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Graphs

Axes, curves drawn from a Python function, number lines and grids.

Axes and a curve

from pymations import *

axes = Axes(x_range=[-3, 3, 1], y_range=[0, 9, 3], x_length=8, y_length=5)
parabola = axes.plot(lambda x: x ** 2, color=BLUE)
label = axes.get_graph_label(parabola, "y = x^2", x_val=2)

play(Create(axes))
play(Create(parabola), Write(label))
wait()
  • x_range=[start, end, step] is the numbers the x axis covers, and how far apart its ticks are. y_range is the same for y.
  • x_length and y_length are how big the axes are on screen, in picture units. Without them, axes are 12 wide and 6 tall.
  • tips=False leaves off the arrow tips. axis_config={"color": GREEN} colours both axes.

axes.plot(f) draws the function f across the x range. The function gets an x and returns a y; lambda x: x ** 2 is a short way to write one. np.sin, np.cos, np.exp and np.sqrt are ready to use. axes.plot(f, x_range=[0, 2]) draws only part of it.

Points on the axes

The axes have their own numbers, which are not picture units. axes.c2p(x, y) ("coordinates to point") turns graph numbers into a place in the picture:

from pymations import *

axes = Axes(x_range=[0, 5, 1], y_range=[0, 5, 1], x_length=6, y_length=6)
dot = Dot(axes.c2p(3, 2), color=YELLOW)
label = MathTex("(3, 2)").next_to(dot, UR, buff=0.1)

play(Create(axes))
play(GrowFromCenter(dot), Write(label))
wait()
HelperWhat it gives
axes.c2p(x, y)The place in the picture for the graph point (x, y)
axes.i2gp(x, graph)The place on graph above x
axes.get_graph_label(graph, "f(x)", x_val=2)A maths label beside the curve, at x_val
axes.get_axis_labels("x", "y")Labels at the ends of the two axes
axes.x_axis, axes.y_axisEach axis on its own

Curves drawn by a parameter

For a curve that is not "y of x", such as a circle or a spiral, give a function of t that returns a point:

from pymations import *

axes = Axes(x_range=[-2, 2, 1], y_range=[-2, 2, 1], x_length=6, y_length=6)
spiral = axes.plot_parametric_curve(
    lambda t: [t * np.cos(t) / 6, t * np.sin(t) / 6, 0],
    t_range=[0, 4 * PI],
    color=ORANGE,
)

play(Create(axes))
play(Create(spiral), run_time=3)

Number lines and grids

from pymations import *

plane = NumberPlane()
line = NumberLine(x_range=[-5, 5, 1], include_numbers=True).shift(DOWN * 3)

play(Create(plane), run_time=2)
play(Create(line))
wait()
  • NumberPlane() is a grid of blue lines covering the whole picture, with the axes in white. It has the same x_range, y_range and c2p as Axes.
  • NumberLine(x_range=[-5, 5, 1]) is one line with ticks. include_numbers=True writes the numbers under the ticks; line.n2p(2) is the place of the number 2.

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