![]() ![]() 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. 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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