Math for Crafters: Everything is a Riemann sum, if you think about it right

 The funny thing about math is the way it sneaks into everything. Or perhaps that’s the point. I don’t know, I just love math in all its forms. So I’m bringing back something I did a while ago, Math for Crafters, and providing another brief insight into my brain. This time, I’m talking about integrals (don’t run away, I promise not to have any scary equations) and the process of adding stitches to a project. 

The basic idea of an integral is that it’s an area. The integral is the area between the graph of a function and the x-axis (presuming it’s not the area between two curves or representing something else…). It comes in two types — definite and indefinite. An indefinite integral produces a new function (or family of functions, because of the constant of integration). A definite integral produces a number, and is the area under the curve between two given points. In this case, we’re mostly talking about definite integrals. 

To find integrals, really what you’re doing is making an infinite number of infinitely thin rectangles and adding their areas together. You can approximate definite integrals using a given number (n) of rectangles that have equal width and height equal to where the rectangle hits the curve at one point (using the height/y-value at the leftmost point of each rectangle gives a left Riemann sum, while the rightmost point gives a right Riemann sum, and averaging those two values gives a midpoint Riemann sum). Look it up if you want a proper definition; I just want to define this briefly. 

Basically, integrals are the accumulation of many tiny changes in area. Is that not what crocheters/knitters do when we form a stitch? Are we not adding a tiny amount, another little rectangle, to the area of our project? We can’t add an infinitely tiny amount, but we can add the area of a single stitch. 

We make a Riemann sum any time we crochet. That’s our magic. We make graphs and curves, area and integrals, teeny-tiny pieces and huge projects — we make math and magic. We have a physical reminder of the importance of a tiny amount, even the tiniest dx. We have infinities at our fingertips.