2015年8月22日 · If we take a slice by a plane containing a line, we get the line together with a conic. Any slice by a plane that doesn't have one of the 27 lines in it will give a plane cubic …

It is noteworthy that many of the named cubic curves look rather similar: the folium of Descartes, the trisectrix of Maclaurin, the (right) strophoid, and the Tschirnhausen cubic look very similar …

2019年12月18日 · I understand that a cubic curve in $\mathbb P^2$ is given by a homogeneous degree $3$ polynomial, so that the space of cubic curves can be identified with $\mathbb …

2021年1月2日 · Since a tangent line is defined by taking the limit of two points on the curve, and an osculating circle is defined by taking the limit of two tangent lines on the curve, I thought …

2022年10月1日 · By similar reasoning, you can show that the derivative of the cubic curve is $$ 3\big\{ (1-t)^2(P_1 - P_0) + 2t(1-t)(P_2 - P_1) + t^2 (P_3- P_2)\big\} $$ So again we can see …

I've been reading about parametrization of algebraic curves recently and the idea of the "genus of a curve" appears quite often (my impression is that a curve is parametrizable exactly when it …

Increase the resolution of the curve, and the approximation gets better and better. Zoom far away from the curve, and at some point the resolution of your curve will exceed the resolution …

2019年12月2日 · There are 10 coefficients in an equation for a cubic. Let us first consider the general case. In a general case, all coefficients are non-zero, and we can normalize the …

2017年1月17日 · Jesko has linked these lecture notes, which contain a complete classification of plane cubics on page 56.. According to this classification, a non-ordinary double point on an …

2020年1月26日 · The experience with this simple cubic has been interesting despite quadratic equations in two variables it is cumbersome to find such points on the curve and then the …