The Brachistochrone, with Steven Strogatz: Brachistochrone - Part 1 of 2

The video features a conversation with Stephen Strogatz about the Brachistochrone problem, a famous mathematical challenge posed by Johann Bernoulli. The discussion covers the problem's history, including contributions by Galileo and Newton, and explores solutions using Fermat's principle and Snell's law. Mark Levy's modern geometric insight is also presented. The video concludes with a challenge to viewers to explore the problem further.

What is the main focus of the conversation with Stephen Strogatz?

• The life of Isaac Newton

• The history of calculus

• The rivalry between mathematicians

• The Brachistochrone problem

What did Galileo initially think was the solution to the Brachistochrone problem?

• A straight line

• An arc of a circle

• A parabola

• A hyperbola

Who was Johann Bernoulli eager to prove himself smarter than?

• Isaac Newton

• Jacob Bernoulli

• Gottfried Leibniz

• All of the above

What did Newton do when he received Johann Bernoulli's challenge?

• Ignored it

• Solved it overnight

• Asked for more time

• Published it under his name

What principle did Johann Bernoulli use to solve the Brachistochrone problem?

• Newton's Laws of Motion

• Archimedes' Principle

• Fermat's Principle of Least Time

• Pythagorean Theorem

What did Johann Bernoulli use to model the Brachistochrone problem?

• A sliding block

• Light traveling through media

• A rolling wheel

• A pendulum

What shape is associated with the solution to the Brachistochrone problem?

• Cycloid

• Hyperbola

• Parabola

• Ellipse

What is Mark Levy known for in relation to the Brachistochrone problem?

• Solving the problem faster than Newton

• Developing a new mathematical theory

• Providing a geometric insight

• Writing a book on calculus

What does the cycloid represent in the context of the Brachistochrone problem?

• The path of least resistance

• The path of shortest distance

• The path of fastest descent

• The path of maximum curvature

What is the challenge posed to the audience at the end of the video?

• To solve the Brachistochrone problem using calculus

• To find a new geometric proof

• To explain the time-minimizing trajectory in T-Theta space

• To calculate the speed of light in different media