I didn’t know how sad I was then, or notice how that oozing sadness had caught fire and morphed into rage. Rage toward p

I knew it wasn’t their fault, and I knew it wasn’t mine. But that didn’t make me less angry, and it didn’t make me less resentful. It made me want more and more and more. But the circumstances of my family didn’t change, and my wanting wasn’t enough. Thirteen came, and I woke to the same world I’d lived in the night before, and all the nights before that one. I stopped wanting the magazines. But it took a little time to figure that out.

Indeed, the midpoint rule is a special case of the so-called Gaussian integration methods, which exploit the symmetries and other properties of the function to be integrated, to make a clever choice of the points in which f(x)=P(x,m), P(x,m) being a polynomial of degree m.

Browsing Cantor’s Paradise articles, one of my favourite publications on Medium, I found an article written by Kazi Abu Rousan, in which the use of the trapezoidal rule for numerical integration is advocated (I am attracted by articles about physics, numerical methods and programming, as well as about the interplay between art and science). It is a well written article, in fact (as usual, on this publication) and I appreciate very much the animated figures that clearly illustrate the method. Bravo!

For the last several years, I’ve been on a mission to find the August 1998 certain issue of Seventeen, the one pictured above. I finally found it via the assistance of a follower, who knew it was on my radar. This is the latest addition to my collection of vintage 90’s magazines that were important to me at a certain age. (I’m thinking of working on a project that considers the impact of publications like these on the adolescent experience of people like me.) There’s something special about this issue, something about Drew Barrymore, the movie Ever After, and Black girls who were teens or pre-teens when that movie came out.

When I think of all the ways I’ve been saved from myself, I think of where I grew up. I think about the phase in my life when I assumed every answer I could ever need about anything could be found in a book. Before I realized books, traditionally, weren’t meant for me or the questions I had. Before I knew where to find the right books.

In fact, there is a trick. The trick consists of the fact that I used a special version of the rectangle rule, known as the midpoint rule. In this case, the height of the rectangle, used to approximate the function, is not f(a), nor f(b), but f((a b)/2). You will have no difficulty in showing that the area of a rectangle whose height is the average of the lengths of the bases of a trapezoid is equivalent to the area of the latter. The two methods are, in fact, completely equivalent. The difference in n is mainly due to the specific properties of f(x) (in particular, to the fact that f(x) is monotonically decreasing).

Many programmers believe that the use of higher order integration algorithms, combined with a large number of integration interval divisions, is useful (and sometimes necessary) to achieve good accuracy. In this article we show that this is not always true.

If you’d asked me at twelve years old which television character I was most like, I would have said Joey Potter from Dawson’s Creek, almost entirely because she was a teenager with a parent in prison. I still haven’t forgiven Dawson for turning in her father. Like…to this day. Honestly, if I’m being real, I haven’t forgiven Dawson for a lot of things, and probably never will. All hail, King Pacey, Master of The Creek.

What I didn’t find in the library, my community taught me. I couldn’t find instances of Black beauty meant for teenage girls in magazines, but I saw it at school, church, and the store. I am so lucky that when I couldn’t find myself in the world, my neighborhood modeled the truth for me. Black beauty was everywhere, and so I never once lamented my Blackness or thought it made me less beautiful. I felt sorry for the people who didn’t know how gorgeous we were, who didn’t think to take our photographs and remember.

Lately, when I tweet or write about my move, someone inevitably asks if Kelly, my husband, moved with me. I’ve been told this happens because I talk about the move using “I” instead of “We.” So here’s me taking the time to let you know that I am one person who speaks for this one person. Kel is here with me, yes, but I am still I. If that doesn’t work for you, I have nothing else to offer. My little family is the center of my world, but I am the center of my life. I’ve found the consistency I was searching for, but it didn’t come from falling in love or getting married or getting a dog. It came from the core of my self. That’s where I speak from, and that’s who you’re hearing. Questions are fine, assumptions are petty.

The midpoint method consists of interpolating a curve in an interval [a,a h] using a constant corresponding to f(ξ), where ξ is the midpoint of the interval. It is equivalent to the trapezoidal method, yet its error is lower if the function is monotone in the interval [figure made by myself and published on “Scientific Programming”, ed. World Scientific]

def rectangles(f, a, b, tol): sum = 0 n = 1 dx = (b - a)/n while abs(sum - original_value) > tol: sum = 0 dx = (b - a)/n x = a 0.5*dx for i in range(0, n): sum = f(x) x = dx sum *= dx n = 1 return sum, n-1

http://wap.dentisalut.com/ltc/videos-marseille-v-montpellier-v-fr-fr-1oin-25.php

ichael Woodward, Ph.D., organizational psychologist and author of “The YOU Plan,” agrees, saying, “The last thing you need is to be lying in bed thinking about an email you just read from that overzealous boss who spends all their waking hours coming up with random requests driven by little more than a momentary impulse.”

Indeed, the article is correct in every detail, yet the conclusion to which it may lead may not be such. Let me start with the example provided in the Kazi’s article. Here the integral of 1/(1 x²) is computed within 0 and 1, finding the number n of steps in which the interval must be divided until the precision is of the order of 10⁻⁶. In the original example, n is increased by 15 each iteration; I just modified the program such that n is increased by 1. Moreover, I stop iterating when the remainder (i.e., the difference between the actual value of the integral and its numerical estimation) is below the given tolerance. Using the trapezoidal rule, I obtain the given precision dividing the [0,1] interval in n=204 parts. Using the rectangles rule, described in Kazi’s article, too, the number of divisions needed to achieve the given precision is n=145. What? Wait…how can dividing the interval in less sub-intervals, and, moreover, using a lower order integration rule, lead to a result consistent with a higher order method with more iterations?

Lately, when I tweet or write about my move, someone inevitably asks if Kelly, my husband, moved with me. I’ve been told this happens because I talk about the move using “I” instead of “We.” So here’s me taking the time to let you know that I am one person who speaks for this one person. Kel is here with me, yes, but I am still I. If that doesn’t work for you, I have nothing else to offer. My little family is the center of my world, but I am the center of my life. I’ve found the consistency I was searching for, but it didn’t come from falling in love or getting married or getting a dog. It came from the core of my self. That’s where I speak from, and that’s who you’re hearing. Questions are fine, assumptions are petty.