How can I highlight individual entries in \binom{n}{k} and create an empty binomial coefficient bracket

[mrs-isi]

Hi everyone,

I’m working on a didactic scene in Manim to explain the Hockey Stick Identity.
In my Manim scene, I have built a main formula using binomial coefficients like this:
\binom{2}{2} + \binom{3}{2} + \binom{4}{2} + \binom{5}{2} = \binom{6}{3}

Now I want to visually transition to the general formula and help the audience understand the role of each part.

What I want to achieve:
• A blank binomial expression (just the brackets with nothing inside) should appear below the main formula.
• Then, all the bottom entries (the 2s) in the top binomial coefficients should light up at the same time in pink (or another color) and stay pink – but only the bottom entries.
• At the same time, the lower part of the blank binomial coefficient should be filled with a pink “k” that also lights up and stays.
• Later, I plan to do something similar for the top entries.

My problem:
• I can’t find a way to isolate or color just the denominator in something like MathTex(r"\binom{3}{2}").
When I try something like: binom.get_parts_by_tex("2")[1] I get an IndexError: list index out of range.
Even when I loop through enumerate(binom), I only get a single submobject that covers the entire expression \binom{3}{2}. I also tried manually creating the binomial using individual arguments:

binom1 = MathTex(r"\binom", "{2}", "{2}", font_size=32)
self.add(binom1)
self.play(binom1[2].animate.set_color(PINK))

But this renders incorrectly or does not behave like a proper \binom{2}{2} visually. So this approach didn’t solve it either.
• I also don’t know how to properly create a blank binomial structure (with no entries), so I can animate inserting the “k” and “n” later.

My questions:
• How can I isolate and animate only the bottom entry (denominator) of a binomial coefficient in Manim?
• How can I create a blank binomial coefficient template that I can fill dynamically during the animation?

Any tips, suggestions or code examples would be highly appreciated. Thanks in advance!
Isa

[uwezi]

You cannot split an equation like this, because the individual parts must remain valid LaTeX code, which for example \binom on its own is not.

The recommended way to do this is to identify the individual indices of your glyphs:

class binomscene(Scene):
    def construct(self):
        binom1 = MathTex(r"\binom{2}{2}", font_size=32)
        self.add(binom1)
        self.add(index_labels(binom1[0]).set_color(RED))

class binomscene(Scene):
    def construct(self):
        binom1 = MathTex(r"\binom{2}{2}", font_size=32)
        self.add(binom1)
        # uncomment following line for index labels
        #self.add(index_labels(binom1[0]).set_color(RED))
        self.play(
            binom1[0][1].animate.set_color(PURE_BLUE),
            binom1[0][2].animate.set_color(PURE_RED),
        )
        self.wait()

binomscene.mp4