Lego Sine waves

 Using LEGO to explore sine waves!

As the circle rotates, a pen moves up & down—creating a sine or cosine curve when paired with horizontal motion. A perfect way to see why radians (not degrees) are the natural language of circles. #Maths #STEM #LEGO #SineWave #Radians

📐 From Circles to Sine Waves – Using LEGO to Visualise Trigonometry

Have you ever wondered where the sine and cosine curves really come from? They aren’t just mysterious waves floating on your calculator’s screen — they’re born from something beautifully simple: a rotating circle.

And what better way to bring this to life than with LEGO?

🧱 The LEGO Sine Machine

We built a basic LEGO model to show how circular motion generates a sine wave. The setup is simple:

• A LEGO wheel rotates steadily (powered by a crank, motor, or your fingers).

• A LEGO “pen” is attached to a point on the wheel’s edge and allowed to move vertically as the wheel turns.

• As the wheel rotates, the pen moves up and down.

• If you slide a piece of paper sideways under the pen (or move the whole setup horizontally), the pen traces out a perfect sine curve.

You’ve just turned rotational motion into a wave. Magic? Not quite — it’s maths.

🔁 The Maths Behind the Model

Each point on the edge of the circle moves in a repetitive cycle:

• At the top of the circle, the pen is at its highest point.

• As the wheel turns, the pen drops.

• At the bottom of the circle, it reaches its lowest point.

• Then it climbs again, back to the top.

This vertical movement is exactly what the sine function describes. If we plotted the horizontal angle of rotation against the vertical height of the pen, we’d get the classic sine wave.

If we instead plotted the horizontal angle against the horizontal distance from the centre, we’d get the cosine wave.

🎯 Why Radians Rule

This is where radians come in.

We’re often taught angles in degrees — 360° in a full turn. But the natural way to describe circular motion in maths is in radians, where a full circle is 2π radians. Why?

• Radians are based on arc length: 1 radian is the angle you get when the arc length equals the radius.

• That means if you turn the wheel by 1 radian, the point on the edge moves a distance equal to the radius — no conversions needed.

• The sine and cosine functions behave cleanly in radians — their calculus (derivatives and integrals) only works neatly in radians.

• And in your LEGO model, the smooth sine curve you see is based on the angle in radians growing linearly with time.

Using degrees would distort this natural relationship and require extra scaling factors. In radians, the maths just flows.

🧪 Classroom & STEM Ideas

This LEGO setup is a brilliant hands-on project for:

• GCSE and A-Level Maths: Visualise sine and cosine curves.

• Physics: Explore waveforms and oscillations.

• Engineering: Connect rotational and linear motion.

• Computing: Animate a sine wave using circular logic.

You could even motorise it and use a felt tip on a long roll of paper to draw continuous sine waves!

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🔄 Final Thoughts

Trigonometry doesn’t have to be all triangles and calculators. Sometimes, the best way to understand a mathematical concept is to build it — brick by brick.

So next time you’re puzzling over sine and cosine, just remember: somewhere, a little LEGO wheel is turning, and a wave is being born.