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. Even if your idea of math is typing juvenile, upside-down messages in a calculator, or asking Siri to figure it out for you, we promise you’ll find something to be wowed by here. 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. Entering the equation from the “Equation forms” pod into the input box, we now ask Wolfram|Alpha for the length of each cable over the main span:
Teen Mathletes Do Battle at Algorithm Olympics | Magazine. 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? Check out our latest 9min slidecast (scripts are pasted below). 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.
Somestuff. Exact Equations Intuition 2 (proofy)