Spirograph Gears

This simulation recreates the spirograph toy. A gear rolls without slipping inside a 96-tooth ring, and a pen fixed to the gear draws a hypotrochoid curve. Students pick a gear from 24 to 63 teeth, drag the red pen dot closer to or farther from the gear center and set the rolling speed. Options stack each layer of the drawing in 3D, snap the pen to holes, loop the drawing or redraw it. Readouts show the gear to ring ratio, the pattern, the pen distance and how much is drawn. The number of petals equals the ring teeth divided by the greatest common divisor, linking art with ratios and number theory.

• Choose 40 teeth, wait for the drawing to finish and read the Pattern readout for the number of petals.
• Change Gear teeth to 45 and compare the petals with the 40 tooth gear.
• Drag the red pen dot toward the gear center and see the loops get smaller.
• Turn Snap pen to holes on, then pick different holes and press Redraw.
• Turn Stack layers off to flatten the drawing, and raise Rolling speed to draw faster.

1. 1Predict the number of petals from the ring and gear tooth counts.
2. 2Explain how a pen's distance from the gear center changes the curve.
3. 3Use the greatest common divisor to find petals and laps.
4. 4Describe how rolling circles create hypotrochoid curves.

پرسش‌هایی که معلم‌ها می‌پرسند