trigonometry-is-my-bitch
trigonometry-is-my-bitch:

How a hole is drilled to be made square. The red shape in the center would be the cutting tool.
it shares the same principle as a Reuleaux triangle but with one rounded corner so that the cut square does not have rounded edges; the cutting tool follows the path of the rounded edge that is tangent to the sides of the outer square. because a tangent line is perpendicular to the radius, as the cutting tool follows the path of the rounded edge it turns precisely 90° to create a sharp edged perfect square.

trigonometry-is-my-bitch:

How a hole is drilled to be made square. The red shape in the center would be the cutting tool.

it shares the same principle as a Reuleaux triangle but with one rounded corner so that the cut square does not have rounded edges; the cutting tool follows the path of the rounded edge that is tangent to the sides of the outer square. because a tangent line is perpendicular to the radius, as the cutting tool follows the path of the rounded edge it turns precisely 90° to create a sharp edged perfect square.

fuckyeahfluiddynamics
fuckyeahfluiddynamics:

The hummingbird has long been admired for its ability to hover in flight. The key to this behavior is the bird’s capability to produce lift on both its downstroke and its upstroke. The animation above shows a simulation of hovering hummingbird. The kinematics of the bird’s flapping—the figure-8 motion and the twist of the wings through each cycle—are based on high-speed video of actual hummingbirds. These data were then used to construct a digital model of a hummingbird, about which scientists simulated airflow. About 70% of the lift each cycle is generated by the downstroke, much of it coming from the leading-edge vortex that develops on the wing. The remainder of the lift is creating during the upstroke as the bird pulls its wings back. During this part of the cycle, the flexible hummingbird twists its wings to a very high angle of attack, which is necessary to generate and maintain a leading-edge vortex on the upstroke. The full-scale animation is here. (Image credit: J. Song et al.; via Wired; submitted by averagegrdy)

fuckyeahfluiddynamics:

The hummingbird has long been admired for its ability to hover in flight. The key to this behavior is the bird’s capability to produce lift on both its downstroke and its upstroke. The animation above shows a simulation of hovering hummingbird. The kinematics of the bird’s flapping—the figure-8 motion and the twist of the wings through each cycle—are based on high-speed video of actual hummingbirds. These data were then used to construct a digital model of a hummingbird, about which scientists simulated airflow. About 70% of the lift each cycle is generated by the downstroke, much of it coming from the leading-edge vortex that develops on the wing. The remainder of the lift is creating during the upstroke as the bird pulls its wings back. During this part of the cycle, the flexible hummingbird twists its wings to a very high angle of attack, which is necessary to generate and maintain a leading-edge vortex on the upstroke. The full-scale animation is here. (Image credit: J. Song et al.; via Wired; submitted by averagegrdy)

saulofortz
saulofortz:

Larry Phillips originally shared:



 
The BrachistochroneThis 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.

saulofortz:

 
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.