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Finished pythagorean triples project

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Grant Sanderson
2017-05-26 09:24:03 -07:00
parent 1a141362e1
commit fde7ae167b
1 changed files with 197 additions and 16 deletions
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213
triples.py
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@ -56,6 +56,7 @@ class IntroduceTriples(TeacherStudentsScene):
(3, 4, 5),
(5, 12, 13),
(8, 15, 17),
(7, 24, 25),
]
self.add(title)
@ -92,11 +93,13 @@ class IntroduceTriples(TeacherStudentsScene):
hyp_line.get_angle(),
about_point = hyp_line.get_center()
)
if c in [5, 13]:
if c in [5, 13, 25]:
if c == 5:
keys = range(0, 5, 2)
elif c == 13:
keys = range(0, 13, 3)
elif c == 25:
keys = range(0, 25, 4)
i_list = filter(
lambda i : (i%c) in keys and (i//c) in keys,
range(c**2)
@ -175,6 +178,8 @@ class CompareToFermatsLastTheorem(TeacherStudentsScene):
low_text.highlight(RED)
self.add(square_expression, top_brace, top_text)
self.change_student_modes(*["pondering"]*3)
self.play(self.teacher.change, "happy", run_time = 0)
self.play(
ReplacementTransform(
square_expression.copy(),
@ -330,6 +335,17 @@ class BabylonianTablets(Scene):
self.play(LaggedStart(FadeIn, triples, run_time = 5))
self.dither()
class AskAboutFavoriteProof(TeacherStudentsScene):
def construct(self):
self.student_says(
"What's you're \\\\ favorite proof?",
target_mode = "raise_right_hand"
)
self.change_student_modes("happy", "raise_right_hand", "happy")
self.teacher_thinks("", target_mode = "thinking")
self.dither()
self.zoom_in_on_thought_bubble()
class PythagoreanProof(Scene):
def construct(self):
self.add_title()
@ -497,18 +513,6 @@ class PythagoreanProof(Scene):
t2, t3 = group
return VGroup(t1, t2, t3)
##TODO, REMOVE
class LastVideoWrapper(Scene):
def construct(self):
title = TextMobject("Pi hiding in prime regularities")
title.to_edge(UP)
screen_rect = ScreenRectangle(height = 6)
screen_rect.next_to(title, DOWN)
self.play(ShowCreation(screen_rect))
self.play(Write(title))
self.dither()
class ReframeOnLattice(PiCreatureScene):
CONFIG = {
"initial_plane_center" : 3*LEFT + DOWN,
@ -977,6 +981,12 @@ class ReframeOnLattice(PiCreatureScene):
morty.to_corner(DOWN+LEFT, buff = MED_SMALL_BUFF)
return morty
class TimeToGetComplex(TeacherStudentsScene):
def construct(self):
self.teacher_says("Time to \\\\ get complex")
self.change_student_modes("angry", "sassy", "pleading")
self.dither(2)
class OneMoreExample(Scene):
CONFIG = {
"unit_size" : 0.5,
@ -2033,6 +2043,55 @@ class PointsWeMiss(VisualizeZSquared):
self.play(Blink(morty))
self.dither(2)
class PointsWeMissAreMultiplesOfOnesWeHit(TeacherStudentsScene):
def construct(self):
words = TextMobject(
"Every point we",
"miss",
"is \\\\ a multiple of one we",
"hit"
)
words.highlight_by_tex("miss", RED)
words.highlight_by_tex("hit", GREEN)
self.teacher_says(words)
self.change_student_modes(*["pondering"]*3)
self.dither(2)
class DrawSingleRadialLine(PointsWeMiss):
def construct(self):
self.add_plane()
self.background_plane.set_stroke(width = 1)
self.add_transformed_color_grid()
self.color_grid.set_stroke(width = 1)
self.add_dots()
self.draw_line()
def draw_line(self):
point = self.background_plane.coords_to_point(3, 4)
dot = Dot(point, color = RED)
line = Line(
self.plane_center,
self.background_plane.coords_to_point(15, 20),
color = WHITE,
)
added_dots = VGroup(*[
Dot(self.background_plane.coords_to_point(3*k, 4*k))
for k in 2, 3, 5
])
added_dots.highlight(GREEN)
self.play(GrowFromCenter(dot))
self.play(Indicate(dot))
self.play(ShowCreation(line), Animation(dot))
self.dither()
self.play(LaggedStart(
DrawBorderThenFill, added_dots,
stroke_color = PINK,
stroke_width = 4,
run_time = 3
))
self.dither()
class DrawRadialLines(PointsWeMiss):
CONFIG = {
"final_unit_size" : 0.2,
@ -2449,6 +2508,95 @@ class ProjectPointsOntoUnitCircle(DrawRadialLines):
self.play(FadeOut(lines))
self.dither()
class ICanOnlyDrawFinitely(TeacherStudentsScene):
def construct(self):
self.teacher_says(
"I can only \\\\ draw finitely",
run_time = 2
)
self.dither(2)
class SupposeMissingPoint(PointsWeMiss):
def construct(self):
self.add_plane()
self.background_plane.set_stroke(width = 1)
self.draw_missing_triple()
self.project_onto_unit_circle()
def draw_missing_triple(self):
point = self.background_plane.coords_to_point(12, 5)
origin = self.plane_center
line = Line(origin, point, color = WHITE)
dot = Dot(point, color = YELLOW)
triangle = Polygon(ORIGIN, RIGHT, RIGHT+UP)
triangle.set_stroke(BLUE, 2)
triangle.set_fill(BLUE, 0.5)
triangle.replace(line, stretch = True)
a = TexMobject("a")
a.next_to(triangle.get_bottom(), UP, SMALL_BUFF)
b = TexMobject("b")
b.add_background_rectangle()
b.next_to(triangle, RIGHT, SMALL_BUFF)
c = TexMobject("c")
c.add_background_rectangle()
c.next_to(line.get_center(), UP+LEFT, SMALL_BUFF)
triangle.add(a, b, c)
words = TextMobject(
"If we missed \\\\ a triple \\dots"
)
words.add_background_rectangle()
words.next_to(dot, UP+RIGHT)
words.shift_onto_screen()
self.add(triangle, line, dot)
self.play(Write(words))
self.dither()
self.words = words
self.triangle = triangle
self.line = line
self.dot = dot
def project_onto_unit_circle(self):
dot, line = self.dot, self.line
template_line = Line(*[
self.background_plane.number_to_point(n)
for n in -1, 1
])
circle = Circle(color = GREEN)
circle.replace(template_line, dim_to_match = 0)
z = self.background_plane.point_to_number(dot.get_center())
z_norm = abs(z)
unit_z = z/z_norm
new_point = self.background_plane.number_to_point(unit_z)
dot.generate_target()
dot.target.move_to(new_point)
line.generate_target()
line.target.scale(1./z_norm, about_point = self.plane_center)
rational_point_word = TexMobject("(a/c) + (b/c)i")
rational_point_word.next_to(
self.background_plane.coords_to_point(0, 6), RIGHT
)
rational_point_word.add_background_rectangle()
arrow = Arrow(
rational_point_word.get_bottom(),
dot.target,
buff = SMALL_BUFF
)
self.play(ShowCreation(circle))
self.add(dot.copy().fade())
self.add(line.copy().set_stroke(GREY, 1))
self.play(*map(MoveToTarget, [dot, line]))
self.dither()
self.play(
Write(rational_point_word),
ShowCreation(arrow)
)
self.dither(2)
class ProofTime(TeacherStudentsScene):
def construct(self):
self.teacher_says("Proof time!", target_mode = "hooray")
@ -2801,6 +2949,9 @@ class BitOfCircleGeometry(Scene):
]
O = circle.get_center()
O_dot = Dot(O, color = WHITE)
self.add(circle, O_dot)
groups = VGroup()
for point, tex, color in (O, "2", MAROON_B), (p2, "", RED):
line1 = Line(point, p0)
@ -2824,9 +2975,13 @@ class BitOfCircleGeometry(Scene):
group = VGroup(line1, line2, dot1, dot2)
group.highlight(color)
group.add(arc, label)
if len(groups) == 0:
self.play(*map(ShowCreation, [dot1, dot2]))
self.play(*map(ShowCreation, [line1, line2]))
self.play(ShowCreation(arc))
self.play(FadeIn(label))
groups.add(group)
self.add(circle, O_dot, groups[0])
self.dither(2)
self.play(ReplacementTransform(
groups[0].copy(), groups[1]
@ -2885,9 +3040,35 @@ class PatreonThanksTriples(PatreonThanks):
],
}
class Thumbnail(Scene):
class Thumbnail(DrawRadialLines):
def construct(self):
pass
self.force_skipping()
self.add_plane()
self.add_transformed_color_grid()
self.color_grid.set_stroke(width = 5)
self.resize_plane()
self.add_dots()
self.create_lines()
self.show_single_line()
self.show_all_lines()
rect = Rectangle(
height = 4.3, width = 4,
stroke_width = 3,
stroke_color = WHITE,
fill_color = BLACK,
fill_opacity = 1,
)
rect.to_corner(UP+RIGHT, buff = 0)
triples = VGroup(*map(TexMobject, [
"3^2 + 4^2 = 5^2",
"5^2 + 12^2 = 13^2",
"8^2 + 15^2 = 17^2",
"\\vdots"
]))
triples.arrange_submobjects(DOWN, buff = MED_LARGE_BUFF)
triples.next_to(rect.get_top(), DOWN)
self.add(rect, triples)