\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016e.00812}
\itemau{Bosch, Robert}
\itemti{Regular polygons and polynomial curves.}
\itemso{Math. Compet. 28, No. 2, 16-24 (2015).}
\itemab
From the text: In this note, we prove that only the square and the equilateral triangle can have all their vertices on a cubic. From the study of the polynomial $p(x)=x^8+3bx^6+3b^2x^4+(b^3+b)x ^2+(b^2+1)$, where $b$ is a real parameter, we find that we can inscribe at most two squares in a cubic, showing examples in both cases. Finally, we show that every regular polygon can be inscribed in a polynomial curve.
\itemrv{~}
\itemcc{I20}
\itemut{regular polygons inscribed in a polynomial curve; cubic curves; cubics; inscribed equilateral triangles; inscribed squares; polynomial functions; simultaneous equations}
\itemli{}
\end