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Toys can help learning maths

Exploring maths concepts with the spirograph

March 18, 2013

Today I decided to give a different tone to this rubric, traveling through fond memories of childhood.

In an ancient trunk I found a toy that provided me with hours of play and exploration: the spirograph.



In fact, I awaited with great expectation the result of the pencil tracing produced by the movement of one of the two circles (one circle was fixed and the other one rolling).

Until then those curves seemed to appear out of sheer magic and the circles seemed to hide some kind of secrecy that allowed the production of such perfect and symmetrical drawings.

Although I could not understand it at the time, the toy has a strong component of mathematical concepts, which can range from the study of symmetries to the study of the functions that graphically represented by the drawings.

Years later I realized what polar coordinates were and also learned that the curves which once fascinated me were, among others, hypocycloids and epicycloids.

The first ones – hypocycloids – are curves describing the path of a fixed point on a circumference, which moves inside another circle, fixed.

If this explanation seems somewhat confusing, maybe the animation helps to better understand the idea:


The hypocycloid curve is shown in red.


Epicycloids, on the other hand, are curves describing the path of a fixed point on a circumference, which moves around another circumference, fixed.


The epicycloid curve is shown in red.


Although it can be regarded only as a toy for drawing, the Spirograph can suit as a basis for the study of these curves (or broader cases, such as hypotrochoids and epitrochoids), as well as other mathematical concepts referred above (symmetry or polar coordinates, for example).

That’s why the Spirograph is a toy that integrates  in itself potentiality to be explored mathematical concepts with various degrees of complexity, a characteristic which is common to many educational toys and so … it is not just a child’s toy.

Written by Susana Pereira

Susana Simões Pereira, maths teacher and PhD in science teaching and communication. I enjoy games and photography and I'm passionate for science and art, specially when together in the same context. You can follow my updates on Twitter, LinkedIn and Facebook.