Spiraling squares – compass and straight edge

Can you see the many spirals in this design?

Students calculate the size of each increasing round of squares and consider what sort of spirals these must be.

The activity: SpiralingSquares.pdf

Working with a little mathematical art is a great way to end your school year.

CCSS: 7th, 8th, HS, 8.G.B, HSG, HSG.CO

Polar graph paper with initial round of squares: PolarPaper+FirstSquares.pdf

For members we have an editable Word docx, solutions to the activity, instructions for creating the design with compass and ruler, and a blank spiraling square picture for simply coloring.

SpiralingSquares.docx      SpiralingSquares-solutions.pdf

Instructions on using compass and straight edge to create this design:  SpiralingSquares-compass-directions.pdf

BlankSquares.pdf for simply coloring.

Below are some other great math/art projects to help students visualize mathematics

Wheel of Theodorus

Work with Pythagorean Theorem and visualizing irrational numbers.

Pythagorean Triples

Discover Pythagorean Triples and find patterns in their development.


Learn about the Fibonacci pattern and find some of the beauty in the sequence.

Pascal's Triangle

Modular Math - Filling in Pascal's Triangle can be tedious and cumbersome unless you know how to use modular math.
Probability - How many ways are there to put 3, 4, 5, etc events in order?
Binomial Expansion - There must be an easier way than long multiplication.


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