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mishadoff.com | ||
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dusty.phillips.codes
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| | | | | Parts in this series An Order to Learn to Program, Part 1 An Order to Learn to Program, Part 2 An Order to Learn to Program, Part 3 An Order to Learn to Program, Part 4 An Order to Learn to Program, Part 5 An Order to Learn to Program, Part 6 Part 4: Binary, bits, and bytes This is part 4 of my series on the order to study topics related to programming. | |
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www.tartley.com
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| | | | | I've been doing some programming tests and puzzles while job hunting lately. One quick challenge was quite nice, reminding me a bit of Project Euler questions, and I nerd sniped myself into doing a 2n | |
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www.jeremykun.com
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| | | | | Numberphile posted a video today describing a neat trick based on complete sequences: The mathematics here is pretty simple, but I noticed at the end of the video that Dr. Grime was constructing the cards by hand, when really this is a job for a computer program. I thought it would be a nice warmup exercise (and a treat to all of the Numberphile viewers) to write a program to construct the cards for any complete sequence. | |
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www.jeremykun.com
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| | | Problem: $ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots = 1$ Solution: Problem: $ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots = \frac{1}{2}$ Solution: Problem: $ \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots = \frac{1}{3}$ Solution: Problem: $ 1 + r + r^2 + \dots = \frac{1}{1-r}$ if $ r < 1$. Solution: This last one follows from similarity of the subsequent trapezoids: the right edge of the teal(ish) trapezoid has length $ r$, and so the right edge of the neighboring trapezoid, $ x$, is found by $ \frac{r}{1} = \frac{x}{r}$, and we see that it has length $ r^2$. | ||
