The brachistochrone
This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.
If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?
Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.
Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.

The brachistochrone

This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.

If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?

Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.

Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.

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imprevade:

I-75 and I-375 Interchange /// Detroit, MI 1.29.2013 /// Todd Hersey

imprevade:

I-75 and I-375 Interchange /// Detroit, MI 1.29.2013 /// Todd Hersey

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kimjongunlookingatthings:

looking at a children’s hospital

appropriate facial expression

kimjongunlookingatthings:

looking at a children’s hospital

appropriate facial expression

oatmealmarketing:

this pic is crucial

oatmealmarketing:

this pic is crucial

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