Which is of course not surprising, given that Wolfram|Alpha has the entire power and knowledge of Mathematica behind it, especially when combined with the fact that this native “smarts” is further augmented with large amounts of curated data and customized processing. When computing integrals, sums, statistics, properties of mathematical objects, or a myriad of other mathematical and mathematics-related problems, it typically returns an extensive and exhaustively complete result. It is immediately clear to anyone who has used the site that Wolfram|Alpha knows a lot about mathematics. While the most general set of geometric similarity (i.e., shape-preserving) operations in the plane includes rotation (change in angle), dilation/expansion (change in size), reflection (flipping about an axis), and translation (change in position), only translation is needed to produce a periodic tiling from a correctly constructed primitive unit. Such tilings are therefore intimately related to the set of symmetry groups of the plane, known as wallpaper groups. Periodic tilings possess an individual motif (more formally known as a primitive unit) that is repeated iteratively in a predictable (periodic) way. Wolfram|Alpha has possessed detailed knowledge on more than 50 common (and uncommon) varieties of periodic tilings for some time, as illustrated, for example, in the case of the basketstitch tiling: Periodic tilings (also known as tessellations) are often beautiful arrangements of one or more shapes, known as tiles, into regular patterns, which if extended infinitely are capable of covering the entire plane without gaps. Mount union wolfram mathematica license series#Any geometric series whose r satisfies -1 < r < 1 is a convergent series, and we can say to what the series converges: A geometric series is a series wherein each term in the sequence is a constant number, r, multiplied by the term before it. Each term in this series is 1/10 times the term before it, making it a geometric series. If you say you’re 99.9 repeating percent sure, then you’re 100 percent sure.” My brother grinned at me and said, “I know you know your geometric sequences. I felt confident about my knowledge, but wanted to leave myself a little wiggle room, just in case. In recent dinner conversation with my brother, I commented that I was “99.9 repeating” percent sure that my favorite author, Jorge Luis Borges, had lived into the 1980s (Wolfram|Alpha later showed me that he did, in fact, live through 1986!).
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