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.

(via visualizingmath)

jogoraz:

Jogo-z

Lost gazing at skies lost in the disguise

blushingcheekymonkey:

anatol petrytsky - an eccentric dance (1922)

blushingcheekymonkey:

anatol petrytsky - an eccentric dance (1922)

(via vivipiuomeno)

fuckyeahfluiddynamics:

Wingtip vortices are a result of the finite length of a wing. Airplanes generate lift by having low-pressure air travelling over the top of the wing and higher pressure air along the bottom. If the wing were infinite, the two flows would remain separate. Instead, the high-pressure air from under the wing sneaks around the wingtip to reach the lower pressure region. This creates the vorticity that trails behind the aircraft. I was first introduced to the concept of wingtip vortices in my junior year during introductory fluid dynamics. As I recall, the concept was utterly bizarre and so difficult to wrap our heads around that everyone, including the TA, had trouble figuring out which way the vortices were supposed to spin. A few good photos and videos would have helped, I’m sure. (Photo credits: U.S. Coast Guard, S. Morris, Nat. Geo/BBC2) fuckyeahfluiddynamics:

Wingtip vortices are a result of the finite length of a wing. Airplanes generate lift by having low-pressure air travelling over the top of the wing and higher pressure air along the bottom. If the wing were infinite, the two flows would remain separate. Instead, the high-pressure air from under the wing sneaks around the wingtip to reach the lower pressure region. This creates the vorticity that trails behind the aircraft. I was first introduced to the concept of wingtip vortices in my junior year during introductory fluid dynamics. As I recall, the concept was utterly bizarre and so difficult to wrap our heads around that everyone, including the TA, had trouble figuring out which way the vortices were supposed to spin. A few good photos and videos would have helped, I’m sure. (Photo credits: U.S. Coast Guard, S. Morris, Nat. Geo/BBC2) fuckyeahfluiddynamics:

Wingtip vortices are a result of the finite length of a wing. Airplanes generate lift by having low-pressure air travelling over the top of the wing and higher pressure air along the bottom. If the wing were infinite, the two flows would remain separate. Instead, the high-pressure air from under the wing sneaks around the wingtip to reach the lower pressure region. This creates the vorticity that trails behind the aircraft. I was first introduced to the concept of wingtip vortices in my junior year during introductory fluid dynamics. As I recall, the concept was utterly bizarre and so difficult to wrap our heads around that everyone, including the TA, had trouble figuring out which way the vortices were supposed to spin. A few good photos and videos would have helped, I’m sure. (Photo credits: U.S. Coast Guard, S. Morris, Nat. Geo/BBC2)

fuckyeahfluiddynamics:

Wingtip vortices are a result of the finite length of a wing. Airplanes generate lift by having low-pressure air travelling over the top of the wing and higher pressure air along the bottom. If the wing were infinite, the two flows would remain separate. Instead, the high-pressure air from under the wing sneaks around the wingtip to reach the lower pressure region. This creates the vorticity that trails behind the aircraft. I was first introduced to the concept of wingtip vortices in my junior year during introductory fluid dynamics. As I recall, the concept was utterly bizarre and so difficult to wrap our heads around that everyone, including the TA, had trouble figuring out which way the vortices were supposed to spin. A few good photos and videos would have helped, I’m sure. (Photo credits: U.S. Coast Guard, S. Morris, Nat. Geo/BBC2)

miamou:

Alexej von Jawlensky

'Meditation' 1934

(via iloverainandcoffee)

William John Kennedy, Andy Warhol holding an unrolled acetate of Marilyn in the Factory, 1964 

(via vivipiuomeno)

taumazo:

Fred Lebain - Un Printemps à New York taumazo:

Fred Lebain - Un Printemps à New York taumazo:

Fred Lebain - Un Printemps à New York taumazo:

Fred Lebain - Un Printemps à New York taumazo:

Fred Lebain - Un Printemps à New York taumazo:

Fred Lebain - Un Printemps à New York

taumazo:

Fred LebainUn Printemps à New York

iloverainandcoffee:

Josef Sudek

natgeofound:

A farmer embraces his dog in his stonewalled field on Inishmore Island in Ireland, March 1971.Photograph by Winfield Parks, National Geographic Creative