Introducing the Polynomial


I’ve done as much as I want with piecewise constant interpolations, at least for the moment. The next step that makes sense to me is to look into polynomials. They’re a powerful tool to use in interpolations, but that doesn’t stand out, because they’re powerful tools for most uses. They’re very popular mathematically, since a few polynomials can turn what was a young student’s natural interest in mathematics into a passionate lifelong loathing, with the occasional dream of being haunted by the “quadratic formula”. It’s worth taking a few paragraphs to see what polynomials are, and why they’re popular among those who get past that class.

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The Jagged Kind Of Flat


I have a couple of other thoughts about these piecewise constant functions which I’ve been using to make interpolations. The basic idea is simple enough; we pretend the population of Charlotte was a constant number, the 840,347 it happened to be on the 1970 Census Day, and then leapt upwards at some point to the 971,391 it would have on the 1980 Census Day. Maybe it leapt up immediately after the 1970 Census; maybe immediately before the 1980; maybe at the exact middle moment between the two; maybe some other day. Are those all the options we have?

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Friday, April 27, 1962 – Paraglider Meeting Produces 21 Changes


Following a review of the design and testing philosophy for the Half-Scale Test Vehicle, part of Phase II-A of the Paraglider Development Program, the Half Scale Test Vehicle Design Review Board has recommended to North American 21 changes in the test vehicle design and the test procedures.
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Some Many Ways Of Flatness


[ We didn’t break 3,100 yet, and too bad that. But over the day I did get my first readers from Turkey and the second from the United Arab Emirates that I’ve noticed. Also while my many posts about trapezoids are drawing search engine results, “frazz sequins” comes up a lot. ]

I think I’ve managed, more or less, acceptance that a piecewise constant interpolation makes the simplest way to estimate the population of Charlotte, North Carolina, when all I had to work with was the population data from the 1970 and the 1980 censuses. In 1970 the city had 840,347 people; in 1980 it had 971,391, and therefore the easiest guess to the population in 1975 would be the 1970 value, of 840,347. We suppose that on the 1st of April, 1970 — that Census Day — the population was the lower value, and then sometime before the 1st of April, 1980, it leapt up at once by the 131,044-person difference. Only … how do I know the population jumped up sometime after 1975?

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Thursday, April 26, 1962 – Agena Launch Vehicle, Paraglider Plans


Lockheed today presents its proposed propulsion development plans for the Gemini-Agena target vehicle. The description includes studies on propulsion system optimization, a program to develop multiple-restart capabilities for the primary propulsion system, and the development program for the secondary propulsion system.
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Flattening the City


[ I’d like to thank all who’ve read me or passed on links to me for getting my total hit count above 3,000. In fact, as I write this, the total seems to be 3,033, which is a pleasantly 3-ish number. I suppose that it’s ungrateful to look for 4,000 right away, but after all, I do hope to be interesting or useful, and both of those seem to correlate pretty strongly with being read. In any case, I’ll see how long it takes to reach 3,100, and be silent about that if it’s a number of days too embarrassing to mention. ]

The task I’ve set myself is finding an approximation to the population of Charlotte, North Carolina, for the year 1975. The tools I have on hand are the data that I’m fairly sure I believe for Charlotte’s population in 1970 and in 1980. I have to accept one thing or I’ll be hopelessly disappointed ever after: I’m not going to get the right answer. I’m not going to do my job badly, at least not on purpose; it’s just that — barring a remarkable stroke of luck — I won’t get Charlotte’s actual 1975 population. That’s the nature of interpolations (and extrapolations). But there are degrees of wrongness. Guessing that Charlotte had no people in it in 1975, or twenty millions of people, would be obviously ridiculously wrong. Guessing that it had somewhere between 840,347 (its 1970 Census population) and 971,391 (its 1980 Census population) seems much more plausible. So let me make my first interpolation to Charlotte’s 1975 population.

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Wednesday, April 25, 1962 – Studebaker to build heat shields


The CTL Division of the Studebaker Corporation, Cincinnati, Ohio, has received a subcontract form McDonnell to provide a pair of backup heatshields for the Gemini spacecraft. The contract is for $457,875.
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Life In North Carolina


[ I’m grateful to all for the help in reading my pages here. I’ve not quite reached 3,000 hits, but it’s within sight. If you do know of people who might be interested in either what I’m doing now — and it should be clearer after today’s post — or articles I’ve written in the past, please let them know, or let me know if I could be doing better at reaching interested audiences. ]

I left off the list of places I’d lived the city of Charlotte, North Carolina. There’s justice in my doing so. We lived there only for a couple years, when I was extremely young. I have only a few memories of the place, most of them based on the popcorn machine they had in my preschool program. I don’t know what else I got out of that, but I certainly appreciated seeing popcorn pop. Also I had two brothers born then. But, mostly, I can’t say that Charlotte made much of an impression on me. I couldn’t identify any major features of it from memory, and challenged to point to it on a map I might point at Delaware instead, or wander off to find a soda. Plus, I last lived there somewhere around 1975. I can accept that the population of South Amboy, New Jersey, may not have changed very much since the mid-1970s, but not that Charlotte’s hasn’t.

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Dense Places I Have Lived


[ I don’t wish to be too shameless here, but I’m closing in on 3,000 visitors to my little blog here. Can we get there? Kindly pass on a reference to people you think might be interested; if I matched my most-popular-ever day I’d reach 3,000 tonight easily. ]

I’ve lived almost my entire life in New Jersey, which has its effects on my world view; for example, it produces an extreme defensiveness about the state — really, has there been a fresh Jersey Joke since Benjamin Franklin’s quip about it being “a barrel tapped at both ends”, and they’re not even sure it wasn’t James Madison who said that instead, if anyone ever did? — and a feeling that one should refer to Bruce Springsteen as “Bruce”, as if we’d ever knowingly been in the same zip code simultaneously. Add to that not understanding what is wrong with other states that you’re forced to pump your own gas, and not being able to get a cackling laughter and a voice-over announcer wailing “Rrrrrrrrraceway Park!” out of the head, and you’ve got a first sketch of my personality. (I seem to have missed going to Action Park. My father insists he took me there; I grant he may have taken my siblings, but I don’t remember ever getting there, and the fact I have all my limbs suggests I never did go there.) But there are some other impressions that one gets from growing up in New Jersey.

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Monday, April 23, 1962 – Malfunction Detection System plan


Martin-Baltimore has submitted to the Air Force Space Systems Divisions a descriptive study and a proposed configuration for the Malfunction Detection System.
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Mid-April 2012 Comics Review


I’ve gotten enough comics, I think, to justify a fresh roundup of mathematics appearances in the comic strips. Unfortunately the first mathematics-linked appearance since my most recent entry is also the most badly dated. Pab Sugenis’s The New Adventures of Queen Victoria took (the appropriate) day to celebrate the birthday of Tom Lehrer, but fails to mention his actual greatest contribution to American culture, the “Silent E” song for The Electric Company. He’s also author of the humorous song “Lobachevsky”, which is pretty much the only place to go if you need a mathematics-based song and can’t use They Might Be Giants for some reason. (I regard Lehrer’s “New Math” song as not having a strong enough melody to count.)

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About Chances of Winning on The Price Is Right


Putting together links to all my essays about trapezoid areas made me realize I also had a string of articles examining that problem of The Price Is Right, with Drew Carey’s claim that only once in the show’s history had all six contestants winning the Item Up For Bids come from the same seat in Contestants’ Row. As with the trapezoid pieces they form a more or less coherent whole, so, let me make it easy for people searching the web for the likelihood of clean sweeps or of perfect games on The Price Is Right to find my thoughts.

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Something I Didn’t Know About Trapezoids


I have a little iPad app for keeping track of how this blog is doing, and I’m even able to use it to compose new entries and make comments. (The entry about the lottery was one of them.) Mostly it provides a way for me to watch the count of unique visits per day, so I can grow neurotic wondering why it’s not higher. But it also provides supplementary data, such as, what search queries have brought people to the site. The “Trapezoid Week” flurry of posts has proved to be very good at bringing in search referrals, with topics like “picture of a trapezoid” or “how do I draw a trapezoid” or “similar triangles trapezoid” bringing literally several people right to me.

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Thursday, April 19, 1962 – IBM Awarded Computer Contract


Block diagram of the Gemini spacecraft guidance and control system, originally published in the Project Gemini Familiarization Charts and at NASA's SP-4002 'Project Gemini: A Chronology' web site.

McDonnell has awarded IBM’s Space Guidance Center, of Owego, New York, a $26.6 million subcontract for the Gemini spacecraft computer system. IBM is also responsible for integrating this digital computer with the spacecraft’s systems and the components electrically connected to it. These components are to include the inertial platform, the rendezvous radar, the time reference system, the digital command system, the data acquisition system, the electronics for attitude control and maneuvers, the autopilot for the launch vehicle, console controls, displays, and aerospace ground equipment.
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Wednesday, April 18, 1962 – Astronaut Applications Open


NASA is accepting applications for additional astronauts and will be doing so through June 1, 1962. The plan is to select between five and ten new astronauts to augment the existing corps of seven. The new astronauts will support Project Mercury operations, and go on to join the Mercury astronauts in piloting the Gemini spacecraft.
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Everything I Know About Trapezoids


The set of posts about the area of a trapezoid seems to form a nearly coherent enough whole that it seems worthwhile to make a convenient reference point so that people searching for “how do you find the area of a trapezoid in the most convoluted and over-explained way possible?” have convenient access to it all. So, this is the path of that whole discussion.

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How Many Trapezoids I Can Draw


I guess this is a good time to give my answer for the challenge of how many different trapezoids there are to draw. At the least it’ll provide an answer to people who seek on Google the answer to how many trapezoids there are to draw. In principle there’s an infinite number that can be drawn, of course, but I wanted to cut down the ways that seem to multiply cases without really being different shapes. For example, rotating a trapezoid doesn’t make it new, and just stretching it out longer in one direction or another shouldn’t. And just enlarging or shrinking the whole thing doesn’t change it. So given that, how many kinds of trapezoids do I see?

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Friday, April 13, 1962


A report is being presented today to the Gemini Project Office regarding the abort criteria for the malfunction detection system. The report is presented by Martin-Baltimore and the Air Force Space Systems Division.

Thursday, April 12, 1962


The Manned Spacecraft Center has confirmed that for the currently planned missions the Agena target satellite’s planned orbital lifetime of five days will be sufficient.

How Many Trapezoids Can You Draw?


All the popular mathematics blogs seem to challenge readers to come up with answers; I might as well try the same, so I can be disheartened by the responses. In a pair of earlier essays I talked about the problem of drawing differently-shaped trapezoids so as to not overlook figures that might be trapezoids just because the intuition focuses on one shape over others.

So how many different shapes of trapezoids are there to draw? Let me lay out some ground rules.

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