1. Descartes and Fermat: The Tangent Problem
By: Lyndsay Burns
Briana Fiegen
MAT 5930

2. René Descartes Born March 1596
Philosopher, Mathematician, and Physicist.
Solved the Tangent Problem by using a geometric approach.
Died February 1650

3. Pierre de Fermat Born August 1601 Mathematician and Lawyer
Solved the Tangent problem by using an algebraic approach
Died in 1665

4. Descartes Method Descartes Tangent Circle Procedure:
Find the equation for the radius of the circle using (x-b)2 + (y-a) 2 = r2
Substitute the equation found for r2 and the value of y2 back into the equation of the circle.
Set your equation equal to zero.
Use b2 – 4ac to find the single root.
Solve for b.
Find the slope of the radius by using point T and point O, the center of the circle.
Lastly, write the equation of the tangent in slope intercept form. T O

5. Fermat’s Method Fermat’s Similar Triangles Procedure:
Set up Similar Triangle Proportion: =
2. Substitute equations in for f(A) and f(A+E).
Solve for s.
Take length of AT and divide by s.
Lastly, write the equation of the tangent in slope intercept form. P T O S E A B

7. Task
YOU DO IT!
Choose a partner and try to find the tangent line of the given curve using the method given to you.