Questions tagged [curves]

Background It is well-known that the disk can roll down various curves, including the straight line and the Brachistochrone curve. The latter is the curve along which both a point rolls down the ...

Given a conic $C$ in the complex projective plane, say $C=\{c:=x^2+y^2+z^2=0\}$, and two “triangles” (given as zeros of products of 3 linear forms $\ell=\{ax+by+cz\}$) $\ell_1\ell_2\ell_3$, $\ell'_1\...

In the left Figure, consider a right triangle $OPA$ with $\angle {AOP} = 90^\circ$. Let $\ell$ be the reflection of $PO$ in $PA$ and $\ell$ meets $OA$ at $A_1$. Let $O_1$ be the center of the circle $(...

Let $C$ be a nodal projective curve over an algebraically closed field of genus at least $2$. There are two natural "differential objects" one can consider: The sheaf of differentials $\...

Two bicyclists ride side by side around a smooth loop with the outside bicyclist a distance of $D$ from the inside bicyclist. How much further does the outside bicyclist ride? If the loop is a circle, ...