## Posts Tagged ‘**mathematics**’

## A Nice Bit of Hex on Pi

3.243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C

89452821E638D01377BE5466CF34E90C6CC0AC29B7C97C50DD3F84D5B5B54709

179216D5D98979FB1BD1310BA698DFB5AC2FFD72DBD01ADFB7B8E1AFED6A267E

96BA7C9045F12C7F9924A19947B3916CF70801F2E2858EFC16636920D871574E

69A458FEA3F4933D7E0D95748F728EB658718BCD5882154AEE7B54A41DC25A59

B59C30D5392AF26013C5D1B023286085F0CA417918B8DB38EF8E79DCB0603A18

0E6C9E0E8BB01E8A3ED71577C1BD314B2778AF2FDA55605C60E65525F3AA55AB

945748986263E8144055CA396A2AAB10B6B4CC5C341141E8CEA15486AF7C72E9

93B3EE1411636FBC2A2BA9C55D741831F6CE5C3E169B87931EAFD6BA336C24CF

5C7A325381289586773B8F48986B4BB9AFC4BFE81B6628219361D809CCFB21A9

91487CAC605DEC8032EF845D5DE98575B1DC262302EB651B8823893E81D396AC

C50F6D6FF383F44239 . . . — CalcCrypto

## Perfect π

Got an iPhone? Bring up the Control Center by swiping up from the bottom of the screen. At the bottom center right of the Control Center, click the icon for the Calculator. Or shortcut these first two steps by simply telling Siri, “Run Calculator.” With the Calculator onscreen, turn the device to landscape view to access the scientific calculator. Near the center of the bottom of the scientific calculator display, click the π button. The scientific calculator displays the value of pi rounded to 16 significant digits: 3.141592653589793. Without clearing the calculator, turn the device to portrait view; the simple calculator now displays the value of pi rounded to 9 significant digits: 3.14159265. Or shortcut all of these steps by asking Siri, “What is the value of pi?” — via Wolfram Alpha, to 29 significant digits: 3.1415926535897932384626433832. Or let Siri take it out farther by asking something like, “What are the first 240 digits of pi?”

## Iff You See Her Say Hello

I doubt I’m improperly disclosing too much about my work to tell that I was recently involved on a project that included discussion about whether a piece of emerging regulatory guidance might want to use the word “iff.” In the sense of the second definition stated at my link given here: the mathematical term of art. I had to smile: one of my favorite hobbies involves collecting iffs.

## Again Of Math and Metaphor

Two books new to my home stacks —

*Morning in the Burned House*, new poems by Margaret Atwood. One of two copies that were on the used bookstore’s poetry shelves, and the book has no marks nor signs of wear; so this might actually be a new book, picked up from some other bookseller’s leftovers rather than a previously owned book. One or two of the poems in this book, I may have read online before, I won’t know for sure until I’ve read through them, first reading to be done over the course of the new several weeks, with initial place being a temporary spot on Daystand. Permanent place will be on my key poetry shelf in the living room. *Update* — Yes, re-reading “Helen of Troy Does Counter Dancing” upon encountering it during transcription of the book’s TOC for my Poetry Register, that one I know I’ve read several times before; it’s been rather frequently passed along elsewhere. But then starting back at the beginning after a preliminary scan of first lines, I know I’ve not previously read the first poem here, “You Come Back” – that closing line is the sort of thing I tend to remember long, the sort of thing that sends that poem to my memorization queue, the spark that has Atwood high on my list of favorite poets, precisely the reason this purchase today was so nice a find.

*Linear Algebra*, by Larry Smith. (The Amazon link here refers to the paperback reprint of the hardbound version I purchased.) First copyrighted in 1978, obviously this is not the same text used by the linear algebra college class I did well at during my second semester at Houghton in early 1973; as I recall, the cover of my linear algebra book back then was a deep blue. Although I’m currently also reading several other math books I own (notably, one on Fermat’s Last Theorem), I’ll be using this linear algebra text to re-launch my own personal mathematics study program, curriculum to follow shortly. Temporary place, as I begin its study: Sewing room book stack. Permanent place: living room math bookshelf.

Susan had been off at the sewing center picking up two machines she’d had off for repair work, but cautioned me against making any purchases at Half-Price Books without checking with her first, then carefully reiterating her caution lest I had thought her to merely be teasing with the running joke about how I’m not to be trusted in a bookstore with spare cash in my pocket — ah, she’s got a surprise coming for me! So I did text her and tried a follow-up phone call after I’d found the Atwood, both book approval attempts seeing no response as she went about her business. Which was what gave me the time to find the linear algebra text — bad enough to let me run free in a bookstore with spare cash, but give me spare time too and I’m seriously dangerous! Finally I simply took the chance and made my purchases without her pre-approved stamp, risking that she’d not managed to find the one Atwood poetry book I’d be most likely to jump at the chance to get, with the even greater risk (ummm, not?) that she’d be giving me a linear algebra textbook. The bookstore clerk had to hear me chat about it, so he took it seriously enough to tell me that the back of my sales receipt described a return policy, should it turn out that I’d matched Suzi’s gift choice. I won’t be needing to use that, thanks anyway.

## Doubling Back

Two and two are four,

Four and four are eight,

Eight and eight are sixteen,

Sixteen and sixteen are thirty two.

Two and two are four…

I heard that counterpoint background to Danny Kaye’s portrayal of Hans Christian Andersen only once, at about the age of 10, when our neighbors invited us over to watch the movie on TV. For a little song like that to a little math-bent mind like mine always was, once was enough to have me singing the tune throughout my childhood. Sometimes to this day I can be heard singing it when the mood hits me.

When I felt like irritating my brothers or others, I would not continue it as in the movie, restarting each cycle at two each time. Instead, my second verse would go, “32 and 32 are 64, 64 and 64 are 128, 128 and 128 are 256, 256 and 256 are 512.” And then to be seriously demented and obnoxious, I was known to have gone higher from there, “512 and 512 are 1,024, …” and so on. I once took that out over ten verses on a band bus before I got shrieked at to have mercy on the other band members.

In 12th grade, I sat for a special test co-sponsored by the Society of Actuaries, little knowing then where my future career would take me. One question on that multiple-choice test was to choose the last digit of 2 to the 400th power minus 1. Raise your hands if you tried to multiply 2 by itself 400 times, go ahead, don’t be shy. Now, how many of you tried a little shortcut, via 2 times 2 is 4, 4 times 4 is 16, 16 times 16 is 256, 256 times 256 is . . . uh . . .?

I selected the correct answer almost immediately, and felt it no genius in doing so. We want only the final digit, so all other digits can be dropped out of our multiplications. So we proceed – 2, 4, 8, 6, 2, 4, 8, 6, 2, 4, 8, 6 . . . and even a near-dunce head such as mine doesn’t take more than that many cycles to figure out the pattern. So any power of 2 that is divisible by 4 will have 6 as its last digit, and 6 minus 1 is 5, which was the answer to the test’s question.

Near-dunce me, it took me over 40 years, until just today, for me to realize that the pattern that gave me the answer to that problem in 12th grade was exactly the same pattern I’d been singing since seeing the Hans Christian Andersen movie. Instead of continuing my song verses with the higher numbers, all I needed to do was to sing the song with only the final digits —

Two and two are four,

Four and four are eight,

Eight and eight take us back to six,

Six and six come back round to two.

Two and two are four…

Virtually every single thought I have ever had concerning mathematics has felt similar to me as this pattern. Right down to how slow my own head is for working it out, other than for the vision of it inside my head.