diff --git a/User-Stories.md b/User-Stories.md index aac7278..4733686 100644 --- a/User-Stories.md +++ b/User-Stories.md @@ -10,7 +10,12 @@ Brief summaries of activities one might try/problems one might solve with dyna3. - *[Copied to the [test problem list](Test-problems)]* Somewhat less farfetched, another natural generalization of ellipse-drawing: find the locus of a point P such that the surface area of tetrahedron $ABCP$ is a constant. (In the plane, an ellipse is the locus of a point $P$ such that the perimeter of $ABP$ is constant.) -A thing I am trying/needing to do right now: +#### An instance of a 2D problem which illustrated a significant success for Geometry Expressions: + +I was trying to produce a collection of relations between points on the x and y axes of standard 2D coordinate planes which, if connected to each other by line segments, would produce "nice" curves as the envelopes. For example, connecting x to k - x produces a segment of a parabola, and connected x to 1/x produces a hyperbola. I wanted to know what relation would produce a quarter-circle. With some calculus, I was able to produce a parametric collection of pairs to connect, but I couldn't perceive what the direct relationship was. [TO BE CONTINUED] + + +#### A thing I was trying/needing to do for a construction Understand the configuration space of http://levskaya.github.io/polyhedronisme/?recipe=aaaD but with: each trapezoid a congruent rectangle and each pentagon constrained to be regular (and hence planar) and each rhombus constrained to be planar. In particular, is it realizable with an arbitrary aspect ratio of rectangle, and if so, for a given ratio, what similarity type of rhombus arises? Actually, in real life, the rectangles will each be a face of a box, so bonus points if we can actually make them part of a rectangular solid.