©2024 Compass Learning Technologies ← GXWeb Showcase → GXWeb SpiroGraph

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Learn How: Create your own GXWeb Activities

Quick GXWeb SpiroGraph Construction: YouTube (2:08)

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Create Your Own GXWeb SpiroGraph

The spirograph is a geometric drawing device that has been a source of interest and fun for young and old for some two hundred years!

But have you ever thought of designing your own spirograph? The amazing free GXWeb software makes creating all manner of beautiful geometry easy, and the spirograph is no exception! GXWeb SpiroGraph Explorer But how does it work? Build Your Own GXWeb Model

 

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GXWeb SpiroGraph Explorer

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\(AB = a\)					▶
		0	0	30
\(AC = b\)					▶
		0	0	12
\(DE = c\)					▶
		0	0	6
\(\angle DAB = \theta\)					▶
		0	0	\(2\pi\)

Show Spiral only Show All RESET Show/Hide Circles Show Construction

App generated by Geometry Expressions

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Build Your Own GXWeb Model

 

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But How Does It Work?

The wonderful curved patterns of a spirograph result from the rotation of a smaller circle of varying radius (\(DE = c\)) as it moves around the inside of a larger circle (radius \(AC = b\)). GXWeb makes it simple to create circles and to place tangent circles inside. Defining the angle DAC (\(\theta\)) made by the center of the inner circle D through the origin A with the positive x-axis (C), we have the means to rotate this circle. The locus of a point E on the circumference of the turning circle gives the surprisingly beautiful array of patterns, just as the hardware Spirograph does! As the inner circle moves around the outer circle inner edge through \(\theta\) degrees, the inner circle turns through multiples of \(\theta\) - the values here given by the variable \(AB = a\).

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GXWeb not only gives us the means to construct beautiful spirals, but even gives the algebraic formula for those curves, as shown!

Explore! Try this yourself!

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Build Your Own GXWeb Model

 

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Construct your own Model with GXWeb

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SpiroGraph Explorer

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SpiroGraph Explorer

 

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©2024 Compass Learning Technologies ← GXWeb Showcase → GXWeb SpiroGraph

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