Trefoil/mathmod...

maxima/lm_trefoil_surface.wxm mathmod/lm_trefoil_knot/mathmodcollection.js

Maxima files...

maxima/lm_tangents.wxm * Lagrange approach to getting tangent line and tangent conic equations

maxima/lm_ratparam_d1.wxm * rational parametrization of curves with relative degree one

maxima/lm_ratparam_d2.wxm * rational parametrization of curves with relative degree two * also works for degree one, but the parametrizations are computationally sub-optimal

Catalogue of various GeoGebra tinkerings...

geogebra/lm scarabaeus.ggb Scarabaeus (x^2 + y^2) (x^2 + y^2 + ax)^2 - b^2(x^2 - y^2)^2 = 0 * a=b=1 * lm_tangents updated * lm_ratparam_d2 updated

geogebra/lm_piriform.ggb Teardrop a^4y^2=b^2x^3(2a-x)=0 | a=b=1 * lm_tangents updated * lm_ratparam_d2 updated

geogebra/lm_vanhoeij.ggb * tacnode from Mark van Hoeij's paper. * got it to work but some hacking to the parametrization required * INVESTIGATE

geogebra/lm_tacnode.ggb Wikipedia Tacnode * tangent line T1 * tangent conic T2 (my work using Lagrange's approach as described by Wildberger) * my parametrization using algorithmic approach

geogebra/lm_watt_linkage.ggb * locus of a watt linkage wih a=4 * with tangent line and tangent conic * no parametrization

geogebra/lm_watt_curve.ggb * Watt's curve with a and b sliders * with tangent line and tangent conic * no parametrization

geogebra/lm_cardioid.ggb * lm_tangents updated * lm_ratparam_d2.wxm created (parametrizations done there)

geogebra/lm_quadrifolium.ggb * all work done in lm_tangents.wxm (updated) * implicit cartesian equation * tangent line T1 * tangent conic T2 * my parametrization using relative degree 2 approach

geogebra/lm_doublefolium.ggb * all work done in lm_tangents.wxm (updated) * implicit cartesian equation * tangent line T1 * tangent conic T2 * my parametrization using simple relative degree 1 approach (maxima file updated)

geogebra/lm_trifolium.ggb Includes a slider for constant 'a' which is just a scaling factor * implicit cartesian equation * tangent line T1 * tangent conic T2 * my parametrization using simple relative degree 1 approach

geogebra/lm_bernoulli.ggb Lemniscate of Bernoulli with: * tangent line T1 * tangent conic T2 (Wildberger via Lagrange's approach) * my parametrization using pencil of circles * my parametrization using algorithmic approach

geogebra/lm_gerono.ggb Lemniscate of Gerono with: * tangent line T1 * tangent conic T2 (my work using Lagrange's approach as described by Wildberger) * my parametrization using pencil of parabolas

geogebra/lm_besace.ggb Besace (Cramer?) * tangent line T1 * tangent conic T2 (my work using Lagrange's approach as described by Wildberger) * my parametrization using algorithmic approach

geogebra/lm_walker.ggb Walker's Tacnode * tangent line T1 * tangent conic T2 (my work using Lagrange's approach as described by Wildberger) * my parametrization using algorithmic approach

geogebra/lm_descartes.ggb Folium of Descartes * implicit and parametrized (probably from Wilberger's Differential Geometry course)

geogebra/lm_lemnscate.ggb * Bernoulli (implicit) & Gerono (parametrized)

geogebra/lm_ramphoid_cusp.ggb * parametrized

geogebra/lm_ceva.ggb Trisectrix of Ceva * rational parametrization and implicit equation

geogebra/lm_pappus.ggb * colinear intersections

geogebra/lm_monge.ggb * colinear circumcentres

geogebra/lm_trefoil_surface.ggb * two parameter surface (taken from Euler Math Toolbox page)

geogebra/lm_trefoil_spacecurve.ggb * simplest trefoil knot description (inc planar curve)

geogebra/lm_watt.ggb * implicit cartesian equation for Watt's curve