Euclid's Muse

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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

Projectile Focus

You are shooting a projectile on a sloping field.  Drag the red point to change the angle of the projectile and try and maximize |AB|. Click the button to see the focus of the parabola. What do you notice?

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Welcome to Saltire Software’s app repository: Euclid’s Muse. This site features hundreds of free math apps created by our users. Upload, share and discuss your favorite apps created with Geometry Expressions. Join today and add to the collection.

News

Mechanical Expressions Beta Extended through March

Greetings everyone! We have some exciting news about our new product: Mechanical Expressions. If you haven’t heard, Mechanical Expressions lets you create models of mechanical phenomena using the same interface as Geometry Expressions. We have just extended the beta through the end of March 2014, so if you have yet to try it out, now […]

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 […]

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