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.

Think!

kateoplis:

The total area of solar panels it would take to power the world, Europe, and Germany | ilovecharts

postcardsfromethiopia:

One afternoon, I walked into a restaurant near my school to grab some lunch by myself, but instead, I got invited to eat with three police officers! 

Total strangers, but in 15 minutes I knew everyone’s background story (where they worked before Leku, how many siblings they have, which towns they are originally from, etc.) and favorite foods. Not surprisingly, most of them said siga (meat – Ethiopians LOVE meat) and bursame, a Sidama Zone dish, made from the roots of the false banana tree.

They also found out where I am from, what I’m doing here in Ethiopia, which compound I live in - turns out one of them knows who my landlord is, and why I cannot have more than 2 cups of coffee a day. (Sleep would be extremely difficult to achieve, and for me saying ‘I love sleep’ is a huge understatement. Inkilf almat’am!)

This is after we ate a meat+soup dish called k’ilk’il and injera. And of course, we must finish lunch with a cup (or 2) of buna.

I don’t record these things on here enough, but almost every day something unexpected happens, and usually it turns out to be a pleasant twist. You meet someone at a buna bet who becomes your new good friend, or you get invited to eat at a teacher’s home because you saw her while walking on a different route than normal, etc. These moments and people truly humble you, and make you remember to take each day as it comes. Be present, wherever you are.

postcardsfromethiopia:

One afternoon, I walked into a restaurant near my school to grab some lunch by myself, but instead, I got invited to eat with three police officers! 

Total strangers, but in 15 minutes I knew everyone’s background story (where they worked before Leku, how many siblings they have, which towns they are originally from, etc.) and favorite foods. Not surprisingly, most of them said siga (meat – Ethiopians LOVE meat) and bursame, a Sidama Zone dish, made from the roots of the false banana tree.

They also found out where I am from, what I’m doing here in Ethiopia, which compound I live in - turns out one of them knows who my landlord is, and why I cannot have more than 2 cups of coffee a day. (Sleep would be extremely difficult to achieve, and for me saying ‘I love sleep’ is a huge understatement. Inkilf almat’am!)

This is after we ate a meat+soup dish called k’ilk’il and injera. And of course, we must finish lunch with a cup (or 2) of buna.

I don’t record these things on here enough, but almost every day something unexpected happens, and usually it turns out to be a pleasant twist. You meet someone at a buna bet who becomes your new good friend, or you get invited to eat at a teacher’s home because you saw her while walking on a different route than normal, etc. These moments and people truly humble you, and make you remember to take each day as it comes. Be present, wherever you are.