Euclid's Muse

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by Nick Halsey

Rotating Ellipses

Two ellipses rotate within a third such that the two smaller ellipses are always tangent to each other and the larger ellipse. Adjusting the variable X demonstrates this rotation. All three ellipses are constrained only by their implicit equations, and the moving ellipses' equations include functions of X that allow them to rotate. Can you figure out what the equations are (the other constants in the equations are a, b, h, and k)?
by Phil Todd

A geometry theorem

H1,H2 and H3 are feet of altitudes, M1,M2,M3 are midpoints. H is the orthocenter.  X2,X3,Y1,Y3,Z1,Z2 are formed by reflecting H1,H2 and H3 in the other altitudes.  X,Y,Z are the intersections between the lines joining midpoints to these reflected points. Observe that H appears to be the incenter of XYZ so long as ABC is acute angled. Otherwise it appears to be one of the excenters

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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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