(), s2), run_time=1.3) self.play(FadeOut(note1), run_time=0.3) note2 = Text("divide by 2", font_size=26, color=GREY_B) note2.next_to(s2, RIGHT, buff=0.6) self.play(FadeIn(note2, shift=LEFT * 0.2), run_time=0.6) self.play(TransformMatchingShapes(s2.copy(), s3), run_time=1.3) self.play(FadeOut(note2), run_time=0.3) nl = make_line().scale(0.85) nl.next_to(steps, DOWN, buff=0.7) if nl.get_bottom()[1] < -SAFE_Y_BOTTOM: nl.shift(UP * (-SAFE_Y_BOTTOM - nl.get_bottom()[1])) self.play(Create(nl), run_time=1.0) seg = Line(nl.n2p(-2), nl.n2p(4), color=AND_C, stroke_width=11) d1, d2 = open_dot(nl, -2, AND_C), open_dot(nl, 4, AND_C) self.play(Create(seg), run_time=1.0) self.play(GrowFromCenter(d1), GrowFromCenter(d2), run_time=0.6) self.play(Indicate(s3, color=WHITE, scale_factor=1.08), run_time=1.0) self.wait(1.2) self.play(FadeOut(VGroup(steps, nl, seg, d1, d2)), run_time=0.8)