Protractor

A scale bent round a vertex to measure an angle against, built from the editor’s own building blocks.

Overview

The protractor is a band of degrees numbered at every division, ruled from end to end by marks about a degree apart, standing on the arms it is read between. Lay it over what is being measured — a vector, a body’s path, a drawing — and resting the pointer on it reads the angle from its zero, on a plate standing on the band. It measures rather than reads the model: it is bound to no term.

It is set by its two arms: a start angle and an end angle, both measured anticlockwise from straight right. A half circle stands the vertex on the bottom edge the way a protractor sits on a page, and a whole turn between the two closes the band into a dial with the vertex in the middle of the box. Wherever the band reaches a direction the box itself stands on — straight right, straight up, straight left, straight down — a spoke is drawn from the band to the vertex, so a half circle carries the upright the drawing under it is squared against.

The numbers read the angle they stand at rather than how far along the band they are, so a protractor set from 30 to 150 is numbered 30 to 150. They keep to round angles: the first stands at the first round one the band reaches and the last at the last, which is why a protractor ending at 112.5 is still numbered to 110.

What it is marked in is one row of its settings. Degrees numbers the band the way a protractor is printed, a number every ten degrees. Radians numbers the same band in the fractions of π those angles are — π/6, π/3, π/2 round the band, and the same fractions on the plate the pointer reads — a number every thirty degrees, with the marks between them still a degree apart.

Both angles are set in whatever the protractor is marked in, and the mark stands inside the field after the number. In degrees they are degrees, written after a degree sign; in radians they are the multiple of π they are — a half turn is 1, a whole turn is 2 — written after a π. Either takes a decimal number, so 112.5° and 0.75π are both set by typing them. What the object holds never changes — it is degrees throughout — only the way the number is written and read.

It is placed from the protractor key on the shapes toolbar, and it is also in the objects palette and in the notebook’s own toolbar, since it is an object built from blocks like the compass or the thermometer: one JSON definition, drawn by the same compiler every other object is drawn by, wherever it stands. Models saved before the change carry the older ProtractorShape, which still opens.

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