Mathematics

10 Amazing Examples of Architecture Inspired by Mathematics. The link between math and architecture goes back to ancient times, when the two disciplines were virtually indistinguishable.

Pyramids and temples were some of the earliest examples of mathematical principles at work. Today, math continues to feature prominently in building design. We’re not just talking about mere measurements — though elements like that are integral to architecture. Thanks to modern technology, architects can explore a variety of exciting design options based on complex mathematical languages, allowing them to build groundbreaking forms. Take a look at several structures past the break that were modeled after mathematics. Mobius Strip Temple You probably made a Mobius Strip in grade school math class, so you should remember that the geometric form is unique in that there is no orientation. Find Arc Length Calculations for Calculus with Wolfram.

Posted by One of the features of calculus is the ability to determine the arc length or surface area of a curve or surface.

An arc length is the length of the curve if it were “rectified,” or pulled out into a straight line. You can also think of it as the distance you would travel if you went from one point to another along a curve, rather than directly along a straight line between the points. To see why this is useful, think of how much cable you would need to hang a suspension bridge.

The shape in which a cable hangs by itself is called a “catenary,” but with a flat weight like a roadway hanging from it, it takes the shape of a more familiar curve: a parabola. The Golden Gate Bridge, shown above, has a main span of 4,200 feet and two main cables that hang down 500 feet from the top of each tower to the roadway in the middle.

Programming

Equation: Formula for Calculating a Skycraper’s Sway. InShare0 Photo courtesy: Taipei 101 A skyscraper is a giant tuning fork.

Give one a good knock — like with an earthquake or a heavy gust of wind — and it’ll start vibrating at its own natural resonance frequency (about seven octaves below the lowest notes on a piano). If you’re on the top floor of, say, the 1,667-foot-tall Taipei 101, you could find yourself swaying back and forth abruptly, a total of up to 2 feet within five seconds. Highly barfogenic. Damping (kg/s). Teen Mathletes Do Battle at Algorithm Olympics. Neal Wu’s last chance for international glory, and maybe America’s, too, begins with a sound like a hippo crunching through a field of dry leaves—the sound of 315 computer prodigies at 315 workstations ripping into 315 gray envelopes in unison.

“You have five hours,” a voice booms across the packed gymnasium. “Good luck.” At his desk on the gym floor, Wu, age 18, pushes his glasses up on his nose and squints. He shouldn’t need luck. This is a coding competition—the International Olympiad in Informatics, held in August at the University of Waterloo in Ontario, Canada—and Wu is one of the world’s top competition programmers. Gold medals awarded at the International Olympiad in Informatics (1999-2009) He just graduated from Baton Rouge Magnet High School in Louisiana; his parents are chemical engineers originally from Shanghai, although Wu was born in the US. Cool or no, there are a lot of expectations on Wu as he shuffles through the contents of his gray envelope.

Statistics

Differential equations tutorial. Overfitting: when accuracy measure goes wrong - Forecasting for Business - Blog - As we already said, the whole point of forecasting is to build models that are accurate on the data you don't have.

Yet, at first glance, this looks like yet another crazy mathematician idea: both weird and utterly unpractical. But in our experience, measuring the real forecast accuracy is a real business problem. Failing at this costs money. Actually, the larger the company, the larger the cost. Still clueless about the real forecast error? Slidecast scripts: Overfitting: your forecasts may not be as good as the measure tells you Forecasting accuracy is critical for many industries such as retail, manufacturing or services. In this slidecast, I am going to introduce a little known problem in forecasting called overfitting. This problem is little known for two reasons. Before getting any further, let me jump to the conclusion.

Overfitting is a very real business problem. Moreover, there is no work-around for overfitting. The key problem is to define what forecasting accuracy actually means.

Randomness

Somestuff. Exact Equations Intuition 2 (proofy)