To celebrate Halloween, last year we discussed what you can do with 1,818 pounds of pumpkin. It was a popular blog post, and it put an awful lot of smiles on peoples’ faces. An entire lamina (filled shape) of smiles, in fact. More »
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Wolfram|Alpha already contains many extensive collections of mathematical data, including curves, surfaces, graphs, knots, and polyhedra. However, one type of object we had not systematically incorporated until recently was the class of plane geometric figures technically known as laminae:
Most people (including the subset of small people who play with sorting toys such as the one illustrated below) are familiar with a number of laminae. A lamina is simply a bounded (and usually connected) region of the Euclidean plane. In the most general case, it has a surface density function ?(x, y) as a function of x– and y-coordinates, but with ?(x, y) = 1 in the simplest case.
Examples of laminae, some of which are illustrated above, therefore include the disk (i.e., filled circle), equilateral triangle, square, trapezoid, and 5-point star. In the interest of completeness, it might be worth mentioning that laminae are always “filled” objects, so the ambiguity about whether the terms “polygon”, “square”, etc. refer to closed sets of line segments or those segments plus their interiors does not arise for laminae.
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A lot of cool things happened this summer on Wolfram|Alpha and the Wolfram|Alpha Blog. And just wait—we have even better stuff planned for the coming months! But in case you missed it, here’s a quick recap of some of our best posts from this summer. More »
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This blog post is the continuation of my last two posts (1, 2) about formulas for curves. So far, we have discussed how to make plane curves that are sketches of animals, faces, fictional characters, and more. In this post, we will discuss the constructions of some filled curves (laminae). More »
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In my last blog post, I discussed how to construct closed-form trigonometric formulas for sketches of people’s faces. Using similar techniques, Wolfram|Alpha has recently added a collection of hundreds of such closed-form curves for faces, shapes, animals, logos, and signatures. More »
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When I was younger, I held the naive and incorrect view that mathematics was divorced from the arts. As I’ve gotten older, I’ve become more aware of not only how mathematics is the foundation for any of the hard sciences, but also how it is intrinsically linked to essentially any form of creativity. Certainly users of our Wolfram Music Theory Course Assistant could have told me that, but I’m not just referring to music. In truth, I’m not even trying to make some highbrow appeal to abstract art, either, although I happen to rather like that sort of thing. What I’m trying to say is that mathematical equations can make pretty pictures.
