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Update User Stories

Glen Whitney 2024-02-07 04:59:15 +00:00
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User-Stories.md

@ -2,6 +2,8 @@ Brief summaries of activities one might try/problems one might solve with dyna3.
- P370 Frugal Firepower from the Playground in Math Horizons Volume 25 no. 4. (the cannonball shipping problem) Find the configurations of five nonoverlapping unit spheres that have the maximal points of contact with planes parallel to the coordinate axes (the problem is really looking for the rectangular solid with minimum $l+w+h$ into which they will fit, but extremal solutions will necessarily have lots of contact). - P370 Frugal Firepower from the Playground in Math Horizons Volume 25 no. 4. (the cannonball shipping problem) Find the configurations of five nonoverlapping unit spheres that have the maximal points of contact with planes parallel to the coordinate axes (the problem is really looking for the rectangular solid with minimum $l+w+h$ into which they will fit, but extremal solutions will necessarily have lots of contact).
- P12 Rigid Hexagon from the Playground in Math Horizons Vol 2 no.1. Specifically, let $ABCDEF$ be six points in space such that $AB=CD=EF=a$, $BC=DE=FA=b$, and $AD=BE=CF=a+b$. Then $ABCDEF$ is a planar equiangular hexagon. So in particular it is rigid, which hopefully dyna3 should detect even though fewer distances are specified than generically produce rigidity. A more extreme version of this is specifying $AB=BC=CD=DE=EF=1$ and $AF=5$, constraining all six points to lie on a line. A question one might explore with dyna3, for which I do not know the answer, is whether there are also (interesting) specifications of exactly 7 or 8 distances that also entail rigidity.
- A slightly farfetched one: put three or more "pins" in a plane (or in space). Constrain an additional point in the plane as the "pencil" such that the length of a string looped around the pins and the pencil in some way (there are multiple configurations) has constant length. Find the locus of positions of the pencil. (Generalizations of ellipse-drawing; note James Clerk Maxwell considered these loci in his youth and apparently wrote an article or report of some kind on his findings.) - A slightly farfetched one: put three or more "pins" in a plane (or in space). Constrain an additional point in the plane as the "pencil" such that the length of a string looped around the pins and the pencil in some way (there are multiple configurations) has constant length. Find the locus of positions of the pencil. (Generalizations of ellipse-drawing; note James Clerk Maxwell considered these loci in his youth and apparently wrote an article or report of some kind on his findings.)
- 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.) - 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.)