Euclid's Muse

your source for INTERACTIVE math apps
by Nick Halsey

Circles, Tangents and Nonagon Diagonals

You may want to see the heptagon version before attempting this one Every diagonal within a regular nonagon is drawn. Circles are centered at each intersection of diagonals along a vertical axis (these same constructions can be made nine times around the nonagon). Each circle can be tangent to at least 4 diagonals when the circle is at least 2 different sizes. Unnecessary diagonals have been hidden. Drag the green points to resize the circles. Can you find all 13 positions where a circle is tangent to at least 4 diagonals? Hint: sometimes the circle is not entirely contained within the nonagon. Ready for more? Check out the hendecagon version!
by Phil Todd

September Problem

The radii of the small circles add up to that of the large circle. Why?
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News

Updates to Euclid’s Muse

We are excited to announce some of the recent updates to Euclid’s Muse. The front page has been reorganized so it’s easier to find what you’re looking for (and it’s much nicer to look at). Join us on the new forums page and help build our community by posting your questions, comments and app creation […]

Announcing Mechanical Expressions!

We’ve just released a new program, Mechanical Expressions. It builds off of Geometry Expressions’ base, adding mechanics inputs and outputs. Its html5/Javascript app exports support dynamic simulations, so keep your eyes open for some popping up here on Euclid’s Muse. For more information about Mechanical Expressions, check out the website: http://mechanicalexpressions.com/.

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