life is beautiful...
life is beautiful...
Post has shared content
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.

#physics   #mathematics﻿
Post has shared content
Visualisation of the first 4 terms of the Fourier series of a square wave
Join the Simple Science and Interesting Things Community and share interesting stuff!

In mathematics, a Fourier series (English pronunciation: /ˈfɔərieɪ/) is a way to represent a wave-like function as a combination of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or complex exponentials)
http://en.wikipedia.org/wiki/Fourier_series

http://en.wikipedia.org/wiki/File:Fourier_series_square_wave_circles_animation.gif﻿
Post has shared content
freaking awesome.﻿
Transparent touchscreen window technology﻿
Post has attachment
Post has shared content
well deserved.﻿
A huge congratulations to #DaftPunk for winning album of the year!

The #Grammys  was certainly a night to remember with incredible performances from Daft Punk, Pharrell and Stevie Wonder, Macklemore, Ryan Lewis and Madonna, Kendrick Lamar and Imagine Dragons and even Beyonce and Jay Z. Which was your favorite performance?

Photo Credit:  ﻿
Post has shared content
Fireworks designed for daytime viewing﻿
Post has shared content
heck yes.﻿
Post has shared content