How to Turn Markdown and LaTeX Equations Into Educational Videos: 10 Golpo Examples

The short answer: Golpo can turn a verified derivation into a visual lesson that reveals each step in the order students need it. Write the narration yourself, wrap short equations in single dollar signs and important display equations in double dollar signs, then paste the complete text into Golpo's Script Only input. Golpo narrates those words and builds the scenes. It keeps fractions, roots, exponents, subscripts, integrals, Greek symbols, and units available to the picture. It does not solve the problem or check the proof.

Quick tip: you do not need to write Markdown or LaTeX from memory. Paste any standard equation into ChatGPT, Claude, Gemini, or even Google and ask it to convert the expression to Markdown-compatible LaTeX before you insert it into Golpo's Script Only input. Check that the conversion has not changed the mathematics. If you use the Golpo API, ask Claude Code, Cursor, Codex, or GitHub Copilot to convert the equation and return a JSON-escaped custom_script value, with every LaTeX backslash doubled, before sending the request to Golpo.

Copyable conversion prompt: Convert this equation to Markdown-compatible LaTeX. Do not solve it or change the mathematics. Return only the equation, wrapped in $$...$$.

API version: Convert this equation to Markdown-compatible LaTeX and return it as a JSON-escaped custom_script string. Preserve the mathematics exactly and double every LaTeX backslash.

This closes an important gap for teachers, tutors, course creators, and education platforms. A script no longer has to flatten x squared, lambda, or a stacked fraction into ordinary prose and hope the visual generator reconstructs the notation. You can provide the intended mathematical expression directly.

This guide contains ten real tests generated from the exact scripts shown below. They cover calculus, integration, algebra, geometry, mechanics, thermodynamics, electricity, radioactive decay, waves, and statistics. The eight Canvas outputs use Editorial, Whiteboard, Chalkboard (B/W), Technical, Modern Minimal, Sharpie, and Chalkboard Color; the two Sketch outputs use Dry Erase and Professional Clean. The examples are deliberately short so you can inspect the notation rather than sit through ten long lessons.

→ Equation syntax  ·  Six-step workflow  ·  10 scripts and outputs  ·  Three-step derivation  ·  API example  ·  Quality checklist  ·  FAQ

The equation syntax Golpo receives

The input uses familiar Markdown math delimiters with LaTeX-style commands inside them. Technically, Markdown itself does not define one universal math standard; this is the convention used by many notebooks, learning platforms, and documentation tools.

• Inline math: use one dollar sign on each side: $x = 1$.
• Display math: use two dollar signs on each side: $$f'(x) = 12x^3 - 10x + 7$$.
• Fractions: \frac{a}{b}.
• Square roots: \sqrt{b^2 - 4ac}.
• Exponents: x^2 or e^{-kt}.
• Subscripts: N_0 or t_{1/2}.
• Greek symbols: \lambda, \mu, \sigma, and \Omega.
• Integrals and limits: \int_0^3 2x\,dx.
• Units inside equations: 36\,\mathrm{N}.

Use display math for the equation the learner must read. Keep spoken transitions outside the delimiters. That separation gives the narrator natural prose and gives the visual system a clean mathematical block.

Script Only in the app is not the same as the API's script-only flag

There is an easy naming trap:

• In the Golpo application: choose the Script Only input when you want to paste the exact narration yourself. That is Script Mode: Golpo renders the supplied words, about 1,050 characters per selected minute. Put visual directions in Video Instructions, not among the spoken lines. See Prompt Mode and Script Mode.
• In REST API v2: put that narration in custom_script. Do not set enable_script_only_mode to true when you want a rendered video. That API field returns only generated script text and skips video rendering.

The current field names and engine options are documented in the Golpo REST API v2 reference.

A reliable six-step workflow for equation videos

1. Verify the mathematics first. Golpo follows the supplied script; it is not a substitute for checking the derivation. Confirm every operator, exponent, unit, substitution, and final result.
2. Write the teaching narration. Add a short sentence before each equation explaining the goal, and a short sentence afterward explaining the result. Equations without transitions feel like a silent answer key.
3. Add the math delimiters. Use $...$ for brief inline values and $$...$$ for the important working lines. Keep opening and closing delimiters balanced.
4. Paste the complete text into Script Only. Do not strip the backslashes or replace the dollar signs before submission.
5. Choose the visual engine and exact style. Canvas Technical, Whiteboard, and Modern Minimal are strong starting points for structured layouts, diagrams, and clean technical visuals. Sketch Dry Erase creates a classroom-board treatment, while Sketch Professional Clean gives hand-drawn lessons a more polished look.
6. Inspect the result, not just the job status. Watch every equation appear. A completed render can still contain a missing minus sign, a confusing uppercase letter, or an ambiguous unit.

Choosing a specific Canvas or Sketch style for mathematical content

Choose	Useful when	Watch for
Canvas Editorial, Whiteboard, Chalkboard (B/W), Technical, Modern Minimal, Sharpie, or Chalkboard Color	You want structured diagrams, technical layouts, clean graphs, or a subject-specific visual treatment.	Choose the named style deliberately and do not overcrowd one frame with several long derivations.
Sketch Dry Erase or Professional Clean	You want a hand-drawn progression, either on a classroom-style board or with a cleaner professional finish.	Inspect similar-looking symbols carefully, especially lowercase and uppercase variables.

10 equation scripts and their real Golpo outputs

Every code block below is the exact custom script submitted for that video. The plain-language block above it shows how a teacher might read the same lesson without the Markdown notation.

1. Calculus derivative and tangent slope — Canvas Editorial

Equation shown: f′(x) = d/dx(3x⁴ − 5x² + 7x) = 12x³ − 10x + 7; therefore f′(1) = 9.

Teaching script

Differentiate each term, evaluate the derivative at x equals one, and conclude that the slope of the tangent line is nine.

Exact Markdown/LaTeX passed to Golpo

From the problem statement, we have:

$$f'(x) = \frac{d}{dx}\left(3x^4 - 5x^2 + 7x\right) = 12x^3 - 10x + 7$$

Evaluating at $x = 1$:

$$f'(1) = 12(1)^3 - 10(1) + 7 = 12 - 10 + 7 = 9$$

Therefore, the slope of the tangent line at $x = 1$ is 9.

Open the calculus output on Golpo.

2. Definite integral and area under a curve — Canvas Whiteboard

Equation shown: A = ∫₀³ 2x dx = [x²]₀³ = 9 square units.

Teaching script

Integrate two x from zero to three, evaluate the antiderivative at both limits, and interpret the result as area.

Exact Markdown/LaTeX passed to Golpo

To find the area under y equals 2x from x equals zero to x equals three, evaluate:

$$A = \int_0^3 2x\,dx$$

An antiderivative of 2x is x squared, so:

$$A = \left[x^2\right]_0^3 = 3^2 - 0^2 = 9$$

Therefore, the area is 9 square units.

Open the integral output on Golpo.

3. Quadratic formula and two roots — Canvas Chalkboard (B/W)

Equation shown: x = (−b ± √(b² − 4ac)) / 2a, producing x = 2 and x = 3.

Teaching script

Identify a, b, and c, substitute them into the quadratic formula, simplify the discriminant, and calculate both roots.

Exact Markdown/LaTeX passed to Golpo

Solve the quadratic equation:

$$x^2 - 5x + 6 = 0$$

Using the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

With a equals 1, b equals negative 5, and c equals 6:

$$x = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2}$$

Therefore, the two roots are $x = 2$ and $x = 3$.

Open the quadratic-formula output on Golpo.

4. Pythagorean theorem — Canvas Technical

Equation shown: c = √(6² + 8²) = √100 = 10.

Teaching script

Use the two legs in the Pythagorean theorem, add their squares, and take the square root to find the hypotenuse.

Exact Markdown/LaTeX passed to Golpo

A right triangle has legs of 6 units and 8 units. The Pythagorean theorem states:

$$c^2 = a^2 + b^2$$

Substitute the two leg lengths:

$$c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Therefore, the hypotenuse is 10 units long.

Open the geometry output on Golpo.

5. Newton's second law — Canvas Technical

Equation shown: F = ma = (12 kg)(3 m/s²) = 36 N.

Teaching script

Multiply the object's mass by its acceleration and report the net force in newtons.

Exact Markdown/LaTeX passed to Golpo

A 12-kilogram object accelerates at 3 meters per second squared. Newton's second law is:

$$F = ma$$

Substitute the mass and acceleration:

$$F = (12\,\mathrm{kg})(3\,\mathrm{m/s^2}) = 36\,\mathrm{N}$$

Therefore, the net force acting on the object is 36 newtons.

Open the mechanics output on Golpo.

6. Ideal gas law — Canvas Modern Minimal

Equation shown: P = nRT/V = (1 × 0.0821 × 300) / 24.6 ≈ 1.00 atm.

Teaching script

Rearrange the ideal gas law for pressure, substitute the amount, temperature, gas constant, and volume, then calculate the pressure.

Exact Markdown/LaTeX passed to Golpo

One mole of an ideal gas is at 300 kelvin in a 24.6-liter container. From the ideal gas law:

$$PV = nRT$$

Solve for pressure:

$$P = \frac{nRT}{V}$$

Using R equals 0.0821 liter-atmospheres per mole-kelvin:

$$P = \frac{(1)(0.0821)(300)}{24.6} \approx 1.00\,\mathrm{atm}$$

Therefore, the gas pressure is approximately one atmosphere.

Open the ideal-gas output on Golpo.

7. Ohm's law and electrical power — Canvas Sharpie

Equation shown: I = V/R = 3 A, followed by P = VI = 36 W.

Teaching script

Divide voltage by resistance to find current, then multiply voltage and current to find the power dissipated.

Exact Markdown/LaTeX passed to Golpo

A 12-volt source is connected across a 4-ohm resistor. Ohm's law gives the current:

$$I = \frac{V}{R} = \frac{12\,\mathrm{V}}{4\,\Omega} = 3\,\mathrm{A}$$

Now calculate the electrical power:

$$P = VI = (12\,\mathrm{V})(3\,\mathrm{A}) = 36\,\mathrm{W}$$

The circuit carries 3 amperes and dissipates 36 watts.

Open the electricity output on Golpo.

8. Radioactive decay and half-life — Canvas Chalkboard Color

Equation shown: N(t) = N₀(1/2)^(t/t½); after 24 days, N(24) = 20 mg.

Teaching script

Use the half-life model, identify that 24 days contains three eight-day half-lives, and calculate the remaining mass.

Exact Markdown/LaTeX passed to Golpo

A radioactive sample begins with 160 milligrams and has a half-life of 8 days. Its remaining mass is modeled by:

$$N(t) = N_0\left(\frac{1}{2}\right)^{t/t_{1/2}}$$

After 24 days, three half-lives have passed:

$$N(24) = 160\left(\frac{1}{2}\right)^{24/8} = 160\left(\frac{1}{2}\right)^3 = 20\,\mathrm{mg}$$

Therefore, 20 milligrams remain.

Open the radioactive-decay output on Golpo.

9. Wave speed, wavelength, and frequency — Sketch Dry Erase

Equation shown: v = fλ; therefore f = v/λ = 340/0.68 = 500 Hz.

Teaching script

Start with the wave equation, rearrange it for frequency, and divide the wave speed by the wavelength.

Exact Markdown/LaTeX passed to Golpo

A sound wave travels at 340 meters per second and has a wavelength of 0.68 meters. The wave equation is:

$$v = f\lambda$$

Solve for frequency:

$$f = \frac{v}{\lambda} = \frac{340\,\mathrm{m/s}}{0.68\,\mathrm{m}} = 500\,\mathrm{Hz}$$

Therefore, the sound wave has a frequency of 500 hertz.

Open the wave-frequency output on Golpo.

10. Statistics and a z-score — Sketch Professional Clean

Equation shown: z = (x − μ)/σ = (85 − 70)/10 = 1.5.

Teaching script

Subtract the mean from the score, divide by the standard deviation, and interpret the result as distance above the mean.

Exact Markdown/LaTeX passed to Golpo

A test score is 85. The class mean is 70, and the standard deviation is 10. The z-score formula is:

$$z = \frac{x - \mu}{\sigma}$$

Substitute the values:

$$z = \frac{85 - 70}{10} = \frac{15}{10} = 1.5$$

Therefore, the score is 1.5 standard deviations above the mean.

Open the statistics output on Golpo.

Create the same equation video with Golpo API v2

In the application, you paste the text into Script Only. In REST API v2, the rendering equivalent is custom_script. The following example uses the same calculus script as the first video:

{
  "prompt": "Explain a calculus derivative and tangent slope",
  "custom_script": "From the problem statement, we have:\n\n$$f'(x) = \\frac{d}{dx}\\left(3x^4 - 5x^2 + 7x\\right) = 12x^3 - 10x + 7$$\n\nEvaluating at $x = 1$:\n\n$$f'(1) = 12(1)^3 - 10(1) + 7 = 12 - 10 + 7 = 9$$\n\nTherefore, the slope of the tangent line at $x = 1$ is 9.",
  "golpo_video_engine": "golpo_canvas",
  "canvas_style_variant": "whiteboard",
  "narration_voice": "female-1",
  "narration_language": "en",
  "timing": "0.5",
  "video_orientation": "horizontal",
  "visibility": "private"
}

For Sketch Classic, change the engine fields to:

{
  "golpo_video_engine": "golpo_sketch",
  "sketch_style_variant": "classic"
}

The API request is asynchronous: submit the generation request, store the returned job ID, and poll the documented status endpoint until a video URL is available. For complete parameter examples, see the Golpo API payload guide and the production API v2 pipeline guide.

How to write equation scripts that teach rather than merely display

Correct typography is only half the job. A useful educational video must control cognitive load.

• One reasoning step per display equation. Do not paste an entire page-long derivation inside one pair of double dollar signs.
• Say what changes between lines. “Substitute the known values” and “solve for pressure” tell the learner why the next equation appears.
• Keep the important invariant visible. If you rearrange an equation, show the original relationship before the rearranged form.
• State units in narration and notation. A result of 36 is incomplete when the answer should be 36 newtons or 36 watts.
• End with interpretation. “The score is 1.5 standard deviations above the mean” teaches more than ending on z = 1.5.
• Split dense proofs into a series. Several short videos are usually easier to check and easier to learn from than one overloaded render.

A three-step derivation students can follow

The ten lessons above show that a checked equation can survive into the video. A derivation needs one more decision: which relationship stays together, and which transformation gets its own frame. Students lose the quotient rule at the minus sign. This script keeps that sign in the narration you approve. Verify it yourself before you generate. The script is ready to paste; the ten videos above are the rendered notation tests.

Students often drop the minus sign in the quotient rule. Start from the function:

$$f(x) = \frac{x^2}{x+1}$$

The quotient rule multiplies the derivative of the numerator by the denominator, then subtracts the numerator times the derivative of the denominator, all over the denominator squared:

$$f'(x) = \frac{2x(x+1) - x^2(1)}{(x+1)^2}$$

Simplify the numerator. Two x times x plus one is 2x squared plus 2x, and subtracting x squared leaves x squared plus 2x, which factors as x times the quantity x plus two:

$$f'(x) = \frac{2x^2 + 2x - x^2}{(x+1)^2} = \frac{x^2 + 2x}{(x+1)^2} = \frac{x(x+2)}{(x+1)^2}$$

The minus sign between those terms is the step to read on screen.

Scene density

Before you render, open Custom Scenes and give each display equation its own scene: the function, the quotient-rule line, then the simplified result. Custom Scenes is on Growth and higher, and on Pay As You Go. The map does not rewrite the narration, and it does not prove the algebra.

Expanded is the teaching cut. Each transformation has room, which is what keeps a fraction readable. Compact is the review card: the function and its derivative stay in one relationship. Notebook is Compact-only. In the API, an unsuffixed style value selects Compact, and _legacy selects Expanded on the ten pre-Notebook styles. Color begins at Growth.

Save a technical Custom Style once—from a photo of a clear board, a short clip, or a description such as dark ink, wide margins, and one equation family per frame—and reuse it on the next worked solution. Custom Style is on Business and higher. API use also needs API access. It will not reproduce a typeface pixel for pixel.

On-screen text from script only, on Canvas and Sketch, limits generated labels to this script. Golpo may show a subset. It is not a caption track, and it is not a check that the minus sign is mathematically correct.

If the minus sign flips

Watch the second scene. The spoken line and the picture should both show subtraction, 2x(x+1) - x^2, not a plus. If the label flips the sign, correct that frame with frame editing. The edit changes the picture. It does not change the narration. The first edited version is free across sessions until finalized. Frame editing is on all paid plans, and later versions are charged on the selected duration of that version.

Then play the Expanded cut on a phone. Each display equation should stay readable without zoom. If the minus sign and the fraction bar collide, split that sentence into its own scene and generate again, or edit the crowded label.

The teacher's voice

To keep this LaTeX script and speak it in a teacher's authorized voice, create a voice clone with permission and select that saved voice for the Script Only lesson. Voice clone is on Business and higher, and on Pay As You Go. It generates new narration. It is not a recording of the class, and it still needs a pronunciation check on "minus" and on the variables.

If the teacher already recorded the explanation, use Own Narration instead. The recording is the soundtrack. It sets the duration and the language, and a language setting does not translate it. Dollar signs in a script do not drive that pass, so put the three equations in Video Instructions and review every symbol. Audio-only upload does not put the teacher on screen. A video recording can use Picture-in-Picture when the teacher should stay visible. Own Narration is on Business, Scale, and Pay As You Go.

Credits for a one-minute lesson

Select 1 minute for this derivation. Standard video is 1 credit per selected minute. A later frame edit of that minute is charged again on the selected duration, so budget another credit and confirm the quote in the project. Voice clone and Custom Style do not change that per-minute rate; they change which plan you need. The next problem the class asks about—a different function, the same style, the same three-scene pattern—is a second 1-credit lesson, not a duplicate of this one. The Free plan is not a downloadable publishing workflow. See pricing.

Equation-video quality checklist

Before publishing or assigning the video, check all of the following:

• The opening and closing dollar signs are balanced.
• Fractions have the intended numerator and denominator.
• Minus signs have not disappeared or become dashes in the wrong place.
• Exponents and subscripts are attached to the correct symbol.
• Greek characters are visually distinct from similar Latin characters.
• Units remain attached to their values.
• Intermediate substitutions match the verified solution.
• The spoken narration describes the same equation shown on screen.
• The final answer is visible long enough to read.
• The equation remains legible on the smallest screen your learners use.

For assessed, medical, engineering, or safety-critical material, require subject-matter review. A clean render is not evidence that the underlying mathematics or science is correct.

Common mistakes

• Using enable_script_only_mode in API v2 and expecting a video. That option stops after script generation. Use custom_script for a supplied script that should be rendered.
• Putting every sentence inside $$...$$. Only the equation belongs inside the display delimiters.
• Leaving unmatched braces or dollar signs. Copy the script into a plain-text editor and check delimiter pairs before submission.
• Trusting an AI-generated derivation without verification. Solve and review first; render second.
• Using a rare LaTeX package command without testing it. Start with common commands such as fractions, roots, Greek symbols, integrals, exponents, and subscripts.
• Choosing style before legibility. The most attractive frame is not useful if a learner cannot distinguish a variable from a unit.

Frequently asked questions

Does Golpo solve the equation for me in Script Only mode?

No. Script Only follows the script you provide. Verify the mathematics first or use a separately reviewed source solution.

Should I use single or double dollar signs?

Use single dollar signs for short inline expressions, such as $x = 1$. Use double dollar signs for equations that deserve their own visual beat.

Which Golpo styles work for equation videos?

Both engines work, but choose a named style rather than stopping at the engine. The real outputs above use Canvas Editorial, Whiteboard, Chalkboard (B/W), Technical, Modern Minimal, Sharpie, and Chalkboard Color, plus Sketch Dry Erase and Professional Clean. Pick the treatment that supports the subject, then inspect the rendered notation before publishing.

Can I create equation videos through the Golpo API?

Yes. In REST API v2, pass the complete Markdown-style equation script in custom_script and select either the Golpo Canvas or Golpo Sketch engine. Do not set enable_script_only_mode to true when you want a rendered video. Submit the asynchronous job and poll for completion.

Should enable_script_only_mode be true when rendering my custom script?

No. In API v2, enable_script_only_mode returns script text without rendering a video. Use custom_script to provide the narration that should be rendered.

What should I check before publishing an equation video?

Check every operator, exponent, subscript, Greek symbol, unit, substitution, intermediate result, and final answer. Also listen for ambiguous narration, and confirm each display equation is readable on a phone.

How do I give each derivation step its own scene?

Use Custom Scenes on Growth and higher, or Pay As You Go, and put each transformation on its own sentence boundary. Expanded gives those steps room. Compact keeps a relationship, such as a function and its derivative, together. The scene map does not rewrite the narration or check the mathematics.

Can the lesson use a teacher's authorized voice?

Yes. A voice clone on Business and higher, or Pay As You Go, speaks a Script Only lesson in an authorized saved voice, so the LaTeX script stays the source. Own Narration instead uses a finished recording as the soundtrack. That recording sets duration and language, and a language setting does not translate it. Put equations in the visual direction for an Own Narration pass, because the audio does not carry LaTeX.

Can I use the workflow for chemistry, engineering, and statistics?

Yes, as the gas-law, circuit, decay, wave, and z-score examples demonstrate. For unfamiliar macros or very dense notation, make a short test render before producing a full lesson. Verify the mathematics independently.

Related Golpo guides

• Turn an exam question into an AI explainer video — use a screenshot when you have the problem but do not want to transcribe it.
• Convert notes into AI videos — build reusable lessons from class notes and study material.
• How to use Golpo AI for education — broader teaching and learning workflows.
• The Golpo prompt cheatsheet — use prompts when you want Golpo to draft the narration rather than supplying it word for word.
• Every Golpo video style — compare Canvas and Sketch treatments before choosing a look.

Make the solution you keep explaining again

Pick the worked solution students ask you to explain again. Verify every line, put each step in Script Only with the equations between dollar signs, and give each transformation its own scene. Generate a one-minute lesson in the technical style you saved. If a minus sign or a label is wrong, correct that frame, then reuse the same style on the next problem.

Create that lesson in Golpo