Table of Contents
- 1 What is the equation of Folium of Descartes?
- 2 What are the tangent to the curve x cube Y cube is equal to 3 xy at the origin?
- 3 Why is the Folium of Descartes important?
- 4 What is the formula for the folium of Descartes?
- 5 What problem did Descartes challenge Fermat to solve?
- 6 How did Rene Descartes contribute to calculus?
What is the equation of Folium of Descartes?
The curve is sometimes known as the noeud de ruban. The folium has an asymptote x + y + a = 0 x + y + a = 0 x+y+a=0.
What are the tangent to the curve x cube Y cube is equal to 3 xy at the origin?
Mathematics Question Therefore, 3axy = 0, which gives x = 0 and y = 0 as two tangents to the curve at origin.
How do you trace cardioid?
A cardioid is given by the equation r = 2 (1 + cos θ).
Why is the Folium of Descartes important?
The folium of Descartes is still studied and understood today. Not only did it provide for the proof of some properties connected to Fermat’s Last Theorem, or as Hessian curve associated to an elliptic curve, but it also has a very interesting property over it: a multiplicative group law.
What is the formula for the folium of Descartes?
The folium of Descartes can be expressed in polar coordinates as which is plotted on the left. This is equivalent to r = 3 a sec θ tan θ 1 + tan 3 θ . {\\displaystyle r= {\\frac {3a\\sec heta an heta } {1+ an ^ {3} heta }}.} .
How is the folium of Descartes related to the trisectrix?
The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation and change variables to find the equation in a coordinate system rotated 45 degrees.
What problem did Descartes challenge Fermat to solve?
Descartes challenged Fermat to find the tangent line to the curve at an arbitrary point since Fermat had recently discovered a method for finding tangent lines. Fermat solved the problem easily, something Descartes was unable to do. Since the invention of calculus, the slope of the tangent line can be found easily using implicit differentiation .
How did Rene Descartes contribute to calculus?
Its claim to fame lies in an incident in the development of calculus. Descartes challenged Pierre de Fermat to find the tangent line to the curve at an arbitrary point since Fermat had recently discovered a method for finding tangent lines. Fermat solved the problem easily, something Descartes was unable to do.