Relationship To The Trisectrix of MacLaurin
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. This amounts to setting . In the plane the equation is
- .
If we stretch the curve in the direction by a factor of this becomes
which is the equation of the trisectrix of Maclaurin.
Read more about this topic: Folium Of Descartes
Famous quotes containing the words relationship to the, relationship to and/or relationship:
“Whatever may be our just grievances in the southern states, it is fitting that we acknowledge that, considering their poverty and past relationship to the Negro race, they have done remarkably well for the cause of education among us. That the whole South should commit itself to the principle that the colored people have a right to be educated is an immense acquisition to the cause of popular education.”
—Fannie Barrier Williams (1855–1944)
“Poetry is above all a concentration of the power of language, which is the power of our ultimate relationship to everything in the universe.”
—Adrienne Rich (b. 1929)
“When any relationship is characterized by difference, particularly a disparity in power, there remains a tendency to model it on the parent-child-relationship. Even protectiveness and benevolence toward the poor, toward minorities, and especially toward women have involved equating them with children.”
—Mary Catherine Bateson (20th century)