Shaping — where it appears
Named by 8 essays across 2 fields — each of them below, with the objects they name alongside it.
A fashioned edge has a quantised angle
A knitted panel is shaped by transferring loops, so its edge steps by whole wales at whole courses and its angle is the arctangent of a fraction. The available angles turn out to be the same for every plain knit there has ever been — in any yarn, at any gauge, at any loop length — because the constant they scale by cancels the loop out. There are eighteen of them, and 16.67° between the last two.
A tube can only be shaped by its loop
On a circular machine the needle count is the cylinder, so a seamless tube's circumference is its wale count times its wale spacing — and the wale spacing is the loop length over one constant. The loop is the only free quantity, the yarn bounds it at both ends, and what is left is a taper of 18.8 per cent bought at the price of a fabric half again as dense.
A heel turns a right angle because of the loop
A sock's heel is knitted in short rows on half the needles until a third are left, then back out again. Down the back line that adds a length of courses, and a tube's back line longer than its front by that much has turned through π times two thirds over the loop's own aspect — 93.8 degrees, on any needle count, in any yarn. The trade's third is the loop's shape in disguise. What the rule does not do is make a bend: the heel supplies two thirds of the fabric a true right angle needs, and every missing stitch is on its sides.
A knitted disc is flat at one shape of loop
A disc lies flat only if its circumference grows by exactly 2π per unit of radius, and a knitted disc's growth is a count of loops in one direction over a count in the other. So it is flat at one value of the loop's aspect and no other. Knitted sideways in wedges of short rows the growth falls as the loop gets wider; knitted outward in rounds it rises. Four wedges and ten increases every two rounds are each flat at an aspect inside the range plain knit moves through when it is washed — and they cross it in opposite directions.
A knitted ball's short rows have to slow down
A knitted disc needs one count to meet 2π; a sphere needs a count that follows a sine. Knitted sideways in gores, a ball's short rows must turn one stitch apart at the pole and ever further apart towards the equator — evenly spaced turns knit two flat discs joined at the rim. The pole is the disc again, so gores come in fours; the equator's row pairs have to come out whole, so only some sizes knit round; and a wash moves a four-gore ball from a ruffled pole to a round one.
A stepped stocking should step most at the ankle
A graduated stocking asks for a girth that rises smoothly up the leg, and a knitting machine gives it one girth, then the next. Over each step the tube is one size on a stretch of leg that is not, so it presses harder at the top of the step than at the bottom, and the pressure up the leg is a saw-tooth. Each tooth is the leg's change of girth across the step divided by the girth squared — so it is largest just above the ankle, where the leg is thinnest and widening fastest. Eight equal steps leave a ring of 4.8 mmHg there; eight steps spaced by the leg's own shape leave 2.7 everywhere.
A ball knitted in rounds washes the other way
A ball can be knitted sideways in gores or outward from one pole in rounds, and both have to follow the same sine. But a gore counts its meridian in stitches and its circumference in rows, and a round counts them the other way, so the loop's aspect sits underneath one construction and on top of the other. A wash raises the aspect — and closes a gored ball's ruffled poles while it opens a round-knitted ball's.
Stacked increases knit a ball with flat sides
A ball knitted in rounds can put its increases anywhere in each increase round. Stack them in lines from pole to pole and every stitch between two lines has a flat knit's neighbours, so the ball is made of flat panels and all its curvature sits on the lines. Flat panels with straight rows close up without stretching in exactly one way: every round a regular polygon, each pole a point. At five lines that ball is 13 per cent taller than it is wide across its ridges and 40 per cent across its flats, and to make it round the stuffing has to stretch the middle of every panel by π²/4m² — nine per cent at five lines, less than a wash moves a course at ten.
Named alongside it
The objects these essays reach for when they reach for this one.
Munden constantsWaleCourseLoop aspectGaussian curvatureShort-rowRelaxationLoop lengthSeamlessTubeCircular knittingContact pressure