Straight line is not the fastest way?

We all know that to go from position A to position B, the straight line is the optimal choice. But the following Math problem will make you look completely different!

Discover one of the most important problems of Mathematics: The Brachistochrone problem.

Brachistochrone classic problem

This is a problem derived from mechanical problems but solved by Mathematics.

Although Newton had previously thought of this problem, it was not until Bernoulli's time that the problem was properly solved and solved.

The problem is called Brachistochrone, which comes from the Greek: Brachistos means "shortest" and chronos means "time". Vietnamese has a book called "short-lived".

The problem is called Brachistochrone, which comes from the Greek: Brachistos means "shortest" and chronos means "time" .

In June 1696, John Bernouilli sent a challenge to the Mathematical World at that time (mainly to his brother James Bernouilli) with the following easily understood problem:

"If there is a ball rolling down from a high point to a lower point, what should the path shape be for the shortest travel time?"

Or more intuitive, you have to make the slide shape shaped like that to get to the destination soon.

Your intuition may assume that it is a straight line but not really, even though it is the shortest line.

The answer here is the Cycloid curve

Cyclid Line (Take a point on a circle and roll it. The trajectory of that point is the image of the Cycloid curve).

In one of his books published in 1638, Galileo also mentioned this problem and proved that q is a circular arc faster than a straight orbit. However, the choice of path is his circular arc is not the right solution.

In the process of seeking answers, a new branch of Mathematics was born, that is, Analyzing many variables.

Today, it is applied to Quantum Mechanics and other issues.

The above animation shows the ball's travel time for each path shape, the interesting thing is that the straight line is the most time-consuming road.

Solution to the problem

The problem is solved by the differential method and the main answer is Cycloid. The problem and solution also illustrate one of the most beautiful principles of classical mechanics: the principle of minimum effect.

If you say it in a similar way, "nature always does things in a very economical and reserved way" !

Nature always optimizes its options.

In particular when we consider the journey of a ray of light, it always chooses which path has the shortest travel time. As for a marble that slides from above, it chooses a Cycloid curve, not a straight line!

"Nature is the greatest mathematician" and this interesting math will help you see the relationship between Mathematics and Physics.